Adaptive robust multivariable control of noninvertible memoryless systems with bounded disturbances: a generalization

Abstract

The discrete-time robust adaptive control for some classes of the uncertain multivariable memoryless (static) systems in the presence of unmeasurable bounded disturbances, whose bounds are assumed to be known is addressed. The systems where the number of the control inputs do not exceed the number of their outputs are considered. The main feature of plants to be controlled is that their gain matrices are noninvertible. The assumption that the elements of these matrices are unknown a priori but there is information about possible bounds on these elements. The problem stated and solvesd here is to design a feedback controller to be capable to cope with the noninvertibility of the gain matrices and also with the parametric uncertainty in order to reject the external disturbances and to ensure the boun­dedness of all the control and output system signals. To solve the problem above mentioned, the robust adaptive approach together with the so-called pseudoinverse or inverse model-based concept is used. Three different cases are studied. In the first case, the robust adaptive controller applicable to the uncertain plant with the square singular gain matrix is designed. The robust method employing the pseudoinverse model-based controllers whose parameters are estimated via a standard recursive adaptation procedure is proposed in the second case to deal with the unknown nonsquare gain matrices having the full rank. The approach proposed in first case is extended to the third case dealing with the control of the unknown plants the gain matrices of which represent the nonsquare matrices of not full rank. Asymptotic properties of the robustly-adaptive controllers proposed in this paper are established. Results of numerical examples given to support the theoretic study.