Collaborative Research: Piecewise Linear Hybrid Systems

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

This proposal deals with the design and analysis of efficient algorithms for the class of hybrid systems called (discrete-time) piecewise linear (PL) systems. The area of hybrid systems concerns issues of modeling, computation and control for systems which combine discrete and continuous components. The subclass of PL systems, which we investigate in this project, provides one systematic approach to discrete-time hybrid systems, naturally blending switching mechanisms with classical linear components. PL systems are of interest as controllers as well as identification models, and they can be thought of as arbitrary interconnections of finite automata and linear systems. Tools from automata theory, logic and related areas of computer science and finite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a ``PL algebra'' formalism. In this project, we will study basic algorithmic and computational problems for these problems with applications to modelling of biological systems. More concretely, basic questions for any class of systems are those of equivalence, and, in particular, whether state spaces are equivalent under a change of variables. This project will address various algorithmic and computational challenges related to this state-space equivalence and isomorphism problem for PL systems, as well as questions of learnability and representability for such systems. The project also suggests the use of PL models for differential gene expression testing.