Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data

• Published in: Proceedings of the Steklov Institute of Mathematics Vol. 323; no. Suppl 1; pp. S85 - S97
• Main Authors: Danilin, A. R., Kovrizhnykh, O. O.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Moscow Pleiades Publishing 01.12.2023; Springer Nature B.V
• Subjects: Asymptotic properties; Geometric constraints; Mathematics; Mathematics and Statistics; Optimal control; Parameters; Performance indices; Rational functions; terminal convex performance index; optimal control; asymptotic expansion; small parameter
• ISSN: 0081-5438; 1531-8605
• DOI: 10.1134/S008154382306007X

In this paper, we investigate a problem of optimal control over a finite time interval for a linear system with constant coefficients and a small parameter in the initial data in the class of piecewise continuous controls with smooth geometric constraints. We consider a terminal convex performance index. We substantiate the limit relations as the small parameter tends to zero for the optimal value of the performance index and for the vector generating the optimal control in the problem. We show that the asymptotics of the solution can be of complicated nature. In particular, it may have no expansion in the Poincaré sense in any asymptotic sequence of rational functions of the small parameter or its logarithms.