eprintid: 495
rev_number: 10
eprint_status: archive
userid: 7
dir: disk0/00/00/04/95
datestamp: 2011-07-27 08:40:43
lastmod: 2012-03-30 10:34:59
status_changed: 2011-07-27 08:40:43
type: article
metadata_visibility: show
contact_email: alberto.bemporad@imtlucca.it
item_issues_count: 0
creators_name: Bemporad, Alberto
creators_name: Giorgetti, Nicolò
creators_id: alberto.bemporad@imtlucca.it
creators_id: 
title: Logic-based solution methods for optimal control of hybrid systems
ispublished: pub
subjects: QA75
subjects: TJ
divisions: CSA
full_text_status: none
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
abstract: 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.
date: 2006-06
date_type: published
publication: IEEE Transactions on Automatic Control
volume: 51
number: 6
publisher: IEEE
pagerange: 963-976
id_number: 10.1109/TAC.2006.876949
refereed: TRUE
issn: 0018-9286
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1643368&isnumber=34438
citation:   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)