Model-Oriented Design of a Discrete One-Dimensional Extremal Control System

The article focuses on model-oriented design of one-dimensional discrete extremal control systems (ECS), enhancing their efficiency under conditions of uncertainty and noise. An analysis of research on parameter adaptation for extremal controllers is conducted, and an extremal control system with controller parameter adaptation is developed. The plant model is represented as a unimodal function with additive noise, and the problem of ECS parameter optimization is formulated as a minimization problem for an integral performance criterion. Linear and quadratic extrapolators, the Recursive Least Squares (RLS) method, and a PI‑controller are employed for the adaptation of the operating step size. An analysis of the influence of integral performance criteria on the quality of control processes is performed. The research confirms that the extremal PI‑controller demonstrates the best performance, including noise immunity and minimal error in the vicinity of the extremum. The practical significance of the work lies in the development of adaptive algorithms for control systems with nonlinear and stochastic characteristics, applied to problems in robotics and the control of complex technological processes. The use of integral criteria focused on minimizing control error is recommended for the design of ECS under high uncertainty conditions.