Robust modified implicit self tuning regulator/MRAC convergence and stability

Abstract

An implicit self tuning regulator (STR) is presented, based on Lyapunov analysis for the control of a class of multi-input and multi-output (MIMO) dynamical system. Linearity in the parameters is assumed to hold, but the estimation error is considered to be non zero; this allows control of a larger class of systems and also has the effect of producing robust controller. Moreover, certainty equivalence is not used in the design overcoming a major problem in adaptive control. It is indicated that gradient-based parameter tuning of the STR, when employed for closed-loop control, can yield unbounded parameter estimates if: (1) linearity in the unknown parameters does not exactly hold, or 2) there are unknown disturbances acting on the system. New on-line tuning algorithms for implicit STR are derived, which are similar to E-modification approach for continuous-time systems, that include a modification to the adaptation gain and a correction term for standard gradient-based tuning. These improved parameter tuning algorithms guarantee tracking as well as bounded parameter estimates in nonideal situations so that PE is not needed. The notions of robust STR is introduced. Finally, this paper provides a comprehensive theory in the development of identification, prediction, and adaptive control schemes for discrete-time systems.