Stability Analysis of Optimal Trajectory for Nonlinear Optimal Control Problems

Abstract

Due to the need for numerical calculation and mathematical modelling, this paper focuses on the stability of optimal trajectories for optimal control problems. The basic ideas and techniques are based on the compactness of the optimal trajectory set and set-valued mapping theorem. Through lack of optimal control stability, the result of generic stability for optimal trajectories is obtained under the perturbations of the right-hand side functions of the state equations; in the sense of Baire category, the right-hand side functions of the state equations of optimal control can be approximated by other functions.

Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution

“…Te application challenge is that the optimal control in the form of a function of time (2) cannot be directly applied to a real object because of the existing uncertainties. Sometimes they are not very signifcant and practically do not afect the value of the functional, but more often, on the contrary, the quality of control can signifcantly decrease or even not reach the goal at all [9]. Optimal control ( 2) is openloop, and any disturbance of the object will lead to the fact that the goal may not be reached and the value of the criterion may not be optimal.…”