Switching Time Optimization for Bang-Bang and Singular Controls

G. Vossen ()
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G. Vossen: RWTH Aachen

Journal of Optimization Theory and Applications, 2010, vol. 144, issue 2, No 11, 409-429

Abstract: 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.

Keywords: Bang-bang control; Singular control; Second-order sufficient conditions; Variational derivatives (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-009-9594-4

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