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A Unified Framework for Hybrid Control: Model and Optimal Control Theory (1998)
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| Venue: | IEEE TRANSACTIONS ON AUTOMATIC CONTROL |
| Citations: | 304 - 9 self |
BibTeX
@ARTICLE{Branicky98aunified,
author = {Michael S. Branicky and Vivek S. Borkar and Sanjoy K. Mitter},
title = {A Unified Framework for Hybrid Control: Model and Optimal Control Theory},
journal = {IEEE TRANSACTIONS ON AUTOMATIC CONTROL},
year = {1998},
volume = {43},
pages = {31--45}
}
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Abstract
Complex natural and engineered systems typically possess a hierarchical structure, characterized by continuousvariable dynamics at the lowest level and logical decision-making at the highest. Virtually all control systems today---from flight control to the factory floor---perform computer-coded checks and issue logical as well as continuous-variable control commands. The interaction of these different types of dynamics and information leads to a challenging set of "hybrid" control problems. We propose a very general framework that systematizes the notion of a hybrid system, combining differential equations and automata, governed by a hybrid controller that issues continuous-variable commands and makes logical decisions. We first identify the phenomena that arise in real-world hybrid systems. Then, we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems, evolving on continuous-variable state spaces and subject to continuous controls and discrete transitions. The model captures the identified phenomena, subsumes previous models, yet retains enough structure on which to pose and solve meaningful control problems. We develop a theory for synthesizing hybrid controllers for hybrid plants in an optimal control framework. In particular, we demonstrate the existence of optimal (relaxed) and near-optimal (precise) controls and derive "generalized quasi-variational inequalities" that the associated value function satisfies. We summarize algorithms for solving these inequalities based on a generalized Bellman equation, impulse control, and linear programming.
Keyphrases
optimal control theory hybrid control unified framework hybrid controller hybrid system discrete transition logical decision-making logical decision issue continuous-variable command linear programming control system today meaningful control problem general framework differential equation enough structure continuous control dynamical system hybrid control problem associated value function satisfies continuous-variable state space flight control interacting collection impulse control continuous-variable control generalized bellman equation previous model optimal control framework quasi-variational inequality engineered system identified phenomenon mathematical model challenging set continuousvariable dynamic computer-coded check real-world hybrid system different type factory floor hierarchical structure hybrid plant
