Algorithms for the Parametric Optimization of Nonlinear Systems Based on the Conditions of Optimal System

Abstract

Abstract The problem of optimal control is formulated for a class of nonlinear objects that can be represented as objects with a linear structure and parameters that depend on the state. The linear structure of the transformed nonlinear system and the quadratic functional of quality allow for the synthesis of optimal control, i.e. parameters of the regulator, move from the need to search for solutions of the Hamilton-Jacobi equation to an equation of the Riccati type with parameters that depend on the state. The main problem of implementing optimal control is related to the problem of finding a solution to such an equation at the pace of object functioning. The paper proposes an algorithmic method of parametric optimization of the regulator. This method is based on the use of the necessary conditions for the optimality of the control system under consideration. The constructed algorithms can be used both to optimize the non-stationary objects themselves, if the corresponding parameters are selected for this purpose, and to optimize the entire managed system by means of the corresponding parametric adjustment of the regulators. The example of drug treatment of patients with HIV is demonstrated the effectiveness of the developed algorithms.