A. Pietrus, T. Scarinci, V.M. Veliov:
"High Order Discrete Approximations To Mayer'S Problems For Linear Systems";
SIAM Journal on Control and Optimization, 56 (2018), 1; S. 102 - 119.

Kurzfassung englisch:
This 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, which may make it more efficient when aiming for a certain precision. 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.

Read More: http://epubs.siam.org/doi/abs/10.1137/16M1079142

optimal control, numerical methods, linear systems, discretization methods, error estimations

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