To the dynamic reconstruction of sliding controls

¹ N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences (IMM UB RAS), 16, S. Kovalevskaya st., Yekaterinburg, 620108, Russia
² Ural Federal University named after the first President of Russia B.N. Yeltsin, 19, Mira st., Ekaterinburg, 620002, Russia

^* e-mail: subb@uran.ru

Abstract

The paper is devoted to the problem of dynamic control reconstruction for controlled deterministic affine systems. The reconstruction has to be carried out in real time using known discrete inaccurate measurements of an observed trajectory of the system. This trajectory is generated by an unknown measurable control with values in a given compact set. A correct formulation of the reconstruction problem for the case of non-convex control restriction set is given. An approach to solving this problem is suggested. This approach is based on auxiliary variational problems with non-classical convex-concave Tikhonov-regularized integral cost. A numerical method for solving dynamic control reconstruction problem is suggested. It reduces the reconstruction problem to solving systems of linear ordinary differential equations. Matching conditions for the approximation parameters (accuracy and step of the known measurements and a Tikhonov regularizing parameter) such that the constructed approximations converge to the solution are obtained. Results of numerical simulation are exposed to illustrate the theory.