Control of systems integrating logic, dynamics, and constraints☆
Abstract
This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as mixed logical dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD systems include linear hybrid systems, finite state machines, some classes of discrete event systems, constrained linear systems, and nonlinear systems which can be approximated by piecewise linear functions. A predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules. Due to the presence of integer variables, the resulting on-line optimization procedures are solved through mixed integer quadratic programming (MIQP), for which efficient solvers have been recently developed. Some examples and a simulation case study on a complex gas supply system are reported.
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This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor A. L. Tits under the direction of Editor T. Başar, and accepted by the Guest Editors J. M. Schumacher, A. S. Morse, C. C. Pantelides, and S. Sastry.