Elena Panteley - Academia.edu (original) (raw)

Papers by Elena Panteley

We present a new result on uniform attractivity of the origin for nonlinear time-varying systems.... more We present a new result on uniform attractivity of the origin for nonlinear time-varying systems. Our theorem generalizes Matrosov's theorem which extends, in a certain manner, Krasovskȋ-LaSalle invariance principle to the case of general nonlinear time-varying systems. We show the utility of our theorem by addressing a control problem of port interconnected driftless systems. The latter includes as special case, the control of chained-form nonholonomic systems which has been extensively studied in the literature.

We study the problem of stability analysis for certain nonlinear systems. Our contributions are n... more We study the problem of stability analysis for certain nonlinear systems. Our contributions are new tools to guarantee uniform global asymptotic stability (UGAS) of nonlinear time-varying (NLTV) systems. Firstly, we provide new de nitions of persistency of excitation (PE). In particular, we g i v e here a new de nition of uniform -PE (u -PE) which, though conceptually equivalent to the original one introduced 7], is mathematically less conservative. We also provide with some properties of -PE pairs and contribute with a result which establishes UGAS of NLTV systems under u -PE.

The problem of input-to-output stability for switched nonlinear systems is considered. Two approa... more The problem of input-to-output stability for switched nonlinear systems is considered. Two approaches for switching between non-exponentially stable systems are proposed guaranteeing input-to-output stability for the switched system.

The stability of (not necessarily compact) sets for nonlinear systems in cascade is addressed. It... more The stability of (not necessarily compact) sets for nonlinear systems in cascade is addressed. It is proved that if two sets are globally asymptotically stable (GAS) for the subsystems taken separately then their cross-product is GAS for the corresponding cascade, provided that the solutions of the latter are globally bounded. In the case of a suitable growth rate of the interconnection in the state of the driven subsystem, we show that this latter requirement can be relaxed to just forward completeness of the cascade. Our results extend similar results on the stability analysis of cascaded systems and find applications in partial stability analysis and adaptive control.

We address the problem of master-slave synchronization of chaotic systems under parameter uncerta... more We address the problem of master-slave synchronization of chaotic systems under parameter uncertainty and with partial measurements. Our approach is based on observer-design theory hence, we view the master dynamics as a system of differential equations with a state and a measurable output and we design an observer (tantamount to the slave system) which reconstructs the dynamic behavior of the master. The main technical condition that we impose is persistency of excitation (PE), a property well studied in the adaptive control literature. In the case of unknown parameters and partial measurements we show that synchronization is achievable in a practical sense, that is, with “small” error. We also illustrate our methods on particular examples of chaotic oscillators such as the Lorenz and the LÜ oscillators. Theoretical proofs are provided based on recent results on stability theory for time-varying systems.

International Journal of Robust and Nonlinear Control, 2015

We provide a theoretical framework that fits realistic challenges related to spacecraft formation... more We provide a theoretical framework that fits realistic challenges related to spacecraft formation with disturbances. We show that the input-to-state stability of such systems guarantees some robustness with respect to a class of signals with bounded average-energy, which encompasses the typical disturbances acting on spacecraft formations. Solutions are shown to converge to the desired formation, up to an offset which is somewhat proportional to the considered moving average of disturbances. The approach provides a tighter evaluation of the disturbances' influence, which allows for the use of more parsimonious control gains.

1.1 16 Pour tout renseignement s'adresser à : For further information, please contact: Topics 1. ... more 1.1 16 Pour tout renseignement s'adresser à : For further information, please contact: Topics 1. Embedded and networked systems Taking into account the network topology (multiple levels, different sizes and time scales) and constraints of communication. Development of new methodologies (modeling, control, state estimation of parameters) to ensure good performances, be robust to disturbances and reliable.

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004

ABSTRACT

IEEE Transactions on Automatic Control, 2015

Motivated by control applications relying on shared resources (such as computation time or bandwi... more Motivated by control applications relying on shared resources (such as computation time or bandwidth), we analyze the stability and robustness of discrete-time switched linear systems driven by a stochastic process. The class of systems we study encompasses Markov Chain and independent and identically distributed switching processes. For these systems, we recall existing definitions of stability and robustness, by relying on the input-to-state (ISS) property. We show that, for the class of systems under concern, δ-moment stability is equivalent to its ISS counterpart and that they both imply almost sure ISS. Several sufficient conditions are provided to guarantee these properties. All the concepts are illustrated by the anytime control of a mechanical system.

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

In previous papers we have introduced a sufficient condition for uniform attractivity of the orig... more In previous papers we have introduced a sufficient condition for uniform attractivity of the origin of a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform δ-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of uδ-PE which is conceptually equivalent to but technically different from its predecessors. We make connections between this property and similar properties previously used in the literature. We also show when this condition is necessary and sufficient for uniform (global) asymptotic stability for a large class of nonlinear time-varying systems.

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

... Antonio Loriat Elena Panteleyt Dobrivoje PopoviC§ Andrew R. Tee15 ... We show the utility of ... more ... Antonio Loriat Elena Panteleyt Dobrivoje PopoviC§ Andrew R. Tee15 ... We show the utility of our theorem by analyzing uniform asymptotic stability of the origin for nonholonomic sys-tems in closed loop with particular smooth time-varying feedbacks previously proposed in the ...

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2000

We present su cient conditions for uniform exponential stability of families of linear time varyi... more We present su cient conditions for uniform exponential stability of families of linear time varying (LTV) systems. That is, LTV systems characterized by c e rtain parameter. Our conditions are in the form of classical concepts in adaptive control, such as persistency of excitation. However, our proofs are based on modern tools which can be interpreted as an \integral" version of Lyapunov theorems rather than on the concept of uniform complete observability which is most common in the literature. Uniformity is established in both, the initial conditions of the system, and the parameter which c haracterizes each system of the`family'.

Proceedings of 35th IEEE Conference on Decision and Control, 1996

In this short paper we deal with the stability analysis problem of cascaded non autonomous nonlin... more In this short paper we deal with the stability analysis problem of cascaded non autonomous nonlinear systems. In particular we answer to the following questions: (1) What happens with the solutions of a time varying nonlinear system which is globally uniformly stable when it is perturbed by the output of a globally exponentially stable system (GES), in particular, when both systems form a cascade?. (2) If a time varying nonlinear system is globally uniformly asymptotically stable (GUAS), is this stability property preserved when it is perturbed by an exponentially decaying input?, (3) Under which conditions the cascaded interconnection of two GUAS non autonomous nonlinear systems, is still GUAS?.

Lecture Notes in Control and Information Science, 2006

2009 IEEE International Conference on Control Applications, 2009

In this brief note a new strict Lyapunov function for mechanical systems controlled by the well-k... more In this brief note a new strict Lyapunov function for mechanical systems controlled by the well-known Passivitybased Control technique of Interconnection and Damping Assignment is proposed. The general, total energy-shaping, formulation of the control technique is considered, which yields a port-Hamiltonian closed-loop system with non-fixed symplectic structure. To construct the proposed Lyapunov function a new systematic mathematical machinery is introduced. The resulting Lyapunov function contains, as particular cases, previous functions obtained for robot manipulators controlled by potential energy-shaping (plus damping injection) schemes. Moreover, the class of robot manipulators considered so far in the literature is restricted, and almost universally accepted, to have only revolute joints, and the class considered here includes both revolute and prismatic joints. As an illustration example, practical bounds for a two-link direct drive robot manipulator are computed.

We present a new result on uniform attractivity of the origin for nonlinear time-varying systems.... more We present a new result on uniform attractivity of the origin for nonlinear time-varying systems. Our theorem generalizes Matrosov's theorem which extends, in a certain manner, Krasovskȋ-LaSalle invariance principle to the case of general nonlinear time-varying systems. We show the utility of our theorem by addressing a control problem of port interconnected driftless systems. The latter includes as special case, the control of chained-form nonholonomic systems which has been extensively studied in the literature.

We study the problem of stability analysis for certain nonlinear systems. Our contributions are n... more We study the problem of stability analysis for certain nonlinear systems. Our contributions are new tools to guarantee uniform global asymptotic stability (UGAS) of nonlinear time-varying (NLTV) systems. Firstly, we provide new de nitions of persistency of excitation (PE). In particular, we g i v e here a new de nition of uniform -PE (u -PE) which, though conceptually equivalent to the original one introduced 7], is mathematically less conservative. We also provide with some properties of -PE pairs and contribute with a result which establishes UGAS of NLTV systems under u -PE.

The problem of input-to-output stability for switched nonlinear systems is considered. Two approa... more The problem of input-to-output stability for switched nonlinear systems is considered. Two approaches for switching between non-exponentially stable systems are proposed guaranteeing input-to-output stability for the switched system.

The stability of (not necessarily compact) sets for nonlinear systems in cascade is addressed. It... more The stability of (not necessarily compact) sets for nonlinear systems in cascade is addressed. It is proved that if two sets are globally asymptotically stable (GAS) for the subsystems taken separately then their cross-product is GAS for the corresponding cascade, provided that the solutions of the latter are globally bounded. In the case of a suitable growth rate of the interconnection in the state of the driven subsystem, we show that this latter requirement can be relaxed to just forward completeness of the cascade. Our results extend similar results on the stability analysis of cascaded systems and find applications in partial stability analysis and adaptive control.

We address the problem of master-slave synchronization of chaotic systems under parameter uncerta... more We address the problem of master-slave synchronization of chaotic systems under parameter uncertainty and with partial measurements. Our approach is based on observer-design theory hence, we view the master dynamics as a system of differential equations with a state and a measurable output and we design an observer (tantamount to the slave system) which reconstructs the dynamic behavior of the master. The main technical condition that we impose is persistency of excitation (PE), a property well studied in the adaptive control literature. In the case of unknown parameters and partial measurements we show that synchronization is achievable in a practical sense, that is, with “small” error. We also illustrate our methods on particular examples of chaotic oscillators such as the Lorenz and the LÜ oscillators. Theoretical proofs are provided based on recent results on stability theory for time-varying systems.

International Journal of Robust and Nonlinear Control, 2015

We provide a theoretical framework that fits realistic challenges related to spacecraft formation... more We provide a theoretical framework that fits realistic challenges related to spacecraft formation with disturbances. We show that the input-to-state stability of such systems guarantees some robustness with respect to a class of signals with bounded average-energy, which encompasses the typical disturbances acting on spacecraft formations. Solutions are shown to converge to the desired formation, up to an offset which is somewhat proportional to the considered moving average of disturbances. The approach provides a tighter evaluation of the disturbances' influence, which allows for the use of more parsimonious control gains.

1.1 16 Pour tout renseignement s'adresser à : For further information, please contact: Topics 1. ... more 1.1 16 Pour tout renseignement s'adresser à : For further information, please contact: Topics 1. Embedded and networked systems Taking into account the network topology (multiple levels, different sizes and time scales) and constraints of communication. Development of new methodologies (modeling, control, state estimation of parameters) to ensure good performances, be robust to disturbances and reliable.

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004

ABSTRACT

IEEE Transactions on Automatic Control, 2015

Motivated by control applications relying on shared resources (such as computation time or bandwi... more Motivated by control applications relying on shared resources (such as computation time or bandwidth), we analyze the stability and robustness of discrete-time switched linear systems driven by a stochastic process. The class of systems we study encompasses Markov Chain and independent and identically distributed switching processes. For these systems, we recall existing definitions of stability and robustness, by relying on the input-to-state (ISS) property. We show that, for the class of systems under concern, δ-moment stability is equivalent to its ISS counterpart and that they both imply almost sure ISS. Several sufficient conditions are provided to guarantee these properties. All the concepts are illustrated by the anytime control of a mechanical system.

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

In previous papers we have introduced a sufficient condition for uniform attractivity of the orig... more In previous papers we have introduced a sufficient condition for uniform attractivity of the origin of a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform δ-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of uδ-PE which is conceptually equivalent to but technically different from its predecessors. We make connections between this property and similar properties previously used in the literature. We also show when this condition is necessary and sufficient for uniform (global) asymptotic stability for a large class of nonlinear time-varying systems.

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

... Antonio Loriat Elena Panteleyt Dobrivoje PopoviC§ Andrew R. Tee15 ... We show the utility of ... more ... Antonio Loriat Elena Panteleyt Dobrivoje PopoviC§ Andrew R. Tee15 ... We show the utility of our theorem by analyzing uniform asymptotic stability of the origin for nonholonomic sys-tems in closed loop with particular smooth time-varying feedbacks previously proposed in the ...

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2000

We present su cient conditions for uniform exponential stability of families of linear time varyi... more We present su cient conditions for uniform exponential stability of families of linear time varying (LTV) systems. That is, LTV systems characterized by c e rtain parameter. Our conditions are in the form of classical concepts in adaptive control, such as persistency of excitation. However, our proofs are based on modern tools which can be interpreted as an \integral" version of Lyapunov theorems rather than on the concept of uniform complete observability which is most common in the literature. Uniformity is established in both, the initial conditions of the system, and the parameter which c haracterizes each system of the`family'.

Proceedings of 35th IEEE Conference on Decision and Control, 1996

In this short paper we deal with the stability analysis problem of cascaded non autonomous nonlin... more In this short paper we deal with the stability analysis problem of cascaded non autonomous nonlinear systems. In particular we answer to the following questions: (1) What happens with the solutions of a time varying nonlinear system which is globally uniformly stable when it is perturbed by the output of a globally exponentially stable system (GES), in particular, when both systems form a cascade?. (2) If a time varying nonlinear system is globally uniformly asymptotically stable (GUAS), is this stability property preserved when it is perturbed by an exponentially decaying input?, (3) Under which conditions the cascaded interconnection of two GUAS non autonomous nonlinear systems, is still GUAS?.

Lecture Notes in Control and Information Science, 2006

2009 IEEE International Conference on Control Applications, 2009

In this brief note a new strict Lyapunov function for mechanical systems controlled by the well-k... more In this brief note a new strict Lyapunov function for mechanical systems controlled by the well-known Passivitybased Control technique of Interconnection and Damping Assignment is proposed. The general, total energy-shaping, formulation of the control technique is considered, which yields a port-Hamiltonian closed-loop system with non-fixed symplectic structure. To construct the proposed Lyapunov function a new systematic mathematical machinery is introduced. The resulting Lyapunov function contains, as particular cases, previous functions obtained for robot manipulators controlled by potential energy-shaping (plus damping injection) schemes. Moreover, the class of robot manipulators considered so far in the literature is restricted, and almost universally accepted, to have only revolute joints, and the class considered here includes both revolute and prismatic joints. As an illustration example, practical bounds for a two-link direct drive robot manipulator are computed.