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A Dynamical System View on Nonlinear Optimal Control Analysis and Design

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Part of the book series: Lecture Notes in Control and Information Sciences - Proceedings ((LNCOINSPRO))

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Abstract

This note presents a view from the theory of dynamical system, such as invariant manifolds and \(\lambda \)-lemma, for the analysis and the design of optimal control for nonlinear systems. The optimal control problems considered are optimal stabilization and optimal transfer problems. The theory of stable manifold and its iterative computation plays the central role for the optimal stabilization design and the \(\lambda \)-lemma which describes the flows around the invariant manifolds is used for analysis of the optimal transfer problem including turnpike property in the optimal control system.

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Authors and Affiliations

  1. Faculty of Science and Engineering, Nanzan University, Yamazato-cho 18, Showa-ku, Nagoya, 466-8673, Japan

    Noboru Sakamoto

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  1. Noboru Sakamoto
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Correspondence to Noboru Sakamoto .

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Editors and Affiliations

  1. Department of Mathematical Modelling of Economic Systems, Saint Petersburg State University, Saint Petersburg, Russia

    Nikolay Smirnov

  2. Department of Control Systems Theory for Electrophysical Facilities, Saint Petersburg State University, Saint Petersburg, Russia

    Anna Golovkina

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Sakamoto, N. (2022). A Dynamical System View on Nonlinear Optimal Control Analysis and Design. In: Smirnov, N., Golovkina, A. (eds) Stability and Control Processes. SCP 2020. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-87966-2_1

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