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T. Scarinci, V.M. Veliov:
"Higher-Order Numerical Scheme for Linear Quadratic Problems with Bang-Bang Controls.";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2017-06 (2017), 6; 18 pages.

This paper considers a linear-quadratic optimal control problem where the control function appears linearly and takes values in a hypercube. It is assumed that the optimal controls are of purely bang-bang type and that the switching function, associated with the problem, exhibits a suitable growth around its zeros. The authors introduce a scheme for the discretization of the problem that doubles the rate of convergence of the Euler´s scheme. The proof of the accuracy estimate employs some recently obtained results concerning the stability of the optimal solutions with respect to disturbances.

optimal control, numerical methods, bang-bang control, linear-quadratic optimal control problems, time-discretization methods

http://publik.tuwien.ac.at/files/publik_261881.pdf