New Approach to the Synthesis of Optimal Terminal Control of Nonlinear Dynamic Systems

Abstract

The problem of constructing common solutions to terminal control problems of nonlinear systems is considered here. Previously proven positions are used that the optimal trajectory is an envelope of a parametric family of surfaces (a parametric family of singular curves), and that optimal control can be found on this family. The fact that at each point of the optimal trajectory the vector-function of Lagrange factors is tangent to it, but also tangent to the singular curve, is played out here. A constructive method of constructing singular curves based on conditional separation of variables in the Hamilton-Jacobi equation is given. The " free" parameters of singular curves are based on the condition of minimizing the terminal functionality, which avoids an explicit solution to the boundary problem for a class of nonlinear dynamic systems, and simplifies computational algorithms. Singular curves are described by a reduced (abbreviated) mathematical model. Thus, to synthesize the law of optimal control, we must use the complete (original) mathematical model of the dynamic system, but to calculate it at one time or another, it is enough reduced model. This consideration defines the principle of informational dualism. An illustrative example is given. It has been shown that this approach can be used to solve some classes of differential games.