Gradient Calculation Using Artificial Neural Networks in the Problem of Determining Nonlinear Control for Nonlinear Objects

The search for optimal control is possible using numerical iterative algorithms based on the Pontryagin maximum principle. This approach involves repeated calculation of the gradient of the functional. This task becomes difficult when working with nonlinear systems. This article proposes to use artificial neural networks, trained to accurately repeat the dynamics of the control object, to find the gradient of the optimized functional. This approach simplifies the process by avoiding an analytical solution. An example of the application of the proposed technique for a nonlinear control object with a limiter such as a rigid mechanical stop is given.