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Hybrid system analysis and control via mixed integer optimization


M. Morari

IFAC Symposium on Dynamics and Control of Process Systems, Cheju Shilla Hotel, Chejudo Island, Korea

The paper discusses a framework for modeling, analyzing and controlling systems whose behavior is governed by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. They are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD models are equivalent to various other system descriptions like Piece Wise Affine (PWA) systems and Linear Complementarity (LC) systems. They have the advantage, however, that all problems of system analysis (like controllability, observability, stability and verification) and all problems of synthesis (like controller design and filter design) can be readily expressed as mixed integer linear or quadratic programs, for which many commercial software packages exist. In this paper we first recall how to derive MLD models and then illustrate their use in predictive control. Subsequently we define "verification" and show how verification algorithms can be used to solve a variety of practical problems like checking the correctness of an emergency shutdown procedure implemented on a PLC, or assessing the performance of a constrained MPC controller. The eventual practical success of these methods will depend on progress in the development of the various optimization packages so that problems of realistic size can be tackled.


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(05)Plenary/Invited/Honorary Lecture

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