A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems |
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Authors: | Nuno P Faísca Pedro M Saraiva Berç Rustem Efstratios N Pistikopoulos |
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Institution: | (1) Centre for Process Systems Engineering, Imperial College London, London, SW7 2AZ, UK;(2) Gepsi-PSE Group, Department of Chemical Engineering, University of Coimbra, 3030-290 Coimbra, Portugal |
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Abstract: | In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical
and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control
theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming
problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the
multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation
problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem
is presented to illustrate the mathematical developments. |
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Keywords: | Hierarchical decision making Multilevel programming Multi-parametric programming Discrete-time systems Closed-loop optimal control |
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