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Logic-based solution methods for optimal control of hybrid systems

Bemporad, Alberto and Giorgetti, Nicolò Logic-based solution methods for optimal control of hybrid systems. IEEE Transactions on Automatic Control, 51 (6). pp. 963-976. ISSN 0018-9286 (2006)

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Combinatorial optimization over continuous and integer variables is a useful tool for solving complex optimal control problems of 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 linear (or quadratic) programs. MIP formulations require the translation of the discrete/logic part of the hybrid problem into mixed-integer inequalities. Although this operation can be done automatically, most of the original symbolic structure of the problem (e.g., transition functions of finite state machines, logic constraints, symbolic variables, etc.) is lost during the conversion, with a consequent loss of computational performance. In this paper, we attempt to overcome such a difficulty by combining numerical techniques for solving convex programming problems with symbolic techniques for solving constraint satisfaction problems (CSP). The resulting "hybrid" solver proposed here takes advantage of CSP solvers for dealing with satisfiability of logic constraints very efficiently. We propose a suitable model of the hybrid dynamics and a class of optimal control problems that embrace both symbolic and continuous variables/functions, and that are tailored to the use of the new hybrid solver. The superiority in terms of computational performance with respect to commercial MIP solvers is shown on a centralized supply chain management problem with uncertain forecast demand.

Item Type: Article
Identification Number: 10.1109/TAC.2006.876949
Uncontrolled Keywords: centralized supply chain management; combinatorial optimization; constraint satisfaction problems; discrete-time system; hybrid dynamical systems; logic-based solution methods; mixed-integer inequalities; mixed-integer linear programming; optimal control; quadratic programming; satisfiability; uncertain forecast demand; combinatorial mathematics; computability; constraint theory; discrete time systems; forecasting theory; integer programming; linear programming; optimal control; quadratic programming; supply chain management; time-varying systems; uncertain systems
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > TJ Mechanical engineering and machinery
Research Area: Computer Science and Applications
Depositing User: Professor Alberto Bemporad
Date Deposited: 27 Jul 2011 08:40
Last Modified: 30 Mar 2012 10:34
URI: http://eprints.imtlucca.it/id/eprint/495

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