Parameter Convergence Analysis of Adaptive Control Systems with Nonlinear Backstepping Design

J.-S. Lin (Taiwan)


adaptive nonlinear backstepping, over parametrization, parameter convergence, strict feedback form


In adaptive control systems, backstepping is a systematic Lyapunov-based design scheme, which can guarantee global stability, output tracking, and transient performance for both output-feedback and strict feedback systems. If the question of parameter convergence to guarantee all the parameter error variables to converge to zero could be answered, then the resulting closed-loop system would have a unique solution with the very desirable property of global asymptotic stability. In this paper, the parameter convergence analysis has been developed for adaptive nonlinear backstepping design with overparametrization approach in parametric-strict-feedback systems. The results show that parameter convergence is able to be guaranteed if and only if an appropriately defined signal matrix is persistently exciting. This implies that all the corresponding regressor vectors must be persistently exciting to guarantee all the parameter estimates to converge to their true values. Therefore, the global exponential stability of the resulting closed-loop system is achieved. Some simulation results are shown to illustrate the parameter convergence analysis in comparison to the adaptive backstepping design with tuning functions approach.

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