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A SAT-based hybrid solver for optimal control of hybrid systems

Bemporad, Alberto and Giorgetti, Nicolò A SAT-based hybrid solver for optimal control of hybrid systems. In: Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, 2993 . Springer-Verlag, pp. 126-141. ISBN 978-3-540-21259-1 (2004)

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Combinatorial optimization over continuous and integer variables was proposed recently as a useful tool for solving complex optimal control problems for linear hybrid dynamical systems formulated in discrete-time. Current approaches are based on mixed-integer linear or quadratic programming (MIP), which provides the solution after solving a sequence of relaxed standard linear (or quadratic) programs (LP, QP). An MIP formulation has the drawback of requiring conversion of the discrete/logic part of the hybrid problem into mixed-integer inequalities. Although this operation can be done automatically, most of the original discrete structure of the problem is lost during the conversion. Moreover, the efficiency of the MIP solver mainly relies upon the tightness of the continuous LP/QP relaxations. In this paper we attempt to overcome such difficulties by combining MIP and techniques for solving constraint satisfaction problems into a “hybrid” solver, taking advantage of SAT solvers for dealing efficiently with satisfiability of logic constraints. We detail how to model the hybrid dynamics so that the optimal control problem can be solved by the hybrid MIP+SAT solver, and show that the achieved performance is superior to the one achieved by commercial MIP solvers.

Item Type: Book Section
Identification Number: 10.1007/978-3-540-24743-2_9
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > T Technology (General)
Research Area: Computer Science and Applications
Depositing User: Professor Alberto Bemporad
Date Deposited: 27 Jul 2011 09:02
Last Modified: 04 Aug 2011 07:29
URI: http://eprints.imtlucca.it/id/eprint/502

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