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219
Lyapunov Conditions for Input-to-State Stability of Impulsive Systems
, 2008
"... This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for impulsive systems, i.e., dynamical systems that evolve according to ordinary differential equations most of the time, but occasionally exhibit discontinuities (or impulses). We provide a set of Lyapunov ..."
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Cited by 29 (1 self)
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This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for impulsive systems, i.e., dynamical systems that evolve according to ordinary differential equations most of the time, but occasionally exhibit discontinuities (or impulses). We provide a set of Lyapunov-based sufficient conditions for establishing these ISS properties. When the continuous dynamics are ISS but the discrete dynamics that govern the impulses are not, the impulses should not occur too frequently, which is formalized in terms of an average dwell-time (ADT) condition. Conversely, when the impulse dynamics are ISS but the continuous dynamics are not, there must not be overly long intervals between impulses, which is formalized in terms of a novel reverse ADT condition. We also investigate the cases where (i) both the continuous and discrete dynamics are ISS and (ii) one of these is ISS and the other only marginally stable for the zero input, while sharing a common Lyapunov function. In the former case we obtain a stronger notion of ISS, for which a necessary and sufficient Lyapunov characterization is available. The use of the tools developed herein is illustrated through examples from a Micro-Electro-Mechanical System (MEMS) oscillator and a problem of remote estimation over a communication network.
A hybrid systems model for power control in multicell wireless data networks, Performance Evaluation 57(4
, 2004
"... Abstract — We present a power control scheme based on noncooperative game theory, using a fairly broad class of convex cost functions. The multicell CDMA wireless data network is modeled as a switched hybrid system where handoffs of mobiles between different cells correspond to discrete switching ev ..."
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Cited by 29 (10 self)
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Abstract — We present a power control scheme based on noncooperative game theory, using a fairly broad class of convex cost functions. The multicell CDMA wireless data network is modeled as a switched hybrid system where handoffs of mobiles between different cells correspond to discrete switching events between different subsystems. Under a set of sufficient conditions, we prove the existence of a unique Nash equilibrium for each subsystem, and prove global exponential stability of an update algorithm. We also establish the global convergence of the dynamics of the multicell power control game to a convex superset of Nash equilibria for any switching (handoff) scheme satisfying a mild condition on average dwell-time. Robustness of these results to feedback delays as well as to quantization is investigated. In addition, we consider a quantization scheme to reduce the communication overhead between mobiles and the base stations. Finally, we illustrate the proposed power control scheme through simulations. I.
Root-mean-square gains of switched linear systems
- IEEE Trans. Automat. Contr
, 2003
"... In this paper we compute the root-mean-square (RMS) gain of a switched linear system when the interval between consecutive switchings is large. The algorithm proposed is based on the fact that a given constant γ provides an upper bound on the RMS gain whenever there is a separation between the stabi ..."
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Cited by 26 (6 self)
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In this paper we compute the root-mean-square (RMS) gain of a switched linear system when the interval between consecutive switchings is large. The algorithm proposed is based on the fact that a given constant γ provides an upper bound on the RMS gain whenever there is a separation between the stabilizing and the antistabilizing solutions to a set of γ-dependent algebraic Riccati equations. The motivation for this problem is the application of robust stability tools to the analysis of hybrid systems. 1
Automata based interfaces for control and scheduling
- In Proc. 10th Int. Workshop on Hybrid Systems: Computation and Control, LNCS 4416
, 2007
"... Abstract. We propose the use of formal languages of infinite words over the alphabet of task identifiers as an interface between control designs and software implementations. We argue that this approach is more flex-ible than the classical real-time scheduling framework based on periodic tasks, and ..."
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Cited by 24 (6 self)
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Abstract. We propose the use of formal languages of infinite words over the alphabet of task identifiers as an interface between control designs and software implementations. We argue that this approach is more flex-ible than the classical real-time scheduling framework based on periodic tasks, and allows composition of interfaces by language-theoretic opera-tions. We show that finite automata over infinite words offer analyzable representation and can capture many interesting interface specifications such as exponential stability of switched linear systems. 1
Robust stability and disturbance attenuation analysis of a class of networked control systems
- In Proc. of the 42th Conf. on Decision and Contr
, 2003
"... Abstract — In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H ∞ ..."
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Cited by 24 (4 self)
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Abstract — In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H ∞ disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such Networked Control System as a discrete-time switched system. Then the NCSs ’ stability and performance problems can be reduced to corresponding problems for the switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based on recent progress in the discrete-time switched systems and piecewise Lyapunov functions. I.
Linear parametrically varying systems with brief instabilities: an application to integrated vision/IMU navigation
- IEEE Trans. on Aerospace and Electronics Systems
, 2001
"... This paper addresses the problem of nonlinear filter design to estimate the relative position and velocity of an unmanned air vehicle (UAV) with respect to a point on a ship using infrared (IR) vision, inertial, and air data sensors. Sufficient conditions are derived for the existence of a particula ..."
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Cited by 22 (10 self)
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This paper addresses the problem of nonlinear filter design to estimate the relative position and velocity of an unmanned air vehicle (UAV) with respect to a point on a ship using infrared (IR) vision, inertial, and air data sensors. Sufficient conditions are derived for the existence of a particular type of complementary filters with guaranteed stability and performance in the presence of so-called out-of-frame events that arise when the vision system loses its target temporarily. The results obtained build upon new developments in the theory of linear parametrically varying systems (LPVs) with brief instabilities–also reported in the paper–and provide the proper framework to deal with out-of-frame events. Field tests with a prototype UAV illustrate the performance of the filter and the scope of applications of the new theory developed. Manuscript received January 10, 2003; revised December 14, 2003; released for publication April 12, 2004.
Lyapunov-Based Switching Supervisory Control of Nonlinear Uncertain Systems
, 2002
"... The problem of controlling nonlinear noisy systems aected by parametric uncertainties is approached via the introduction of a supervisor which switches on, in feedback to the plant, one controller selected from a nite set of predesigned controllers. A Lyapunov-based falsication criterion allows one ..."
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Cited by 22 (4 self)
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The problem of controlling nonlinear noisy systems aected by parametric uncertainties is approached via the introduction of a supervisor which switches on, in feedback to the plant, one controller selected from a nite set of predesigned controllers. A Lyapunov-based falsication criterion allows one to ensure robust stability in the presence of uncertain constant parameters and exogenous bounded disturbances. 1 Introduction One of the well-estabilished approaches for dealing in control with plant model uncertainty is the introduction of adaptation in the feedback loop [2]. However, conventional continuous adaptation is not always capable of performing satisfactorily. This may be particulartly true whenever the plant switches among dierent modes of operation or if closed-loop signals are not suciently exciting. In both circumstances undesirable transients may typically arise due to slow adaptation. In recent years, switching supervisory control (SSC) has emerged as an alternative ...
Multiple Model Adaptive Control with Safe Switching
, 2001
"... The purpose of this paper is to marry the two concepts of Multiple Model Adaptive Control and Safe Adaptive Control. In its simplest form, Multiple Model Adaptive Control involves a supervisor switching among one of a finite number of controllers as more is learnt about the plant, until one of the c ..."
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Cited by 19 (4 self)
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The purpose of this paper is to marry the two concepts of Multiple Model Adaptive Control and Safe Adaptive Control. In its simplest form, Multiple Model Adaptive Control involves a supervisor switching among one of a finite number of controllers as more is learnt about the plant, until one of the controllers is finally selected and remains unchanged. Safe Adaptive Control is concerned with ensuring that when the controller is changed in an adaptive control algorithm, the frozen plant-controller combination is never (closed loop) unstable. This is a nontrivial task since by definition of an adaptive control problem, the plant is not fully known. The proposed solution method involves a frequency-dependent performance measure and employs the Vinnicombe metric. The resulting safe switching guarantees depend on the extent to which a closed loop transfer function can be accurately identified.
On input-to-state stability of impulsive systems
- in Proc. 44th IEEE Conf. Decision and Control, 2005
, 2005
"... Abstract — This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for systems with impulsive effects. We provide a set of Lyapunov-based sufficient conditions to establish these properties. When the continuous dynamics are stabilizing but the impulsive effects ..."
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Cited by 15 (5 self)
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Abstract — This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for systems with impulsive effects. We provide a set of Lyapunov-based sufficient conditions to establish these properties. When the continuous dynamics are stabilizing but the impulsive effects are destabilizing, the impulses should not occur too frequently, which can be formalized in terms of an average dwell-time condition. Conversely, when the impulses are stabilizing and the continuous dynamics are destabilizing, there must not be overly long intervals between impulses, which is formalized in terms of a reverse average dwell-time condition. We also investigate limiting cases of systems that remain stable for arbitrarily small/large average dwell-times. I.
