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A Local Search Scheme for the Inequality-Constrained Optimal Control Problem

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Mathematical Optimization Theory and Operations Research (MOTOR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12755))

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Abstract

This paper addresses the nonconvex optimal control (OC) problem with the cost functional and inequality constraint given by the functionals of Bolza. All the functions in the statement of the problem are state-DC, i.e. presented by a difference of the state-convex functions. Meanwhile, the control system is state-linear. Further, with the help of the Exact Penalization Theory we propose the state-DC form of the penalized cost functional and, using the linearization with respect to the basic nonconvexity of the penalized problem, we study the linearized OC problem.

On this basis, we develop a general scheme of the special Local Search Method with a varying penalty parameter. Finally, we address the convergence of the proposed scheme.

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Acknowledgement

The research was funded by the Ministry of Education and Science of the Russian Federation within the framework of the project “Theoretical foundations, methods and high-performance algorithms for continuous and discrete optimization to support interdisciplinary research” (No. of state registration: 121041300065-9).

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of SB RAS, Irkutsk, Russia

    A. S. Strekalovsky

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  1. A. S. Strekalovsky
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Correspondence to A. S. Strekalovsky .

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Editors and Affiliations

  1. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, Russia

    Alexander Kazakov

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Strekalovsky, A.S. (2021). A Local Search Scheme for the Inequality-Constrained Optimal Control Problem. In: Pardalos, P., Khachay, M., Kazakov, A. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2021. Lecture Notes in Computer Science(), vol 12755. Springer, Cham. https://doi.org/10.1007/978-3-030-77876-7_2

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  • DOI: https://doi.org/10.1007/978-3-030-77876-7_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77875-0

  • Online ISBN: 978-3-030-77876-7

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