Discrete Stochastic Regulator on a Manifold, Minimizing Dispersion of the Output Macrovariable

Abstract

A theoretical result is presented in the form of a new algorithm for the synthesis of a control system over a non-linear object, whose mathematical model represents a stochastic matrix difference equation having noise with a zero mean and finite dispersion in the righthand part. The new algorithm for synthesizing stochastic control for such an object is based on a three-stage procedure. In the first stage, the structure of the control system is formed in accordance with the classical method of analytical design of aggregated regulators (ADAR) in a fixed-noise assumption. In the second stage, the conditional mathematical expectation of the resulting expression for the first-stage control is determined. In the third stage, the control model is refined by excluding the noise variable from the control formula based on decomposing the initial control system affected by the new control. It is shown that the proposed control strategies minimize the target macro variable dispersion and ensure a stable, on average, achievement of the target manifold. A detailed example of an application of the algorithm for synthesizing control over the motion of an immobile center of mass is given, whose analog is represented by the objects such as by robot-manipulators, is given. The results of numerical modeling are presented, which confirm the operability of the constructed controller. Numerical simulations of the designed control system was performed using the authentic working equipment data.