Properties of solutions of dynamic control reconstruction problems

Abstract

This paper is devoted to inverse problems of the control theory, namely, the dynamic control reconstruction problem. It is the problem of online reconstruction of unknown controls (the input) using known inaccurate measurements of the realized trajectory (the output). Deterministic affine controlled systems are considered. A method for solving this problem is suggested. It relies on auxiliary variational problems on extremum of a regularized integral residual functional. The key feature of this method is using a functional which is convex in control variables and concave in state variables. Properties of the solutions obtained by this method are studied. It is shown that the obtained solutions have oscillating character and are bounded. Results of numerical simulations are provided. © Published under licence by IOP Publishing Ltd.