Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays

Vadim Azhmyakov, Erik I. Verriest, Luz A. Guzman Trujillo, Sebastien Lahaye, Nicolas Delanoue

Research output: Contribution to journalArticlepeer-review

Abstract

Our contribution deals with a class of Optimal Control Problems (OCPs) of dynamic systems with randomly varying time delays. We study the minimax-type OCPs associated with a family of delayed differential equations. The presented minimax dynamic optimization has a natural interpretation as a robustness (in optimization) with respect to the possible delays in control system under consideration. A specific structure of a delayed model makes it possible to reduce the originally given sophisticated OCP to an equivalent convex program in an Euclidean space. This analytic transformation implies a possibility to derive the necessary and sufficient optimality conditions for the original OCP. Moreover, it also allows consideration of the wide range of effective numerical procedures for the constructive treatment of the obtained convex-like OCP. The concrete computational methodology we follow in this paper involves a gradient projected algorithm. We give a rigorous formal analysis of the proposed solution approach and establish the necessary numerical consistence properties of the resulting robust optimization algorithm.

Original languageEnglish
Pages (from-to)18-23
Number of pages6
JournalIFAC-PapersOnLine
Volume51
Issue number25
DOIs
StatePublished - 1 Jan 2018

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