SDC-methods of optimal control of nonlinear systems on a finite time interval

Abstract

The problem of precise terminal control of nonlinear systems with State-Dependent Coefficients (SDC) over a finite time interval is solved. The purpose of the article is to develop a method for synthesizing suboptimal control, which ensures high accuracy of bringing the system output to a set value by a fixed point in time. Further development of the method of inverse integration of the Riccati equation with state-dependent coefficients is discussed by using a terminal controller synthesized for the auxiliary control problem in reverse time to determine the state of the system during reverse integration instead of the standard stabilizing regulator (SDRE regulator). The effectiveness of the method is been tested on the reference task of controlling the Van der Pol oscillator. The simulation results are presented, demonstrating a higher accuracy of the proposed terminal method of inverse integration compared with the classical approach using the SDRE controller, and comparability with the iterative method of approximating the sequence of the Riccati equation. The method is recommended for the tasks of precise control of complex objects at finite time intervals.