А.N. Tselykh , V. S. Vasilev , L.А. Tselykh , Е.S. Podoplelova
224-233
2025-07-24
Abstract ▼
Constructing optimal control in the complete absence of data on the system dynamics is a pressing problem. In this paper, we propose a solution to a finite-horizon linear quadratic problem (LCP) for a time-invariant system with a graph dynamics matrix. Unlike the control problem, stability and complete controllability of the system are not assumed. The construction of the control trajectory is controlled by the direction of increase in the change in the state of variables over a small number of steps, which is determined by the conditional principal eigenvector of the adjacency matrix of the graph model. The solution of classical optimal control is carried out in an autonomous mode and requires complete knowledge of the system dynamics. In the absence of complete knowledge of the system dynamics, solving optimal control problems for systems with uncertainty, including discrete linear systems, has attracted considerable interest in recent years. The main approach when complete information about the system is unavailable is the design of optimal control, in which the system parameters are initially determined, and then an algebraic equation in the dual space is solved. An important difference from the standard discrete control problem is that the control model was modified to estimate changes in the state of variables under controls transmitted through the dynamics matrix. The proposed algorithm using a graph matrix implements recurrent calculations of dynamic and adjoint equations, as well as the Powell method for solving a system of linear algebraic equations (SLAE). The authors introduced a new interpretation of the mathematical construction of the system dynamics matrix in a standard discrete control problem on a finite time interval, which can be used to design any controlled dynamic system with unobservable parameters.
