On the Optimal Control of Multidimensional Dynamic Systems Evolving with State Suprema

Vadim Azhmyakov1, Erik I. Verriest2, Luz Adriana Guzman Trujillo3, Stefan Pickl4

  • 1Universidad de Medellin
  • 2Georgia Inst. of Tech.
  • 3University of Medellin - University of Angers
  • 4UBw München

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Regular Session

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10:00 - 12:00 | Mon 17 Dec | Facet | MoA02

Optimal Control I

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Abstract

This paper constitutes a further generalization of the numerical solution approaches to Optimal Control Problems (OCPs) of systems evolving with state suprema. We study multidimensional control systems described by differential equations with the sup-operator in the right hand sides. A specific state-observer model and the linear type feedback control design under consideration imply a resulting closed-loop system that can formally be characterized as a multidimensional Functional Differential Equation (FDE) with delays. We study OCPs associated with the obtained FDEs and establish some fundamental solution properties of this class of problems. A particular structure of the resulting dynamic optimization problem makes it possible to consider the originally given sophisticated OCP in the framework of the nonlinear separate programming in some Euclidean spaces. This fact makes it possible to apply effective and relative simple splitting type computational algorithms to the initially given sophisticated OCPs for systems evolving with state suprema.

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