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2020 | OriginalPaper | Chapter

Comparison of Direct and Indirect Approaches for Numerical Solution of the Optimal Control Problem by Evolutionary Methods

Authors : Askhat Diveev, Elizaveta Shmalko

Published in: Optimization and Applications

Publisher: Springer International Publishing

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Abstract

The optimal control problem with phase constraints is considered. A new indirect approach of synthesized optimal control is proposed as an alternative to direct methods. A comparative study of direct and indirect approaches is carried out on the problem of optimal control for a small group of mobile robots in the complex environment with phase constraints by evolutionary algorithms. With a direct approach to the numerical solution of the optimal control problem, the control function is searched in the form of piece-wise functional approximation. The indirect approach of synthesized optimal control comes from the engineering practice. Instead of reducing the optimal control problem to the problem of finite-dimensional optimization, we firstly make the object stable relative to some point in the state space by solving an additional task of synthesis of stabilizing control and then we find the coordinates of stabilization points as the desired parameters of optimal control.

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previous chapter Preconditioned Subspace Descent Methods for the Solution of Nonlinear Systems of Equations
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Metadata
Title
Comparison of Direct and Indirect Approaches for Numerical Solution of the Optimal Control Problem by Evolutionary Methods
Authors
Askhat Diveev
Elizaveta Shmalko
Copyright Year
2020
Book
Optimization and Applications

Print ISBN: 978-3-030-38602-3

Electronic ISBN: 978-3-030-38603-0

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-38603-0_14

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