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A Unified Framework for Hybrid Control: Model and Optimal Control Theory

Branicky, Michael S and Borkar, Vivek S and Mitter, Sanjoy K (1998) A Unified Framework for Hybrid Control: Model and Optimal Control Theory. In: IEEE Transactions on Automatic Control, 43 (1). pp. 31-45.

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Abstract

Complex natural and engineered systems typically possess a hierarchical structure, characterized by continuous-variable 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.

Item Type: Journal Article
Additional Information: ©1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: automata;control systems;differential equations;dynamic programming;hierarchical systems;hybrid systems;optimal control;state-space methods
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 25 Aug 2008
Last Modified: 19 Sep 2010 04:15
URI: http://eprints.iisc.ernet.in/id/eprint/1453

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