Feedback control of nonlinear objects

Abstract

Automatic feedback control of nonlinear objects is a relevant direction in the control of such objects. Optimal control of linear dynamic objects is widespread. For nonlinear objects, there is a known approach based on the use of the maximum principle, the so-called program control, when the problem of determining optimal motion trajectories is solved without taking into account the deviation of the object's state variables from the response of the control system (signals at the output of the control system). An analytical review of literature sources is performed, which offer approaches to modeling the problems of optimal control of nonlinear objects, in particular, the solution of the Riccati matrix equation. In the first section of the article, a method for solving the Riccati matrix equation is proposed, based on an iterative numerical-analytic approach, which provides an opportunity to obtain a solution of the Riccati matrix equation in quadratures with further use to determine the optimal trajectories of an object subject to automatic control. In the second section of the article, a method for optimal control of a biomedical object, which are inherently nonlinear objects, is proposed using the example of optimal control for determining the optimal dose of drugs. To determine the optimal trajectory of the corresponding system of nonlinear ordinary differential equations, an iterative numerical-analytic method for solving the corresponding Cauchy problem is used. The results of mathematical modeling are presented.