Hybrid fuzzy model-based control of nonholonomic systems: A unified viewpoint

This paper proposes a unified hybrid fuzzy model-based control scheme for uncertain nonholonomic systems. Compared with typical hybrid fuzzy control, the stability analysis is performed based on a new concept of constructing a semicommon Lyapunov function and a new definition called as exponential-like model following. This advancement provides a strict stability analysis but results in relaxed gain conditions. In detail, a unified hybrid Takagi-Sugeno fuzzy model is first introduced for representing well-known nonholonomic systems with a momentum conservation constraint or a no-slip constraint. Then, the hybrid fuzzy controller is derived to ensure robust nonlinear model following control, i.e., an asymptotic convergence with adjustable ultimate bound and arbitrary disturbance attenuation in an L-2-gain sense. Furthermore, an iterative linear matrix inequality technique is proposed to guarantee the stability and avoid the need of a common positive-definite matrix. Finally, the applications are carried out on a hopping robot and a car-like mobile robot. Numerical simulations and experiment results show the expected performances.