Algorithms for the synthesis of adaptive control of multidimensional dynamic objects based on the input and output parameters of systems

The article examines the problem of synthesizing adaptive control algorithms for multidimensional dynamic objects characterized by unknown parameters in the model structure. The proposed approach is based on minimizing the conditional mathematical expectation of losses, which allows us to take into account the stochastic nature of the system's uncertainties. To solve the dual control problem with a two-step horizon, the stochastic dynamic programming method is used, which ensures the optimization of control based on the input and output parameters of the multidimensional object. Evaluation of unknown parameters and the covariance matrix is performed using the Kalman filter, which contributes to increased approximation accuracy and algorithm stability. To obtain a suboptimal solution in a closed form, the decomposition of nominal covariance to second-order terms relative to nominal control is used. The conducted numerical experiments based on the Monte Carlo method demonstrate effectiveness.