Robust adaptive control of uncertain MIMO non-linear systems — feedforward Takagi–Sugeno fuzzy approximation based approach

Abstract

This paper proposes a robust adaptive controller using a feedforward Takagi–Sugeno (T–S) fuzzy approximator for a class of multi-input multi-output (MIMO) non-linear plants that is highly unknown. Different to typical fuzzy approximation approaches, the desired commands are taken as input variables of a T–S fuzzy system. Meanwhile, the unknown feedforward terms required during steady state are adaptively approximated and compensated. This allows a simpler architecture during implementation and drops the typical boundedness assumption on fuzzy universal approximation errors. Furthermore, according to H∞ control techniques, non-linear damping design, and sliding mode control, the controllers are synthesised to assure either only the disturbance attenuation, the attenuation of both disturbances and estimated fuzzy parameter errors, or globally asymptotic stable tracking. A linear matrix inequality (LMI) technique then provides a straightforward gain design. Finally, numerical simulations are carried out on a two-link robot to illustrate the expected performance.