Indirect Adaptive Fuzzy Control Design With Guaranteed Tracking Error Performance For Uncertain Canonical Nonlinear Systems

In this paper, we consider the fuzzy controller design problem for output tracking of uncertain strict-feedback nonlinear systems. For comparison, a basic fuzzy control scheme is first constructed based on an existing approach representative in the field. The scheme can effectively reduce the number of parameter estimates, which benefits from the operation of handling the square of the norm of fuzzy weight vector. However, as a tradeoff of such an operation, the asymptotic tracking performance cannot be ensured and the <inline-formula><tex-math notation="LaTeX">$L_2$</tex-math></inline-formula>-norm transient performance of tracking error cannot be established. To eliminate these performance costs without losing the advantage of the basic fuzzy control scheme, we further propose a performance-oriented fuzzy control scheme. It guarantees that all closed-loop signals are bounded and the tracking error converges to a prescribed interval asymptotically. Moreover, the <inline-formula><tex-math notation="LaTeX">$L_2$</tex-math></inline-formula>-norm transient performance of tracking error is also established, which explicitly indicates that the transient performance of tracking error can be improved through changing controller design parameters with the performance-oriented fuzzy control scheme. Simulation examples are given to verify the obtained results.