Convergence results for the discrete regularization of linear-quadratic control problems with bang–bang solutions

Martin Seydenschwanz ()

Computational Optimization and Applications, 2015, vol. 61, issue 3, 760 pages

Abstract: We analyze a combined regularization–discretization approach for a class of linear-quadratic optimal control problems. By choosing the regularization parameter $$\alpha $$ α with respect to the mesh size $$h$$ h of the discretization we approximate the optimal bang–bang control. Under weaker assumptions on the structure of the switching function we generalize existing convergence results and prove error estimates of order $${\mathcal {O}}(h^{1/(k+1)})$$ O ( h 1 / ( k + 1 ) ) with respect to the controllability index $$k$$ k . Copyright Springer Science+Business Media New York 2015

Keywords: Linear-quadratic optimal control; Bang–bang control; Regularization; Discretization; 49J15; 49M25; 49N10; 49J30 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10589-015-9730-z

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