HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 05 Feb 2023 14:08:02 GMT2023-02-05T14:08:02Z502581- On the Stability of Piecewise Genetic Regulatory Networkshttp://hdl.handle.net/10722/199361Title: On the Stability of Piecewise Genetic Regulatory Networks
Authors: Li, J; Chesi, G; Shen, T
Abstract: The hybrid dynamics of the genetic regulatory
networks (GRNs) have attracted much research attention in
recent years. This paper is concerned with the stability analysis
of piecewise GRNs. Depending on whether the state partitions
and mode transitions are known or unknown as a priori, the
proposed networks are divided into two categories, i.e., switched
GRNs and hybrid GRNs. It is shown that, by using common
polynomial Lyapunov functions and piecewise polynomial Lyapunov
functions, two conditions are established to ensure the
globally asymptotically stability for switched and hybrid GRNs,
respectively. Moreover, it is shown that, by using the sum of
squares (SOS) techniques, stability conditions in form of linear
matrix inequalities (LMIs) for both models can be obtained.
An example with synthetic hybrid GRN model is provided to
illustrate the use of the proposed methodology.
Description: The 2013 International Conference of Systems Biology and Bioengineering (ICSBB'13) is held under the World Congress on Engineering (WCE) 2013; The article can be viewed at: http://www.iaeng.org/publication/WCE2013/WCE2013_pp1391-1396.pdf
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1993612013-01-01T00:00:00Z
- On the synthesis of linear H ∞ filters for polynomial systemshttp://hdl.handle.net/10722/157157Title: On the synthesis of linear H ∞ filters for polynomial systems
Authors: Li, P; Lam, J; Chesi, G
Abstract: This paper is concerned with the H ∞ filtering problem for polynomial systems. By means of Lyapunov theory and matrix inequality techniques, sufficient conditions are first obtained to ensure that the filtering error system is asymptotically stable and satisfies H ∞ performance constraint. Then, a sufficient condition for the existence of desired filters is established with a free matrix introduced, which will greatly facilitate the design of filter matrices. By virtue of sum-of-squares (SOS) approaches, a convergent iterative algorithm is developed to tackle the polynomial H ∞ filtering problem. Note that the approach can be efficiently implemented by means of recently developed SOS decomposition techniques, and the filter matrices can be designed explicitly. Finally, a numerical example is given to illustrate the main results of this paper. © 2011 Elsevier B.V. All rights reserved.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1571572012-01-01T00:00:00Z
- Designing image trajectories in the presence of uncertain data for robust visual servoing path-planninghttp://hdl.handle.net/10722/62098Title: Designing image trajectories in the presence of uncertain data for robust visual servoing path-planning
Authors: Chesi, G
Abstract: Path-planning allows one to steer a camera to a desired location while taking into account the presence of constraints such as visibility, workspace, and joint limits. Unfortunately, the planned path can be significantly different from the real path due to the presence of uncertainty on the available data, with the consequence that some constraints may be not fulfilled by the real path even if they are satisfied by the planned path. In this paper we address the problem of performing robust path-planning, i.e. computing a path that satisfies the required constraints not only for the nominal model as in traditional path-planning but rather for a family of admissible models. Specifically, we consider an uncertain model where the point correspondences between the initial and desired views and the camera intrinsic parameters are affected by unknown random uncertainties with known bounds. The difficulty we have to face is that traditional path-planning schemes applied to different models lead to different paths rather than to a common and robust path. To solve this problem we propose a technique based on polynomial optimization where the required constraints are imposed on a number of trajectories corresponding to admissible camera poses and parameterized by a common design variable. The planned image trajectory is then followed by using an IBVS controller. Simulations carried out with all typical uncertainties that characterize a real experiment illustrate the proposed strategy and provide promising results. © 2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/620982009-01-01T00:00:00Z
- Multiview Stereo Object Reconstruction with a One-Line Search Methodhttp://hdl.handle.net/10722/199074Title: Multiview Stereo Object Reconstruction with a One-Line Search Method
Authors: Zhang, J; Chesi, G
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1990742013-01-01T00:00:00Z
- Intelligent Modeling and Verification (Editorial)http://hdl.handle.net/10722/199075Title: Intelligent Modeling and Verification (Editorial)
Authors: Luo, G; Chesi, G; Song, X; Yang, X
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1990752013-01-01T00:00:00Z
- Homogeneous Polynomial Lyapunov Functions for Robust Local Synchronisation with Time-varying Uncertaintieshttp://hdl.handle.net/10722/199079Title: Homogeneous Polynomial Lyapunov Functions for Robust Local Synchronisation with Time-varying Uncertainties
Authors: Han, D; Chesi, G; Luk, CK
Abstract: This study studies robust local synchronisation in multi-agent systems with time-varying parametric uncertainties constrained in a polytope. In contrast to the existing methods with non-convex conditions via using quadratic Lyapunov function, a new criteria is proposed based on using homogeneous polynomial Lyapunov functions where the original system is suitably approximated by an uncertain polytopic system. Furthermore, the corresponding tractable conditions of linear matrix inequalities have been provided by exploiting the squares matrix representation. Then, the polytopic synchronisation margin problem is, for the first time, proposed and investigated via handling generalised eigenvalue problems. Lastly, numerical examples illustrate the usefulness of the proposed method.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/1990792014-01-01T00:00:00Z
- Rational Lyapunov Functions for Estimating and Controlling the Robust Domain of Attractionhttp://hdl.handle.net/10722/184510Title: Rational Lyapunov Functions for Estimating and Controlling the Robust Domain of Attraction
Authors: Chesi, G
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1845102013-01-01T00:00:00Z
- Performance limitation analysis in visual servo systems: Bounding the location error introduced by image points matchinghttp://hdl.handle.net/10722/158602Title: Performance limitation analysis in visual servo systems: Bounding the location error introduced by image points matching
Authors: Chesi, G; Yung, HL
Abstract: Visual servoing consists of positioning a robot endeffector based on the matching of some object features in the image. However, due to the presence of image noise, this matching can never be ensured, hence introducing an error on the final location of the robot. This paper addresses the problem of estimating the worst-case location error introduced by image points matching. In particular, we propose some strategies for computing upper bounds and lower bounds of such an error according to several possible measures for certain image noise intensity and camera-object configuration. These bounds provide an admissible region of the sought worst-case location error, and hence allow one to establish performance limitation of visual servo systems. Some examples are reported to illustrate the proposed strategies and their results. © 2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1586022009-01-01T00:00:00Z
- Computing equilibrium points of genetic regulatory networkshttp://hdl.handle.net/10722/129200Title: Computing equilibrium points of genetic regulatory networks
Authors: Chesi, G
Abstract: Computing equilibrium points of genetic regulatory networks is a problem of primary importance for numerous investigations in these systems. This paper addresses this problem for differential equation models, with the regulation function expressed in a general form which includes both SUM form and PROD form for saturation functions of any type. Specifically, a recursive algorithm is proposed, which provides at each recursion a region guaranteed to contain all equilibrium points. This region progressively shrinks, and asymptotically converges to the sought set of equilibrium points. Moreover, the proposed algorithm can also allow one to delimit and find limit cycles. Some numerical examples are reported to illustrate and validate the proposed algorithm, including examples where standard mathematical tools fail to compute the sought equilibrium points. © 2009 Springer Berlin Heidelberg.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1292002009-01-01T00:00:00Z
- On the synthesis of adaptive parameter-dependent output feedback controllers through LMI-based optimizationhttp://hdl.handle.net/10722/227530Title: On the synthesis of adaptive parameter-dependent output feedback controllers through LMI-based optimization
Authors: Chesi, G
Abstract: This paper addresses the problem of designing adaptive output feedback controllers for stabilizing plants affected by parameters. A novel approach is proposed that allows one to design a fixed-order fixed-degree adaptive parameter-dependent output feedback controller by solving convex optimization problems with Linear Matrix Inequalities (LMIs). The proposed approach is based on the construction of a function that provides a stability margin of the closed-loop system depending on the controller. The conservatism of the proposed approach can be reduced by increasing the size of the LMIs. Copyright (c) IARIA, 2016.
Description: Best Paper Award
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2275302016-01-01T00:00:00Z
- Analysis and synthesis of nonlinear systems with uncertain initial conditionshttp://hdl.handle.net/10722/57490Title: Analysis and synthesis of nonlinear systems with uncertain initial conditions
Authors: Chesi, G; Hung, YS
Abstract: This technical note considers the problem of computing extremal values of the trajectories over a given set of initial conditions as well as finding output controllers minimizing these extremal values under time-domain constraints for nonlinear systems. It is shown that upper bounds of the sought extremal values as well as candidates of the sought controllers can be computed by solving a one-parameter sequence of bilinear matrix inequality (BMI) optimizations obtained through the square matricial representation (SMR) of polynomials. Moreover, a necessary and sufficient condition is proposed to establish the tightness of the found upper bound in spite of the conservatism introduced by the nonconvexity of BMI optimizations and the chosen degree of the Lyapunov function and relaxing polynomials. © 2008 IEEE.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/574902008-01-01T00:00:00Z
- Solving polynomial systems via LMI: determination of optimal SMR matriceshttp://hdl.handle.net/10722/99691Title: Solving polynomial systems via LMI: determination of optimal SMR matrices
Authors: Chesi, G
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/996912008-01-01T00:00:00Z
- Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systemshttp://hdl.handle.net/10722/153329Title: Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems
Authors: Chesi, G; Garulli, A; Tesi, A; Vicino, A
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1533292009-01-01T00:00:00Z
- Welcoming message from the CACSD-SU program chairhttp://hdl.handle.net/10722/155684Title: Welcoming message from the CACSD-SU program chair
Authors: Chesi, G
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1556842011-01-01T00:00:00Z
- Welcoming message from the CACSD-SU president chairhttp://hdl.handle.net/10722/155691Title: Welcoming message from the CACSD-SU president chair
Authors: Chesi, G
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1556912011-01-01T00:00:00Z
- Polynomial Parameterizations in Robust Control and Visual Servoinghttp://hdl.handle.net/10722/253034Title: Polynomial Parameterizations in Robust Control and Visual Servoing
Authors: Chesi, G
Abstract: This talk describes some recent results that we have proposed in control and robotics based on the use of polynomial parameterizations. In particular, in the first part of the talk we consider the problem of establishing robust stability of linear systems affected by polytopic parametric uncertainty. For this problem we propose the class of homogeneous polynomially parameter-dependent quadratic Lyapunov functions (HPD-QLFs) which is motivated by the property that a polytope of matrices is stable if and only there exists a HPD-QLF. The main result is a condition for determining the sought HPD-QLF which amounts to solving linear matrix inequalities (LMIs) derived via the complete square matricial representation of homogeneous matricial forms and the Lyapunov matrix equation. In the second part of the talk we consider the problem of realizing visual servoing for robot manipulators taking into account constraints such as camera visibility and obstacle avoidance while minimizing a cost function such as spanned image area and trajectory length. To solve this problem we propose a path-planning scheme based on polynomial parameterizations of the camera trajectory in the six dimensional space obtained through the introduction of a parameter-dependent object reconstruction and an extension of the Euler parameters. This scheme allows one to consider all possible camera trajectories and establish their feasibility through simple computations.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/2530342007-01-01T00:00:00Z
- Optimal ellipsoidal stability domain estimates for odd polynomial systemshttp://hdl.handle.net/10722/158232Title: Optimal ellipsoidal stability domain estimates for odd polynomial systems
Authors: Chesi, G; Genesio, R; Tesi, A
Abstract: The algorithms for computing estimates of the domain attraction of an equilibrium point consists of two distinct steps: the selection of a Lyapunov function and the estimation of the domain of attraction computed for the chosen Lyapunov function. These steps can be cast as a non-convex minimization problem that is in general difficult to solve in the presence of local extrema. To overcome this difficulty, a convex optimization method for obtaining optimal ellipsoidal estimates of polynomial systems having a single homogeneous nonlinear term other than the linear one is proposed. The methods by which these optimal ellipsoidal estimates can be acquired for general odd polynomial systems are discussed.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/10722/1582321997-01-01T00:00:00Z
- A visual servoing algorithm based on epipolar geometryhttp://hdl.handle.net/10722/158312Title: A visual servoing algorithm based on epipolar geometry
Authors: Chesi, G; Prattichizzo, D; Vicino, A
Abstract: A visual servoing algorithm for mobile robots is proposed. The main feature of the algorithm is that it exploits object profiles rather than solving correspondence problems using object features or texture. This property is crucial for mobile robot navigation in unstructured environments where the 3D scene exhibits only surfaces whose main features are their apparent contours. The framework is based on the epipolar geometry, which is recovered from object profiles and epipolar tangencies. Special symmetry conditions of epipoles are used to generate the mobile robot control law. For the sake of simplicity, mobile robot kinematics is assumed to be holonomic and the camera intrinsic parameters are assumed partially known. Such assumption can be relaxed to extend the application field of the approach.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/1583122001-01-01T00:00:00Z
- Polynomially parameter-dependent lyapunov functions for robust H ∞ performance analysishttp://hdl.handle.net/10722/158710Title: Polynomially parameter-dependent lyapunov functions for robust H ∞ performance analysis
Authors: Chesi, G; Garulli, A; Tesi, A; Vicino, A
Abstract: The computation of robust H ∞ performance of linear systems subject to polytopic parametric uncertainty is known to be a difficult problem in robust control. in this paper, quadratic parameter-dependent Lyapunov functions, with polynomial dependence on the uncertain parameters, are exploited to provide upper bounds to the robust H ∞ performance. It is shown that such bounds can be computed via convex optimizations constrained by LMIs. Numerical examples show that the proposed technique is a powerful alternative to existing methods based on linearly parameter-dependent Lyapunov functions. Copyright © 2005 IFAC.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/1587102005-01-01T00:00:00Z
- Robust analysis of linear systems affected by time-invariant hypercubic parametric uncertaintyhttp://hdl.handle.net/10722/158388Title: Robust analysis of linear systems affected by time-invariant hypercubic parametric uncertainty
Authors: Chesi, G
Abstract: In this paper, a new technique for establishing the stability of a linear system polynomially affected by time-invariant uncertainty constrained in a hypercube is presented for both continuous-time and discrete-time case. Specifically, a necessary and sufficient condition not based on the use of Lyapunov functions and checkable through LMIs is provided. The contribution of this technique with respect to existing approaches that provide necessary and sufficient conditions for establishing the stability consists of a significantly smaller computational burden in quite frequent cases.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1583882003-01-01T00:00:00Z
- Estimating the domain of attraction: A light LMI technique for a class of polynomial systemshttp://hdl.handle.net/10722/158389Title: Estimating the domain of attraction: A light LMI technique for a class of polynomial systems
Authors: Chesi, G
Abstract: The problem of computing the Largest Estimate of the Domain of Attraction (LEDA) of an equilibrium point for a given Lyapunov function is considered for a class of polynomial systems described by a linear and a homogeneous polynomial term. Such a class contains well known examples in control theory as the prey-predatory system, mass-spring systems with softening/hardening springs and electric circuits with vacuum tubes. It is shown that a lower bound of the LEDA can be obtained through a convex optimization constrained by a Linear Matrix Inequality (LMI). The contribution of the proposed technique with respect to the existing approaches consists of requiring a significantly smaller computational burden and guaranteeing the lower bound tightness for some system dimensions and degrees.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1583892003-01-01T00:00:00Z
- Robust stability of polytopic systems via polynomially parameter-dependent Lyapunov functionshttp://hdl.handle.net/10722/158390Title: Robust stability of polytopic systems via polynomially parameter-dependent Lyapunov functions
Authors: Chesi, G; Garulli, A; Tesi, A; Vicino, A
Abstract: In this paper robust stability of state space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the Homogeneous Polynomially Parameter-Dependent Quadratic Lyapunov Functions (HPD-QLFs). The choice of this class, which contains parameter-dependent quadratic Lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form, is motivated by the property that a polytope of matrices is stable if and only there exists a HPD-QLF. The main result of the paper is a sufficient condition for determining the sought HPD-QLF, which amounts to solving Linear Matrix Inequalities (LMIs) derived via the Complete Square Matricial Representation (CSMR) of homogeneous matricial forms and the Lyapunov matrix equation. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1583902003-01-01T00:00:00Z
- Automatic segmentation and matching of planar contours for visual servoinghttp://hdl.handle.net/10722/158282Title: Automatic segmentation and matching of planar contours for visual servoing
Authors: Chesi, G; Malis, E; Cipolla, R
Abstract: In this paper we present a complete system for segmenting, matching and tracking planar contours for use in visual servoing. Our system can be used with arbitrary contours of any shape and without any prior knowledge of their models. The system is first shown the target view. A selected contour is automatically extracted and its image shape is stored. The robot and object are then moved and the system automatically identifies the target. The matching step is done together with the estimation of the homography matrix between the two views of the contour. Then, a 2 1/2 D visual servoing technique is used to reposition the end-effector of a robot at the target position relative to the planar contour. The system has been successfully tested on several contours with very complex shapes such as leaves, keys and the coastal outlines of islands.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/1582822000-01-01T00:00:00Z
- Camera pose estimation from less than eight points in visual servoinghttp://hdl.handle.net/10722/158431Title: Camera pose estimation from less than eight points in visual servoing
Authors: Chesi, G; Hashimoto, K
Abstract: The problem of estimating the camera pose in eye-in-hand visual servoing is considered for the case in which the available point correspondences are less than eight Two strategies based on the properties of the essential matrix are hence described, which mainly consist of the computation of the roots of a one-variable polynomial in the seven points case and the minimization of a two-variables polynomial through a gradient algorithm in the six points case.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/1584312004-01-01T00:00:00Z
- Static-eye against hand-eye visual servoinghttp://hdl.handle.net/10722/158351Title: Static-eye against hand-eye visual servoing
Authors: Chesi, G; Hashimoto, K
Abstract: In this paper, a comparison between static-eye and hand-eye configurations for the point-to-point visual servoing task realized with position-based and image-based control laws is presented. For these four configurations, the effect of uncertainty on intrinsic and extrinsic calibration parameters is investigated. The results show local stability for all configurations with small calibration errors and a steady state error for the hand-eye position-based one. Simulations have been carried out in order to confirm the theoretical results and evaluate the effects of the uncertainty in terms of stability region.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/1583512002-01-01T00:00:00Z
- LMI-based techniques for solving quadratic distance problemshttp://hdl.handle.net/10722/158323Title: LMI-based techniques for solving quadratic distance problems
Authors: Chesi, G; Garulli, A; Tesi, A; Vicino, A
Abstract: The computation of the minimum distance from a point to a surface in a finite dimensional space is a key issue in several system analysis and control problems. This paper presents a general framework in which some classes of minimum distance problems are tackled via LMI techniques. Exploiting a suitable representation of homogeneous forms, a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one-parameter family of LMI optimization problems. Several properties of the proposed technique are discussed. In particular, tightness of the lower bound is investigated, providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori. Extensive numerical simulations are reported showing promising performances of the proposed method.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/1583232001-01-01T00:00:00Z
- LMI-based trajectory planning for closed-loop control of robotic systems with visual feedbackhttp://hdl.handle.net/10722/158618Title: LMI-based trajectory planning for closed-loop control of robotic systems with visual feedback
Authors: Chesi, G
Abstract: Closed-loop robot control based on visual feedback is an important research area, with useful applications in various fields. Planning the trajectory to be followed by the robot allows one to take into account multiple constraints during the motion, such as limited field of view of the camera and limited workspace of the robot. This paper proposes a strategy for path-planning from an estimate of the point correspondences between the initial view and the desired one, and an estimate of the camera intrinsic parameters. This strategy consists of generating a parametrization of the trajectories connecting the initial location to the desired one via polynomials. The trajectory constraints are then imposed by using suitable relaxations and LMIs (linear matrix inequalities). Some examples illustrate the proposed approach.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1586182009-01-01T00:00:00Z
- Improving camera displacement estimation in eye-in-hand visual servoing: A simple strategyhttp://hdl.handle.net/10722/158369Title: Improving camera displacement estimation in eye-in-hand visual servoing: A simple strategy
Authors: Chesi, G; Hashimoto, K
Abstract: The problem of estimating the camera displacement in eye-in-hand visual servoing is considered, and a simple strategy based on the idea that the estimates accuracy can be improved if the fact that the point correspondences used throughout the visual servoing are relative to the same 3D points is taken into account is presented. In particular, an accurate scaled euclidean reconstruction of the object is built in the first steps of the visual servoing by suitably using existing linear methods, and from this reconstruction the camera displacement is suitably estimated. Extensive proves performed in random conditions have shown that the proposed approach provides significantly better results with respect to the existing linear methods actually used in visual servoing.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1583692003-01-01T00:00:00Z
- Parameter-dependent homogeneous Lyapunov functions for robust stability of linear time-varying systemshttp://hdl.handle.net/10722/158384Title: Parameter-dependent homogeneous Lyapunov functions for robust stability of linear time-varying systems
Authors: Chesi, G; Garulli, A; Tesi, A; Vicino, A
Abstract: In this paper robust stability of linear state space models with respect to time-varying uncertainties with bounded variation rates is considered. A new class of parameter-dependent Lyapunov functions to establish stability of a polytope of matrices in presence of a polytopic bound on the variation rate of the uncertain parameters is introduced, i.e., the class of Homogeneously Parameter-Dependent Homogeneous Lyapunov Functions (HPD-HLFs). Such a class, where the dependence on the uncertain parameter vector and the state vector are both expressed as polynomial homogeneous forms, generalizes those successfully employed in the special cases of unbounded variation rates or time-invariant uncertainties. The main result of the paper is a sufficient condition to determine the sought HPD-HLF, which amounts to solving a set of Linear Matrix Inequalities (LMIs) derived via a suitable parameterization of polynomial homogeneous forms. Also, lower bounds for the maximum scaling factor of the variation rates polytope for which the stability of the system is preserved, are shown to be computable in terms of Generalized Eigen value Problems (GEVPs). Several numerical examples are provided to show the effectiveness of the proposed approach.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/1583842004-01-01T00:00:00Z
- On the estimation of the domain of attraction for uncertain polynomial systems via LMIshttp://hdl.handle.net/10722/158385Title: On the estimation of the domain of attraction for uncertain polynomial systems via LMIs
Authors: Chesi, G
Abstract: Estimating the Domain of Attraction (DA) of equilibrium points is a problem of fundamental importance in systems engineering. Several approaches have been proposed for the case of known polynomial systems allowing one to find the Largest Estimate of the DA (LEDA) for a given Lyapunov Function (LF). However, the problem of estimating the Robust DA (RDA), that is the DA guaranteed for all possible uncertainties in an uncertain system, it is still an unsolved problem. In this paper, some methods are proposed for dealing with such a problem in the case of systems depending polynomially in the state and in the uncertainty which is supposed to belong to a polytope. Specifically, the issue of estimating the Robust LEDA (RLEDA), that is the intersection of all LEDAs in the uncertain system, is considered for common and parameter-dependent LFs, providing constant and parameter-dependent lower bounds through LMI optimizations. In order to obtain easy descriptions of the RLEDA in the case of parameter-dependent LFs, an LMI method for computing approximations with simple shape is presented.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/1583852004-01-01T00:00:00Z
- On the robust stability of continuous-time and discrete-time time-invariant uncertain systems with rational dependence on the uncertainty: A non-conservative conditionhttp://hdl.handle.net/10722/129697Title: On the robust stability of continuous-time and discrete-time time-invariant uncertain systems with rational dependence on the uncertainty: A non-conservative condition
Authors: Chesi, G
Abstract: A key problem in automatic control consists of investigating robust stability of systems with uncertainty. This paper considers linear systems with rational dependence on time-invariant uncertainties constrained in the simplex. It is shown that a sufficient condition for establishing whether the system is either stable or unstable can be obtained by solving a generalized eigenvalue problem constructed through homogeneous parameter-dependent quadratic Lyapunov functions (HPD-QLFs). Moreover, it is shown that this condition is also necessary for establishing either stability or instability by using a sufficiently large degree of the HPD-QLF. Some numerical examples illustrate the use of the proposed approach in both cases of continuous-time and discrete-time uncertain systems. ©2010 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1296972010-01-01T00:00:00Z
- LMI techniques for optimization over polynomials in control: A surveyhttp://hdl.handle.net/10722/135115Title: LMI techniques for optimization over polynomials in control: A survey
Authors: Chesi, G
Abstract: Numerous tasks in control systems involve optimization problems over polynomials, and unfortunately these problems are in general nonconvex. In order to cope with this difficulty, linear matrix inequality (LMI) techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems. This survey aims to provide the reader with a significant overview of the LMI techniques that are used in control systems for tackling optimization problems over polynomials, describing approaches such as decomposition in sum of squares, Positivstellensatz, theory of moments, Plya's theorem, and matrix dilation. Moreover, it aims to provide a collection of the essential problems in control systems where these LMI techniques are used, such as stability and performance investigations in nonlinear systems, uncertain systems, time-delay systems, and genetic regulatory networks. It is expected that this survey may be a concise useful reference for all readers. © 2006 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1351152010-01-01T00:00:00Z
- Robust stability of time-varying uncertain systems with rational dependence on the uncertaintyhttp://hdl.handle.net/10722/135114Title: Robust stability of time-varying uncertain systems with rational dependence on the uncertainty
Authors: Chesi, G
Abstract: Robust stability of time-varying uncertain systems is a key problem in automatic control. This note considers the case of linear systems with rational dependence on an uncertain time-varying vector constrained in a polytope, which is typically addressed in the literature by using the linear fractional representation (LFR). A novel sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI) feasibility test by exploiting homogeneous polynomial Lyapunov functions, the square matrix representation and an extended version of Polya's theorem which considers structured matrix polynomials. It is shown that this condition is also necessary for second-order systems, and that this condition is less conservative than existing LMI conditions based on the LFR for any order. © 2010 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1351142010-01-01T00:00:00Z
- Fast multiple-view L2 triangulation with occlusion handlinghttp://hdl.handle.net/10722/135116Title: Fast multiple-view L2 triangulation with occlusion handling
Authors: Chesi, G; Hung, YS
Abstract: Multiple-view L2 triangulation is a key problem in computer vision. This paper addresses the standard case where all image points are available, and the case where some image points are not available. In the latter case, it is supposed that the unknown image point belongs to a known region such as a line segment or an ellipse, as it happens for instance due to occlusions. For this problem we propose two methods based on linear matrix inequalities (LMIs). The first method, named TFML, exploits the fundamental matrix and is fast (the average computational time with two and three-views is 0.01 and 0.05 s on Matlab) at the expense of possible conservatism, which however it is shown to occur rarely in practice, and which can be immediately detected. The second method, named TPML, exploits the projection matrix, is slower, but allows one to reduce the conservatism by using techniques for optimization over polynomials. Various examples with synthetic and real data illustrate the proposed strategy. © 2010 Elsevier Inc. All rights reserved.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1351162011-01-01T00:00:00Z
- Establishing robust stability of discrete-time systems with time-varying uncertainty: the Gram-SOS Approachhttp://hdl.handle.net/10722/211752Title: Establishing robust stability of discrete-time systems with time-varying uncertainty: the Gram-SOS Approach
Authors: Chesi, G
Abstract: This paper addresses the problem of establishing robust asymptotical stability of discrete-time linear systems polynomially affected by time-varying uncertainty confined into a polytope. A linear matrix inequality (LMI) condition for establishing robust asymptotical stability is proposed by introducing a novel approach for establishing the existence of a common homogeneous polynomial Lyapunov function (HPLF). This approach consists, firstly, of introducing a Gram matrix built with respect to the state and parametrized by an arbitrary vector function of the uncertainty, and secondly, of requiring that a transformation of the introduced Gram matrix is a sum of squares (SOS) of matrix polynomials. The approach, hence, is referred to as a Gram-SOS approach. It is shown that the proposed LMI condition is sufficient for any degree of the HPLF candidate, that includes quadratic robust stability as a special case, and that is also necessary for a sufficiently large degree of the HPLF candidate. Numerical examples also show that the proposed LMI condition can outperform alternative ones in terms of conservatism and computational burden. © 2014 Elsevier Ltd.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2117522014-01-01T00:00:00Z
- Time-invariant uncertain systems: A necessary and sufficient condition for stability and instability via homogeneous parameter-dependent quadratic Lyapunov functionshttp://hdl.handle.net/10722/129189Title: Time-invariant uncertain systems: A necessary and sufficient condition for stability and instability via homogeneous parameter-dependent quadratic Lyapunov functions
Authors: Chesi, G
Abstract: This paper investigates linear systems with polynomial dependence on time-invariant uncertainties constrained in the simplex via homogeneous parameter-dependent quadratic Lyapunov functions (HPD-QLFs). It is shown that a sufficient condition for establishing whether the system is either stable or unstable can be obtained by solving a generalized eigenvalue problem. Moreover, this condition is also necessary by using a sufficiently large degree of the HPD-QLF. © 2009 Elsevier Ltd. All rights reserved.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1291892010-01-01T00:00:00Z
- Assessing robust stability properties of uncertain genetic regulatory networkshttp://hdl.handle.net/10722/135868Title: Assessing robust stability properties of uncertain genetic regulatory networks
Authors: Chesi, G
Abstract: This paper investigates robust stability properties of genetic regulatory networks (GRNs) affected by uncertainty. Specifically, we consider GRNs with SUMand PROD regulatory functions, where the coefficients are affected polynomially by unknown parameters constrained in a polytope, and where the saturation functions are not exactly known. It is shown that a condition for ensuring that the GRN has a globally asymptotically stable equilibrium point for all admissible uncertainties can be obtained in terms of a convex optimization problem with linear matrix inequalities (LMIs). Moreover, it is shown that a lower bound of the worst-case convergence rate of the trajectories to the equilibrium point over all the admissible uncertainties can be computed by solving a quasi-convex optimization problem with LMIs. The proposed techniques are illustrated by some numerical examples. ©2010 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1358682010-01-01T00:00:00Z
- Robustness analysis of genetic regulatory networks affected by model uncertaintyhttp://hdl.handle.net/10722/135120Title: Robustness analysis of genetic regulatory networks affected by model uncertainty
Authors: Chesi, G
Abstract: A fundamental problem in systems biology consists of investigating robustness properties of genetic regulatory networks (GRNs) with respect to model uncertainty. This paper addresses this problem for GRNs where the coefficients are rationally affected by polytopic uncertainty, and where the saturation functions are not exactly known. First, it is shown that a condition for ensuring that the GRN has a globally asymptotically stable equilibrium point for all admissible uncertainties can be obtained in terms of a convex optimization problem with linear matrix inequalities (LMIs), hence generalizing existing results that mainly consider only the case of GRNs where the coefficients are linearly affected by the uncertainty and the regulatory functions are in SUM form. Second, the problem of estimating the worst-case convergence rate of the trajectories to the equilibrium point over all admissible uncertainties is considered, and it is shown that a lower bound of this rate can be computed by solving a quasi-convex optimization problem with LMIs. Third, the paper considers the problem of estimating the set of uncertainties for which the GRN has a globally asymptotically stable equilibrium point. This problem is addressed, first, by showing how one can compute estimates with fixed shape by solving a quasi-convex optimization problem with LMIs, and second, by deriving a procedure for computing estimates with variable shape. Numerical examples illustrate the use of the proposed techniques. © 2010 Elsevier Ltd. All rights reserved.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1351202011-01-01T00:00:00Z
- On the robust stability of uncertain discrete-time networked control systems over fading channelshttp://hdl.handle.net/10722/227526Title: On the robust stability of uncertain discrete-time networked control systems over fading channels
Authors: Su, L; Chesi, G
Abstract: This paper addresses the problem of establishing robust stability in the mean square sense of uncertain discrete-time networked control systems over fading channels for all admissible uncertainties. It is supposed that the plant is connected to the controller in closed-loop via a fading channel which is modeled through noise processes in multiplicative form. The uncertainty is constrained into a convex bounded polytope and affects the plant whose coefficients are allowed to depend polynomially on the uncertainty. It is shown that robust stability of the uncertain closed-loop system in the mean square sense for all admissible uncertainties is equivalent to the existence of suitable Lyapunov functions with polynomial dependence on the uncertainty. It is also shown that a sufficient and necessary condition for establishing the existence of such Lyapunov functions can be obtained through convex optimization.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2275262015-01-01T00:00:00Z
- Topological entropy control via static feedback synthesis for continuous-time linear time-invariant systemshttp://hdl.handle.net/10722/227527Title: Topological entropy control via static feedback synthesis for continuous-time linear time-invariant systems
Authors: Chesi, G
Abstract: The topological entropy is a measure that quantifies the unstable of a dynamical system, and plays a key role in feedback stabilization. This paper addresses the problem of designing static feedback controllers for reducing the topological entropy in continuous-time linear time-invariant systems. It is shown that a sufficient condition for determining a controller (if any) that reduces the topological entropy under a desired upper bound can be obtained by solving a convex optimization problem, in particular a semidefinite program (SDP). Moreover, it is shown that this condition is also necessary by sufficiently increasing the size of the SDP. Some numerical examples illustrate the proposed methodology.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2275272015-01-01T00:00:00Z
- On the Synthesis of Linear H-Infinity Filters for Polynomial Systemshttp://hdl.handle.net/10722/227882Title: On the Synthesis of Linear H-Infinity Filters for Polynomial Systems
Authors: Chesi, G
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/2278822013-01-01T00:00:00Z
- SOS Programming-Based Robust Stability Analysis of Genetic Regulatory Networks with Time-Invariant and Time-Varying Uncertaintyhttp://hdl.handle.net/10722/227883Title: SOS Programming-Based Robust Stability Analysis of Genetic Regulatory Networks with Time-Invariant and Time-Varying Uncertainty
Authors: Chesi, G
Description: Invited Speech
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/2278832011-01-01T00:00:00Z
- Robustness Analysis of Uncertain Systems with Time-Varying Uncertaintyhttp://hdl.handle.net/10722/237805Title: Robustness Analysis of Uncertain Systems with Time-Varying Uncertainty
Authors: Chesi, G
Description: Invited Speech - T-2: Systems with Uncertainty [The 2010 IEEE International Symposium on Computer-Aided Control System Design (CACSD) Symposium hosted a special track on Systems with Uncertainty]
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/2378052010-01-01T00:00:00Z
- Genetic networks with SUM regulatory functions: Characterizing the equilibrium pointshttp://hdl.handle.net/10722/129724Title: Genetic networks with SUM regulatory functions: Characterizing the equilibrium points
Authors: Chesi, G
Abstract: Genetic networks with SUM regulatory functions are a fundamental class of models studied in systems biology. A primary issue for these models consists of establishing the number of the equilibrium points and their location. Unfortunately, this is a difficult problem, indeed existing methods very often do not allow one to solve it. This paper proposes a study of this problem, and describes an approach that exploits the properties of SUM regulatory functions in order to correctly characterize these points of interest. This is verified by some numerical examples, which illustrate the proposed solution and show the advantages with respect to existing methods. ©2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1297242009-01-01T00:00:00Z
- Toward non-conservative stability conditions for equilibrium points of genetic networks with SUM regulatory functionshttp://hdl.handle.net/10722/129649Title: Toward non-conservative stability conditions for equilibrium points of genetic networks with SUM regulatory functions
Authors: Chesi, G
Abstract: An important problem in systems biology consists of establishing whether an equilibrium point of a genetic regulatory network is stable. This paper investigates this problem for genetic networks with SUMregulatory functions. It is shown that a sufficient condition for global asymptotical stability of an equilibrium point of these networks can be derived in terms of convex optimizations with LMI constraints by exploiting polynomial Lyapunov functions and SOS techniques. This condition is interesting because does not introduce approximations of the nonlinearities present in the genetic regulatory network, and the conservatism can be decreased by increasing the degree of the involved polynomials. ©2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1296492009-01-01T00:00:00Z
- Optimal object configurations to minimize the positioning error in visual servoinghttp://hdl.handle.net/10722/129203Title: Optimal object configurations to minimize the positioning error in visual servoing
Authors: Chesi, G
Abstract: Image noise unavoidably affects the available image points that are used in visual-servoing schemes to steer a robot end-effector toward a desired location. As a consequence, letting the image points in the current view converge to those in the desired view does not ensure that the camera converges accurately to the desired location. This paper investigates the selection of object configurations to minimize the worst-case positioning error due to the presence of image noise. In particular, a strategy based on linear matrix inequalities (LMIs) and barrier functions is proposed to compute upper and lower bounds of this error for a given maximum error of the image points. This strategy can be applied to problems such as selecting an optimal subset of object points or determining an optimal position of an object in the scene. Some examples illustrate the use of the proposed strategy in such problems. © 2010 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1292032010-01-01T00:00:00Z
- Image noise induced errors in camera positioninghttp://hdl.handle.net/10722/57440Title: Image noise induced errors in camera positioning
Authors: Chesi, G; Hung, YS
Abstract: The problem of evaluating worst-case camera positioning error induced by unknown-but-bounded (UBB) image noise for a given object-camera configuration is considered. Specifically, it is shown that upper bounds to the rotation and translation worst-case error for a certain image noise intensity can be obtained through convex optimizations. These upper bounds, contrary to lower bounds provided by standard optimization tools, allow one to design robust visual servo systems. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/574402007-01-01T00:00:00Z
- Quantifying the unstable in linearized nonlinear systemshttp://hdl.handle.net/10722/227286Title: Quantifying the unstable in linearized nonlinear systems
Authors: Chesi, G
Abstract: It has been shown that quantifying the unstable in linear systems is important for establishing the existence of stabilizing feedback controllers in the presence of communications constraints. In this context, the instability measure is defined as the sum of the real parts (continuous-time case) or the product of the magnitudes (discrete-time case) of the unstable eigenvalues. This paper addresses the problem of quantifying the unstable in linearized systems obtained from nonlinear systems for a family of constant inputs, i.e., quantifying the largest instability measure over all admissible equilibrium points and all admissible constant inputs. It is supposed that the dynamics of the nonlinear system is polynomial in both state and input, either continuous-time or discrete-time, and that the set of constant inputs is a semialgebraic set. Two cases are considered: first, when the equilibrium points are known polynomial functions of the input, and, second, when the equilibrium points are unknown (polynomial or non-polynomial) functions of the input. It is shown that upper bounds of the sought instability measure can be established through linear matrix inequalities (LMIs) by searching for polynomially-dependent Lyapunov function candidates. Moreover, it is shown that these upper bounds are nonconservative for a sufficiently large degree of the Lyapunov function candidates under some conditions. Lastly, necessary and sufficient conditions are provided for establishing whether the obtained upper bounds are nonconservative. Some numerical examples also show the advantages of the proposed method with respect to grid techniques.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2272862015-01-01T00:00:00Z
- H∞ and H2 norms of 2D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functionshttp://hdl.handle.net/10722/227287Title: H∞ and H2 norms of 2D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functions
Authors: Chesi, G; Middleton, RH
Abstract: This paper addresses the problem of determining the H∞ and H2 norms of 2-D mixed continuous-discrete-time systems. The first contribution is to propose a novel approach based on the use of complex Lyapunov functions with even rational parametric dependence, which searches for upper bounds on the sought norms via linear matrix inequalities (LMIs). The second contribution is to show that the upper bounds provided are nonconservative by using Lyapunov functions in the chosen class with sufficiently large degree. The third contribution is to provide conditions for establishing the tightness of the upper bounds. The fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient LMI condition for establishing positive semidefiniteness of even Hermitian matrix polynomials. This result is also exploited to derive an improved necessary and sufficient LMI condition for establishing exponential stability of 2-D mixed continuous-discrete-time systems. Some numerical examples illustrate the proposed approach. It is worth remarking that nonconservative LMI methods for determining the H∞and H2 norms of 2-D mixed continuous-discrete-time systems have not been proposed yet in the literature.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2272872015-01-01T00:00:00Z
- Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertaintyhttp://hdl.handle.net/10722/227289Title: Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertainty
Authors: Chesi, G; Middleton, RH
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2272892016-01-01T00:00:00Z