Supervisory control with state-dependent dwell-time logic and constraints

Persis, Claudio De; Santis, Raffaella De; Morse, A. Stephen

doi:10.1016/j.automatica.2003.09.005

Cited by 49 publications

(31 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A number of authors have further extended this work and derived analogous results for other classes of switched nonlinear systems [128,41]. Further developments have also included the work of Zhai et al [190] in which the authors modify this result so that the lowest average dwell-timeτ * D ensures that the switched system achieves a chosen L 2 gain, while several other authors have extended the results to allow for switching between stable and unstable subsystems, e.g.…”

Section: Constraints On the Rate Of Switchingmentioning

confidence: 95%

Stability Criteria for Switched and Hybrid Systems

Shorten¹,

Wirth²,

Mason³

et al. 2007

SIAM Rev.

900

558

View full text Add to dashboard Cite

The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, and to review some problems that remain open. An important contribution of our work is to bring together material from several areas of research and to present results in a unified manner. We begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions. Closely related to the concept of stability are the notions of exponential growth rates and converse Lyapunov theorems, both of which are discussed in detail. In particular, results on common quadratic Lyapunov functions and piecewise linear Lyapunov functions are presented, as they represent constructive methods for proving stability, and also represent problems in which significant progress has been made. We also comment on the inherent difficulty of determining stability of switched systems in general which is exemplified by NP-hardness and undecidability results. We then proceed by considering the stability of switched systems in which there are constraints on the switching rules, through both dwell time requirements and state dependent switching laws. Also in this case the theory of Lyapunov functions and the existence of converse theorems is reviewed. We briefly comment on the classical Lur'e problem and on the theory of stability radii, both of which contain many of the features of switched systems and are rich sources of practical results on the topic. Finally we present a list of questions and open problems which provide motivation for continued research in this area.

show abstract

Section: Constraints On the Rate Of Switchingmentioning

confidence: 95%

Stability Criteria for Switched and Hybrid Systems

Shorten¹,

Wirth²,

Mason³

et al. 2007

SIAM Rev.

900

558

View full text Add to dashboard Cite

show abstract

“…Finally, the Lyapunov functions we provide here are lower bounded near 0 by positive definite quadratic functions, while the Lyapunov function construction of [11] would not have this property. We also use the idea of weighting functions, which have been used in other contexts [1], [4], [19]. The global strict DRAFT Lyapunov-based framework can potentially generalize the UGAS proofs for adaptive systems.…”

Section: Draftmentioning

confidence: 99%

Uniform Global Asymptotic Stability of a Class of Adaptively Controlled Nonlinear Systems

Mazenc

Queiroz

Malisoff

2009

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

We give a new explicit, global, strict Lyapunov function construction for the error dynamics for adaptive tracking control problems, under an appropriate persistency of excitation condition. We then allow time-varying uncertainty in the unknown parameters. In this case, we construct input-to-state stable Lyapunov functions under suitable bounds on the uncertainty, provided the regressor also satisfies an affine growth condition. This lets us quantify the effects of uncertainties on both the tracking and the parameter estimation. We illustrate our results using Rössler systems.

show abstract

“…The proposed technique is inspired by the supervisory control framework, see e.g., [6], [8], [9], [10]. Indeed, like in works on supervisory control, the scheme consists of a multi-estimator and a supervisor, which selects one of the observers at each time instant.…”

Section: Introductionmentioning

confidence: 99%

“…ESTIMATION SCHEME The estimation scheme is inspired by works on supervisory control (e.g., [6], [8], [9], [10]). It consists of a bank of local observers, called multi-observer, and a supervisor, as depicted in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

A multi-observer approach for the state estimation of nonlinear systems

Hamid

Daafouz

2015

2015 54th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

Abstract-We present a prescriptive approach for the state estimation of nonlinear systems. We first assume that we know a local observer, i.e. a dynamical system whose state converges to the plant state when it is initialized nearby the plant initial condition. We sample the set where the plant initial condition is assumed to lie with a finite number of points; noting that this set can be arbitrarily large. A local observer is initialized at each of these sampled points to form a bank of observers called multi-observer. A supervisor is then constructed to select one of these observers at any time instant. The selected state estimate is guaranteed to converge to the state of the plant, provided the number of samples is sufficiently large and a detectability property holds, which is expressed in terms of Lyapunov-based conditions. An explicit lower bound on the required number of observers is given when an estimate of the basin of convergence of the local observer is available. We explain how to apply the approach to nonlinear systems with globally Lipschitz and differentiable nonlinearities. Simulations results are presented for a Wilson-Cowan oscillator.

show abstract

Supervisory control with state-dependent dwell-time logic and constraints

Cited by 49 publications

References 16 publications

Stability Criteria for Switched and Hybrid Systems

Stability Criteria for Switched and Hybrid Systems

Uniform Global Asymptotic Stability of a Class of Adaptively Controlled Nonlinear Systems

A multi-observer approach for the state estimation of nonlinear systems

Contact Info

Product

Resources

About