Control of dynamic systems with restrictions on input and output signals

TL;DR

This paper extends a control method for systems with input-output restrictions by introducing coordinate changes that simplify the problem, enabling stability analysis via linear matrix inequalities and demonstrating effectiveness through examples.

Contribution

It proposes a generalized approach with two coordinate transformations to handle systems with arbitrary input-output ratios and constraints, improving control design.

Findings

The method reduces constrained control problems to unconstrained ones.

Stability is verified through linear matrix inequalities.

Examples demonstrate the method's efficiency.

Abstract

The paper considers the generalization of the method proposed by I.B. Furtat, P.A. Gushchin in "Automation and Remote Control", 2021, No. 4 for systems with an arbitrary ratio of the number of input and output signals and with a guarantee of their being in a given set. To solve the problem, two coordinate changes are proposed. The first coordinate change reduces the output variable of the system to a new variable which dimension does not exceed the control dimension. The second coordinate change allows one to pass from a constrained control problem to an unconstrained one. In order to illustrate the efficiency of the method, the solution of two problems is considered. The first task is state feedback control of linear systems, taking into account the constraints on the control signal and phase variables. The second task is output feedback control of linear systems with a restriction on output and control. In both problems, checking the stability of the closed-loop system is formulated in terms of the solvability of linear matrix inequalities. The obtained results are accompanied by examples of modeling that illustrate the efficiency of the proposed method.