## Abstract

The topic of this paper is the synthesis of discrete supervisory control for hybrid systems Σ with discrete external signals. Such systems are in general neither l-complete nor can they be represented by finite state machines. Our solution to the control problem is as follows: we find the strongest l-complete approximation (abstraction) Σ_{l} for Σ, represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists on the approximation level, we synthesize the maximally permissive supervisor for Σ_{l}. We show that it also solves the control problem for the underlying hybrid system Σ. If no solution exists, approximation accuracy can be increased by computing the strongest k-complete abstraction Σ_{k}, k > l. The basic ideas regarding the approximation step are explained within the framework of Willems' behavioral systems theory. Implementation issues are treated in a state space framework, and the main results are interpreted from a traditional control engineering point of view.

Original language | English |
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Pages (from-to) | 83-107 |

Number of pages | 25 |

Journal | Discrete Event Dynamic Systems: Theory and Applications |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2002 |