Synthesis of Minimally Restrictive Legal Controllers for a Class of Hybrid Systems

In this paper, we study the control of Composite Hybrid Machines (CHMs) subject to safety specifications. CHMs are a fairly general class of hybrid systems modeled in modular fashion as the concurrent operation of Elementary Hybrid Machines (EHMs). The formalism has a well-defined synchronous-composition operation that permits the introduction of the controller as a component of the system. The task of a legal controller is to ensure that the system never exits a set of specified legal configurations. Among the legal controllers, we are particularly interested in designing a minimally-restrictive (or minimally-interventive) one, which interferes in the system's operation only when constraint violation is otherwise inevitable. Thus, when composed to operate concurrently with another legal controller, our controller will never interfere with the operation of the other. Therefore, a minimally-restrictive controller provides maximum flexibility in embedding additional controllers designed for other control objectives to operate concurrently, while eliminating the need to re-investigate or re-verify the legality of the composite controller. We describe in detail an algorithm for controller synthesis and examine through several examples questions associated with algorithm termination and controller existence.

[1]  Joseph Sifakis,et al.  An Approach to the Description and Analysis of Hybrid Systems , 1992, Hybrid Systems.

[2]  Michael Heymann,et al.  Discrete event control of nondeterministic systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[3]  Joseph Sifakis,et al.  From ATP to Timed Graphs and Hybrid Systems , 1991, REX Workshop.

[4]  Pravin Varaiya,et al.  What's decidable about hybrid automata? , 1995, STOC '95.

[5]  W. Wonham,et al.  Supervisory control of timed discrete-event systems under partial observation , 1995, IEEE Trans. Autom. Control..

[6]  Roger W. Brockett,et al.  Hybrid Models for Motion Control Systems , 1993 .

[7]  W. M. Wonham,et al.  Decentralized control and coordination of discrete-event systems with partial observation , 1990 .

[8]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[9]  Feng Lin,et al.  On-line control of partially observed discrete event systems , 1994, Discret. Event Dyn. Syst..

[10]  Anil Nerode,et al.  Models for Hybrid Systems: Automata, Topologies, Controllability, Observability , 1992, Hybrid Systems.

[11]  Michael Heymann,et al.  Nonblocking Supervisory Control of Nondeterministic Systems , 1997 .

[12]  Panos J. Antsaklis,et al.  Hybrid System Modeling and Autonomous Control Systems , 1992, Hybrid Systems.

[13]  W. M. Wonham,et al.  The control of discrete event systems , 1989 .

[14]  Michael S. Branicky,et al.  Universal Computation and Other Capabilities of Hybrid and Continuous Dynamical Systems , 1995, Theor. Comput. Sci..

[15]  Walter Murray Wonham,et al.  On observability of discrete-event systems , 1988, Inf. Sci..

[16]  Jean-Raymond Abrial.  Steam-Boiler Control Specification Problem , 1995, Formal Methods for Industrial Applications.

[17]  P. Ramadge,et al.  Supervisory control of a class of discrete event processes , 1987 .

[18]  Zohar Manna,et al.  Verifying Hybrid Systems , 1992, Hybrid Systems.

[19]  Feng Lin,et al.  Control Synthesis for a Class of Hybrid Systems Subject to Configuration-Based Safety Constraints , 1997, HART.

[20]  S. Chung,et al.  Limited lookahead policies in supervisory control of discrete event systems , 1992 .

[21]  Oded Maler,et al.  Hybrid and Real-Time Systems , 1997 .

[22]  Joseph Sifakis,et al.  On the Synthesis of Discrete Controllers for Timed Systems (An Extended Abstract) , 1995, STACS.

[23]  Michael Heymann,et al.  Discrete-event control of nondeterministic systems , 1998 .

[24]  Zohar Manna,et al.  From Timed to Hybrid Systems , 1991, REX Workshop.

[25]  M. Heymann.  Concurrency and discrete event control , 1990, IEEE Control Systems Magazine.

[26]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[27]  Amir Pnueli,et al.  Symbolic Controller Synthesis for Discrete and Timed Systems , 1994, Hybrid Systems.