Finite-Time Output Regulation of Flow Fields Using Barrier Function-based Sliding Mode Control

A novel sliding mode control method based on barrier functions is developed, which achieves finite-time output regulation of a fluid flow field amidst the challenges posed by model parameter fluctuations and actuator perturbations. The result is achieved through the use of a smooth, barrier function-based adaptive gain switching law. To the best of the authors' knowledge, this is the first result that provides rigorous proof that a barrier function-based sliding mode control law achieves finite-time output regulation of a fluid flow field, particularly in the presence of actuator dynamic uncertainty and perturbations. The theoretical results are achieved through innovative error system development and proof of finite time convergence is provided through Lyapunov stability analysis. Detailed comparative numerical simulation results are provided to demonstrate that the proposed barrier function-based control method demonstrates faster output convergence as compared to both a standard (fixed-gain) sliding mode control method and our recent barrier function-based control method [1].