Adaptive control of MIMO time-varying systems with indicator function based parametrization

This paper studies a new solution framework for adaptive control of a class of MIMO time-varying systems with indicator function based parametrization, motivated by a general discrete-time MIMO Takagi–Sugeno (T–S) fuzzy system model in an input–output form with unknown parameters. An indicator (membership) function based parametrization has some favorable capacity to deal with certain large parameter variations. A new discrete-time MIMO system prediction model is derived for approximating a nonlinear dynamic system, and its system properties are clarified. An adaptive control scheme is developed, with desired controller parametrization and stable parameter estimation for control of such uncertain MIMO time-varying systems. A control singularity problem is addressed and the closed-loop stability and output tracking properties are analyzed. This work provides a new method for multivariable T–S fuzzy system modeling and adaptive control. An illustrative example and simulation results are presented to demonstrate the proposed novel concepts and to verify the desired adaptive control system performance.