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Switching Time Optimization for Bang-Bang and Singular Controls

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Abstract

Optimal control problems with the control variable appearing linearly are studied. A method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented. This method is based on the transformation of the control problem into a finite-dimensional optimization problem. Therein, first and second-order optimality conditions are thoroughly discussed. Explicit representations of first and second-order variational derivatives of the state trajectory with respect to the switching times are given. These formulas are used to prove that the second-order sufficient conditions can be verified on the basis of only first-order variational derivatives of the state trajectory. The effectiveness of the proposed method is tested with two numerical examples.

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  1. Lehr- und Forschungsgebiet für Nichtlineare Dynamik, RWTH Aachen, Steinbachstrasse 15, 52074, Aachen, Germany

    G. Vossen

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  1. G. Vossen
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Correspondence to G. Vossen.

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Communicated by H.J. Oberle.

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Vossen, G. Switching Time Optimization for Bang-Bang and Singular Controls. J Optim Theory Appl 144, 409–429 (2010). https://doi.org/10.1007/s10957-009-9594-4

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