Adaptive fuzzy PD control with stable H^∞ tracking guarantee

For indirect adaptive fuzzy H^∞ tracking control (AFHC) of perturbed uncertain nonlinear systems, sliding-mode control (SMC) compensation usually has to be applied to ensure stability and H^∞ robustness of the closed-loop system. We prove that indirect AFHC without SMC compensation is sufficient to guarantee stable H^∞ tracking under given initial conditions and parameter constraints. The control structure only includes an indirect adaptive fuzzy control term and a proportional derivative (PD) control term. A certainty equivalent control law is slightly modified such that both a lumped perturbation and adaptive laws are independent of the PD control term. This modification is significant since it not only plays a key role in stability analysis, but also alleviates some drawbacks of existing AFHC approaches for practical applications. An illustrative example has been provided to verify correctness of the theoretical result.