This paper examines the development of regularized algorithms for synthesizing control devices in control systems for polynomial objects, described by multidimensional Volterra functional series. The synthesis problem is solved using a two-stage procedure. In the first stage, the optimization problem is initially solved for an open-loop system. The second stage involves determining the parameters of the control device, i.e., its impulse response functions, by using the relationship between the characteristics of the open-loop and closed-loop systems. Regular algorithms are presented for finding the impulse response functions of the control device based on methods for regularizing the solution of operator equations with positive-definite matrices and an approximately defined right-hand side. The presented regularized algorithms for synthesizing control devices in systems for polynomial objects can be easily implemented using modern computing tools. Furthermore, the concepts and methods of the regularization approach prove highly effective for increasing the accuracy of the control device synthesis procedure.
Igamberdiyev et al. (Thu,) studied this question.