Application of Non-Simulators in the Problem of Finding Quasi-Optimal Control of a Nonlinear Object

The problem of finding quasi-optimal control of a complex dynamic object containing nonlinearity under incomplete information conditions is difficult to solve. One of the problems in solving it is the impossibility of using analytical approaches, such as the Pontryagin maximum principle. This is due to the fact that the description of such systems using differential equations has discontinuous right-hand sides. Another feature is the lack of information about the control object. All that is known about it is that it contains nonlinearity from a known class, as well as its response to various control actions. Such an object is called a “gray box”. In this paper, we consider the problem of finding quasi-optimal software control of a complex dynamic object containing nonlinearity under incomplete information conditions. To solve it, the authors propose to apply a modified numerical method based on the Pontryagin maximum principle and the algorithm of successive approximations, developed by F. L. Chernous'ko and I. A. Krylov, using a neurosimulator of the control object that accurately repeats its dynamics. An example of the operation of the presented method is given.