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Pareto Optimality, Game Theory And Equilibria pp 541–570Cite as

The Extended Linear Complementarity Problem and Its Applications in Analysis and Control of Discrete-Event Systems

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 17))

In this chapter, we give an overview of complementarity problems with a special focus on the extended linear complementarity problem (ELCP) and its applications in analysis and control of discrete-event systems such as traffic signal controlled intersections, manufacturing systems, railway networks, etc. We start by giving an introduction to the (regular) linear complementarity problem (LCP). Next, we discuss some extensions, with a particular emphasis on the ELCP, which can be considered to be the most general linear extension of the LCP. We then discuss some algorithms to compute one or all solutions of an ELCP. Next, we present a link between the ELCP and max-plus equations. This is then the basis for some applications of the ELCP in analysis and model-based predictive control of a special class of discrete-event systems. We also show that — although the general ELCP is NP-hard — the ELCP-based control problem can be transformed into a linear programming problem, which can be solved in polynomial time.

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  1. Delft Center for Systems and Control, Delft University of Technology, Netherlands

    Bart De Schutter

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  1. Bart De Schutter
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Editors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos , Altannar Chinchuluun  & Panos M. Pardalos ,  & 

  2. Department of Production Engineering and Management, Technical University of Crete, 73100, Greece

    Athanasios Migdalas

  3. Department of Production Engineering and Management, Aristotle University of Thessaloniki, Greece

    Leonidas Pitsoulis

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De Schutter, B. (2008). The Extended Linear Complementarity Problem and Its Applications in Analysis and Control of Discrete-Event Systems. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds) Pareto Optimality, Game Theory And Equilibria. Springer Optimization and Its Applications, vol 17. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77247-9_21

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