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Synthesis of optimal control based on the use of physical principles


A.A. Kostoglotov, A.I. Kostoglotov, A.A. Kuznetsov, S.V. Lazarenko

In the case of a nonlinear mathematical model of the control object, as widespread methods AKOR Letov–Kalman and of extended operation A.A. Krasovskii that are not always in practice possible to obtain the desired result. In the first case, it was difficult to identify the structure and parameters of the control laws. And the second is obtained only an approximate solution. Using the known principles of Pontryagin, Bellman, Lagrangian approach leads to optimal control programs, and the problem of synthesis requires additional hypotheses. In this paper, we propose a new method to obtain optimum conditions for a finite period of time, that is, providing direct control design problems. It is based on the theorem of the combined maximum principle holds for dynamical systems, whose motion satisfies the principle of Hamilton–Ostrogradskii. In this case, the combination of the physical principles of hydraulics of the synthesis of optimal controller selects the best in terms of its objective function parameters. In this paper we propose a new method for solving the synthesis problem of optimal control and the choice of controller parameters based on the combined use of the maximum principle and the laws of hydraulics. Its use does not require the solution of the boundary maximum principle, L.S. Pontryagin and does not involve the use of Bellman's function.

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