Optimal control of a class of hybrid systems

Cassandras, Christos G.; Pepyne, D.L.; Wardi, Yoraı̈

doi:10.1109/9.911417

Cited by 261 publications

(48 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We refer to Attia et al (2005Attia et al ( , 2010, , Azhmyakov and Noriega Morales (2010), Branicky et al (1998), Cassandras et al (2001), Egerstedt et al (2006), Garavello and Piccoli (2005), Liberzon (2003), Lygeros (2003, Moor and Raisch (1999) and Shaikh andCaines (2007), Sussmann (1999) for some concrete definitions and concepts of hybrid/switched control systems. Note that for some classes of the above systems the possible switching mechanisms are formalized by different types of the characteristic functions β.…”

Section: Problem Formulation and The Classical Proximal Point Methodsmentioning

confidence: 99%

“…The same is true in connection with various numerical solution schemes associated with OCPs. We refer to (see e.g., Azhmyakov and Noriega Morales 2010;Büskens and Maurer 2000;Cassandras et al 2001;Maurer 1976;Polak 1997;Sakawa et al 1981;Teo et al 1991) for theoretical and some computational aspects. The necessary optimality conditions for convex minimization problems (3) and (4) are also sufficient.…”

Section: Some Computational Issuesmentioning

confidence: 98%

“…The study of hybrid and switched systems has gained lots of interest in the recent years (see Attia et al 2005Attia et al , 2010Axelsson et al 2008a, b;Azhmyakov et al , 2009Azhmyakov et al , 2011Cassandras et al 2001;Ding et al 2008Ding et al , 2009Egerstedt et al 2006;Garavello and Piccoli 2005;Shaikh and Caines 2007;Sussmann 1999;Verriest et al 2004;Xu and Antsaklis 2003a, b). Many applications from different disciplines have been studied in this modeling framework.…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

A Proximal Point Based Approach to Optimal Control of Affine Switched Systems

Azhmyakov

Raisch

2011

Discrete Event Dyn Syst

View full text Add to dashboard Cite

This paper focuses on the proximal point regularization technique for a class of optimal control processes governed by affine switched systems. We consider switched control systems described by nonlinear ordinary differential equations which are affine in the input. The affine structure of the dynamical models under consideration makes it possible to establish some continuity/approximability properties and to specify these models as convex control systems. We show that, for some classes of cost functionals, the associated optimal control problem (OCP) corresponds to a conventional convex optimization problem in a suitable Hilbert space. The latter can be reliably solved using standard first-order optimization algorithms and consistent regularization schemes. In particular, we propose a conceptual numerical approach based on the gradient-type method and classic proximal point techniques.

show abstract

Section: Problem Formulation and The Classical Proximal Point Methodsmentioning

confidence: 99%

Section: Some Computational Issuesmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

A Proximal Point Based Approach to Optimal Control of Affine Switched Systems

Azhmyakov

Raisch

2011

Discrete Event Dyn Syst

View full text Add to dashboard Cite

show abstract

“…Related to the above-mentioned MPC approaches, which are predominantly studied in the discrete-time context, there are also optimal control approaches for continuous-time hybrid systems (e.g. Branicky et al 1998;De Schutter 2000;Rantzer & Johansson 2000;Cassandras et al 2001;Hedlund & Rantzer 2002;Xu & Antsaklis 2004 and the references therein). Also hybrid extensions are available for the celebrated Pontryagin's maximum principle, giving necessary conditions for optimality in optimal control problems (e.g.…”

Section: (C) Other Control Methodsmentioning

confidence: 99%

Stability analysis and controller synthesis for hybrid dynamical systems

Heemels¹,

Schutter

Lunze

et al. 2010

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

show abstract

“…Most of them can be roughly divided into two groups: those using continuoustime models (see, for example Cassandras et al 2001;Xu and Antsaklis 2003) and those using discrete-time models (see, for example Bemporad and Morari 1999). Regarding continuous-time models, the main considered issues are the study of necessary trajectories to be optimal and the computation of optimal control laws by means of Hamilton-Jacobi-Bellman equations or the maximum principle.…”

Section: Control Under Finite Server Semanticsmentioning

confidence: 99%

On fluidization of discrete event models: observation and control of continuous Petri nets

Silva

Júlvez

Mahulea

et al. 2011

Discrete Event Dyn Syst

101

View full text Add to dashboard Cite

As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.

show abstract

Optimal control of a class of hybrid systems

Cited by 261 publications

References 16 publications

A Proximal Point Based Approach to Optimal Control of Affine Switched Systems

A Proximal Point Based Approach to Optimal Control of Affine Switched Systems

Stability analysis and controller synthesis for hybrid dynamical systems

On fluidization of discrete event models: observation and control of continuous Petri nets

Contact Info

Product

Resources

About