Regulatory Control of Hybrid Systems Based on Discrete Abstractions: Theory & Applications

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

The dynamic behavior of complex systems typically involves the interaction of continuous and discrete dynamics. The study of such hybrid dynamic processes is central in the analysis and design of modern engineering systems. The aim of the proposed work is to develop new method- ologies and computer algorithms to solve important feedback control problems in hybrid systems. This work is motivated by the need to address challenging problems in the control and coordi- nation of modern complex engineering applications such as multiple robotic systems mounted on space or underwater platforms, eets of autonomous vehicles, and chemical and manufacturing plants. The proposed work uses a hybrid system framework for regulatory feedback control that is based on discrete abstractions and it o_ers signi_cant promise in addressing successfully a number of open control design issues. The proposed approach utilizes discrete approximations or abstrac- tions of the continuous dynamics, which are re_ned appropriately using the concept of quasideter- minism, to provide adequate information so that a controller can be designed to meet the control speci_cations. It is proposed to extend initial control synthesis results that use piecewise-linear models to more general systems, and also develop additional design methods based on Lyapunov functions and on Petri net supervisory control methodologies. The proposed research includes the exploration of realistic applications from the areas of manufacturing and autonomous vehicles. The impact of this work will be in both theory and applications. In particular, it will provide a theoretical design framework for regulatory feedback control of hybrid systems and will also in uence the areas of reachability analysis, hybrid automata, and veri_cation algorithms. Fur- thermore, it will provide algorithms for the control of autonomous systems which will be tested on our Complex Systems Simulation Facility.