Analysis and Design of Hybrid Systems 2006 (eBook)

A Proceedings volume from the 2nd IFAC Conference, Alghero, Italy, 7-9 June 2006

Christos Cassandras, Alessandro Giua, Carla Seatzu, Janan Zaytoon (Herausgeber)

eBook Download: PDF | EPUB

2006 | 1. Auflage
448 Seiten
Elsevier Science (Verlag)
978-0-08-047584-4 (ISBN)

Infos

This volume contains the proceedings of ADHS'06: the 2nd IFAC Conference on Analysis and Design of Hybrid Systems, organized in Alghero (Italy) on June 7-9, 2006.
ADHS is a series of triennial meetings that aims to bring together researchers and practitioners with a background in control and computer science to provide a survey of the advances in the field of hybrid systems, and of their ability to take up the challenge of analysis, design and verification of efficient and reliable control systems. ADHS'06 is the second Conference of this series after ADHS'03 in Saint Malo.

* 65 papers selected through careful reviewing process
* Plenary lectures presented by three distinguished speakers
* Featuring interesting new research topics

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This volume contains the proceedings of Analysis and Design of Hybrid Systems 2006: the 2nd IFAC Conference on Analysis and Design of Hybrid Systems, organized in Alghero (Italy) on June 7-9, 2006. ADHS is a series of triennial meetings that aims to bring together researchers and practitioners with a background in control and computer science to provide a survey of the advances in the field of hybrid systems, and of their ability to take up the challenge of analysis, design and verification of efficient and reliable control systems. ADHS'06 is the second Conference of this series after ADHS'03 in Saint Malo. 65 papers selected through careful reviewing process Plenary lectures presented by three distinguished speakers Featuring interesting new research topics

Inhalt

Front Cover 1
Analysis and Design of Hybrid Systems 2006 2
Copyright Page 3
Table of Contents 8
Part 1: Plenary Lectures 14
Chapter 1. Chattering Problem for Sliding Mode Control Systems 14
Chapter 2. Challenges and opportunities for system theory in embedded controller design 15
Chapter 3. Optimal Control in Hybrid Systems 17
Part 2: WA1 - Observers for Hybrid Systems 19
Chapter 4. Convergent design of switched linear systems 19
Chapter 5. Observer design for a class of discrete time piecewise-linear systems 25
Chapter 6. Designing switched observers for switched systems using multiple Lyapunov functions and dwell-time switching 31
Chapter 7. Critical states detection with bounded probability of false alarm and application to air traffic management 37
Part 3: WA2 - Continuous and Hybrid Petri Nets 43
Chapter 8. Tracking control of join-free timed continuous Petri net systems 43
Chapter 9. On sampling continuous timed Petri nets: reachability “equivalence“ under infinite servers semantics 50
Chapter 10. Modelling distributed manufacturing systems via first order hybrid Petri nets 57
Chapter 11. Simulation of railway stations based on hybrid Petri nets 63
Part 4: WB1 - Modeling and Simulation of Hybrid Systems 69
Chapter 12. Modeling an impact control strategy using HYPA 69
Chapter 13. Human skill modeling based on stochastic switched dynamics 77
Chapter 14. Building efficient simulations from hybrid bond graph models 84
Chapter 15. Robust control strategies for multi-inventory systems with average flow constraints 90
Part 5: WB2 - Control of Hybrid Systems 1 96
Chapter 16. Hybrid constrained formation flying control of micro-satellites 96
Chapter 17. A gradient-based approach to a class of hybrid optimal control problems 102
Chapter 18. Optimal mode-switching for hybrid systems with unknown initial state 108
Chapter 19. Beyond the construction of optimal switching surfaces for autonomous hybrid systems 114
Part 6: WC1 - Structural Analysis and Approximation of Hybrid Systems (Invited) 119
Chapter 20. Approximate simulation relations for hybrid systems 119
Chapter 21. Stabilizability based state space reductions for hybrid systems 125
Chapter 22. Reachability computation for uncertain planar affine systems using linear abstractions 131
Chapter 23. Exact differentiation via sliding mode observer for switched systems 137
Part 7: WC2 - Control of Hybrid Systems 2 143
Chapter 24. Robust H-infinity control of uncertain discrete-time switching symmetric Composite systems 143
Chapter 25. The elevator dispatching problem: hybrid system modeling and receding horizon control 149
Chapter 26. Robust piecewise linear sheet control in a printer paper path 155
Chapter 27. Stabilization of max-plus-linear systems using receding horizon control-The unconstrained case 161
Part 8: TA1 - Stochastic Hybrid Systems 167
Chapter 28. Online classification of switching models based on subspace framework 167
Chapter 29. Functional abstractions of stochastic hybrid systems 173
Chapter 30. Stochastic hybrid NETCAD systems for modeling call admission and routing control in networks 179
Chapter 31. Parameter identification for piecewise deterministic Markov processes: a case study on a biochemical network 185
Chapter 32. Using path integral short time propagators for numerical analysis of stochastic hybrid systems 192
Part 9: TA2 - Controller Design Based on Hybrid Models of Industrial Plants (Invited) 198
Chapter 33. Challenges in start-up control of a heat exchange reactor with exothermic reactions a hybrid approach
Chapter 34. Feedback stabilization of the operation of an hybrid chemical plant 204
Chapter 35. A solar cooling plant: a benchmark for hybrid systems control 212
Chapter 36. Timed discrete event control of a parallel production line with continuous output 218
Chapter 37. Dynamic optimization of an industrial evaporator using graph search with embedded nonIinear programming 224
Part 10: TB1 - Diagnosis and Identification 230
Chapter 38. Using neural networks for the identification of a class of hybrid dynamic systems 230
Chapter 39. Fault tolerant control design for switched systems 236
Chapter 40. Discrete-event modelling and fault diagnosis of discretely controlled continuous systems 242
Chapter 41. Use of an object oriented dynamic hybrid simulator for the monitoring of industriaI processes 248
Part 11: TB2 - Applications of Hybrid Control (Invited) 254
Chapter 42. Model predictive control of nonlinear mechatronic systems: an application to a magnetically actuated mass spring damper 254
Chapter 43. Subtleties in the averaging of hybrid systems with applications to power electronics 260
Chapter 44. Adaptive cruise controller design: a comparative assessment for PWA systems 266
Chapter 45. Idle speed control - a benchmark for hybrid system research 272
Part 12: TC1 - Hybrid Simulation Tools: Principles, Challenges and Applications (Invited) 278
Chapter 46. Simulation and verification of hybrid systems using Chi 278
Chapter 47. Hybrid system simulation with SIMEVENTS 280
Chapter 48. HyVisual: a hybrid system modeling framework based on Ptolemy II 283
Chapter 49. TrueTime: simulation of networked computer control systems 285
Chapter 50. CODIS - A framework for continuous/discrete systems co-simulation 287
Part 13: TC2 - Stability 1 289
Chapter 51. On the finite-time stabilization of a nonlinear uncertain dynamics via switched control 289
Chapter 52. Search for period-2 cycles in a class of hybrid dynamical systems with autonomous switchings. Application to a thermal device 296
Chapter 53. Stabilizability of bimodal piecewise linear systems with continuous vector field 303
Chapter 54. Global input-to-state stability and stabilization of discrete-time piece-wise affine systems 309
Part 14: FA1 - Model Predictive Control 315
Chapter 55. Feasible mode enumeration and cost comparison for explicit quadratic model predictive control of hybrid systems 315
Chapter 56. An efficient algorithm for predictive control of piecewise affine systems with mixed inputs 322
Chapter 57. Explicit model predictive control of the boost DC-DC converter 328
Chapter 58. A new dual-mode hybrid MPC algorithm with a robust stability guarantee 334
Chapter 59. Robust model predictive control for piecewise affine systems subject to bounded disturbances 342
Part 15: FA2 - Stability 2 348
Chapter 60. Stabilization of switched linear systems with unknown time varying delays 348
Chapter 61. Stabilizing dynamic controller of switched linear systems 354
Chapter 62. Dynamic output feedback stabilization of continuous-time switched systems 360
Chapter 63. Practical stabilization of discrete-time linear LTI SISO systems under assigned input and output quantization 366
Chapter 64. Box invariance of hybrid and switched systems 372
Part 16: FBI - Verification and Safety 378
Chapter 65. Performance verification of discrete event systems using hybrid model-checking 378
Chapter 66. Verification-integrated falsification of non-deterministic hybrid systems 384
Chapter 67. An evaluation of two recent reachability analysis tools for hybrid systems 390
Chapter 68. Safety and reliability analysis of protection systems for power systems 396
Chapter 69. A hybrid approach for safety analysis of aircraft systems 402
Part 17: FB2 - Abstraction Based Approaches to Hybrid Control 408
Chapter 70. Detecting and enforcing monotonicity for hybrid control systems synthesis 408
Chapter 71. Hybrid system control using an on-line discrete event supervisory strategy 415
Chapter 72. Non-deterministic reactive systems, from hybrid systems and behavioural systems perspectives 422
Chapter 73. Control-invariance of sampled-data hybrid systems with periodically clocked events and jitter 430
Author Index 436

Textauszug

Convergent Design of Switched Linear Systems

R.A. van den Berg [e-mail]; A.Y. Pogromsky [e-mail]; J.E. Rooda [e-mail]    Eindhoven University of Technology Department of Mechanical Engineering P.O.Box 513, 5600 MB Eindhoven, The Netherlands

Abstract

This paper deals with the design of switching rules for switched linear systems with inputs, in such a way that the resulting closed-loop system is exponentially convergent. Two types of switching rules are addressed, that is state-based and observer-based rules. The developed theory is illustrated by two examples. Copyright © 2006 IFAC

Keywords

Convergent systems

switched systems

continuous time systems

exponential stability

performance evaluation

observer

1 INTRODUCTION

A switched linear system is a hybrid/nonlinear system which consists of several linear subsystems and a switching rule that decides which of the subsystems is active at each moment in time. These systems have been a subject of growing interest in the last decades, see e.g. (Liberzon and Morse, 1999; DeCarlo et al., 2000) and references therein. Because of the combination of multiple linear systems/controllers, a well-tuned switched linear system can achieve better performance then a single linear system, or can achieve certain control goals that cannot be realized by linear systems (Morse, 1996; Narendra and Balakrishnan, 1997; Feuer et al., 1997).

Besides these extended possibilities that switched linear systems have with respect to linear systems, the design of such a switched system also brings along difficulties. For example, if all the linear subsystems of a switched system are stable, this does not automatically guarantee the stability of that switched system. A good example of this apparent contradiction is given in (Branicky, 1998). Another property that a linear time invariant (LTI) system with asymptotically stable homogeneous part has, but is not natural for a nonlinear/hybrid system, is that any solution of an LTI system with a bounded input converges to a unique solution that depends only on the input. Nonlinear/hybrid system that do possess this property are referred to as convergent. Solutions of convergent system “forget” their initial conditions and after some transient depend only on the system input, which can be a command or reference signal.

Convergency of nonlinear/hybrid systems is an interesting property, since it results in a limit solution that is independent of the initial conditions of the system. This is useful in for example synchronization problems (Pogromsky et al., 2002). Another possible area of interest is the performance analysis of nonlinear systems. For general nonlinear systems simulation-based analysis is quite impossible, since all possible initial conditions need to be evaluated in order to obtain a. reliable analysis. For a. convergent system, however, this problem does not exist, since all initial conditions lead to the same limit solution. Therefore simulation can be used to analyse and optimize performance of convergent systems. This motivates studies related to the design of convergent systems.

The property that all solutions of a system “forget” their initial conditions and converge to some steady-state solution has been addressed in a number of publications, e.g. (Fromion et al., 1996; Lohmiller and Slotine, 1998; Fromion et al., 1999; Pavlov et al., 2004; Angeli, 2002; Pavlov et al., 2005b). In this paper, the focus lies on the convergent design of switched linear systems using only the switching rule as “design variable”. Two different cases are considered. First, the case is considered in which the switching rule is based on static state feedback. Secondly, the case is considered in which full state information is not available. In this case a switching rule is discussed that is based on an observer.

The outline of this paper is as follows. In Section 2 a basic definition on stability is recalled that is required in the remainder of this article. Section 3 presents various definitions and properties of convergent systems. In Section 4 the design of a switching rule is discussed that makes the closed-loop switched linear system convergent. The main results of this section are presented in two theorems which give sufficient conditions under which such a switching rule can be found. Two examples are provided in Section 5 to illustrate these theorems. Section 6 concludes the paper.

2 PRELIMINARIES

In this article exponential stability will be considered. For the sake of completeness, this definition is given here.

Definition 1. A solution t,t0,x¯0 of a system ˙=fxt, defined for all t ∈ (t∗,+∞), is said to be exponentially stable if there exist positive δ, C, β such that x0−x¯0∥<δ implies

xtt0x0−xt,t0,x¯0∥≤Ce−βt−t0∥x0−x¯0∥

3 CONVERGENT SYSTEMS

In this section definitions and properties of convergent systems are presented. Those systems are very closely related to systems with globally exponentially stable solutions and the definitions presented here extend those given by Demidovich (Demidovich, 1967).

The following class of systems is considered

˙=fx,wt

  (1)

with state x ∈ n and input w ∈ ℂ¯m. Here, ℂ¯m is the class of bounded (for all t ∈ ) piecewise continuous inputs w(t) :  → m.

Assume that the function f (x, w) satisfies some regularity conditions to ensure the existence of a Filippov solution, see e.g. (Filippov, 1988), p.76.

Definition 2. System (1) is said to be exponentially convergent if there is a solution ¯t=xt,t0,x¯0 satisfying the following conditions for every input w(t) ∈ ℂ¯m: (i) ¯t is defined and bounded for all t ∈ (−∞, +∞), (ii) ¯t is globally exponentially stable for every input w(t) ∈ ℂ¯m.

The solution ¯t is called a limit solution. As follows from the definition of convergency, any solution of a convergent system “forgets” its initial condition and converges to some limit solution which is independent of the initial conditions. For exponentially convergent systems this limit solution ¯t is unique, i.e. it is the only solution defined and bounded for all t ∈ (−∞, +∞) (Pavlov et al., 2005a).

For system (1) consider a scalar continuously differentiable function V(x). Define a time derivative of this function along solutions of system (1) as follows

˙=∂Vx∂xx˙tt0x0a.e.

Definition 3. System (1) is called quadratically convergent if there exists a positively definite matrix P = PT > 0 and a number α > 0 such that for any input w ∈ ℂ¯m for the function V(x1, x2) = (x1 − x2)TP(x1 − x2) it holds that

˙x1x2t≤−αVx1x2.

  (2)

Lemma 4. (Pavlov et al., 2005a) If system (1) is quadratically convergent, then it is exponentially convergent.

The proof of this lemma is based on the following result, which will be also used in the sequel.

Lemma 5. (Yakubovich, 1964) Consider system (1) with a given input w(t) defined for all t ∈ . Let ⊂ℝn be a compact set which is positively invariant with respect to dynamics (l). Then there is at least one solution ¯t, such that ¯t∈D for all t ∈ (−∞,+∞).

Note that for convergent nonlinear systems performance can be evaluated in almost the same way as for linear systems. Due to the fact that the limit solution of a convergent system only depends on the input and is independent of the...

Produkt-Details

• Erscheint lt. Verlag: 21.11.2007
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik ► Architektur
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-047584-1 / 0080475841
• ISBN-13: 978-0-08-047584-4 / 9780080475844