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A. Pietrus, T. Scarinci, V.M. Veliov:
"High Order Discrete Approximations to Mayer's Problems for Linear Systems.";
Report No. 2016-04, 2016; 19 pages.

The paper presents a discretization scheme for Mayer's type optimal control problems of linear systems. The scheme is based on second order Volterra-Fliess approximations, and on an augmentation of the control variable in a control set of higher dimension. Compared
with the existing results, it has the advantage of providing a higher order accuracy without a substantial increase of computations. Error estimations (depending on the controllability index of the system at the solution) are proved by using a recent result about stability of the optimal solution with respect to disturbances. Numerical results are provided, which show the sharpness of the error estimations.

optimal control, numerical methods, linear systems, error estimation

http://publik.tuwien.ac.at/files/publik_255136.pdf