Learning Error Feedback Design of Direct Adaptive Fuzzy Control Systems

Abstract

In the paper, based on the finite <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain property, a way of estimating learning errors for direct adaptive fuzzy control systems is proposed, and then, a novel adaptive law with this estimated learning error is further proposed to improve the learning performance of the system in the sense of Lyapunov. In the literature, there is no direct way of estimating learning errors for direct adaptive fuzzy control systems. Based on the robust control approach proposed in our previous study, a way of estimating learning errors for direct adaptive fuzzy control can be derived, and as shown in our simulation, it can be found that such estimation is effective, as expected. It can be found that by incorporating this estimated learning error into the adaptive law, the proposed approach indeed can have much better learning performance. Besides, owing to good learning capability, the proposed control scheme can also have better tracking control performance. Simulation results clearly demonstrated the effectiveness of the proposed design.