Robust 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 a 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. Finally, this paper provides a comprehensive theory in the development of identification, prediction, and adaptive control schemes for discrete-time systems.