ON THE SOLVABILITY OF THE CAUCHY-BELLMAN PROBLEM FOR NONLINEAR OPTIMIZATION OF OSCILLATORY PROCESSES

Abstract

When solving the problem of optimal process control, a distinction is made between the cases of programmatic optimal control and the synthesis of optimal control. In program control, optimal control is defined as a function of the independent variables of the problem. With this approach, research was carried out based on the maximum principle (in the case of ordinary differential equations – L.S. Pontryagin’s principle, in the case of systems with distributed parameters, the maximum principle of Pontryagin type, A.G. Butkovsky, A.I. Egorov, T.K. Sirazetdinov, V.I. Plotnikov) [1]. Control problems where it is necessary to synthesize optimal control are solved mainly by the dynamic programming method, which is based on the Bellman optimality principle. In this case, the desired optimal control should be found as a function (or functional) of the independent variables of the problem and the state of the controlled process.