A Multi–Parametric Optimization Strategy for Multilevel Hierarchical Control problems

Abstract In this work the three–level hierarchical control problem and the decentralised control problem are investigated and a general optimisation strategy is developed for solving these problems based on recent developments on multi–parametric programming. The main idea is to recast each optimisation subproblem in the multilevel hierarchy as a multi–parametric programming problem and then transform the multilevel problem into a single-level optimisation problem. This allows for the control policies (decisions) at each level of the multilevel optimisation problem to be obtained as explicit functions of the state of the dynamic systems involved in each level and the control policies of the higher levels. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.

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