A solution for enhancement of transient performance in nonlinear adaptive control: Optimal adaptive reset based on barrier Lyapunov function

In this paper, an adaptive controller based on barrier Lyapunov function combined with an optimal reset rule is devised in order to improve the transient performance of nonlinear adaptive control. A novel reset rule is designed such that the estimated parameters of the adaptive controller jump to the optimal values in a way that optimizes a cost function representing the transient performance index. It is proved that asymptotic tracking is achieved and the output remains in a desired bound by ensuring boundedness of the barrier Lyapunov function. Besides, the convergence rate is increased by resetting the estimated parameters to optimal values. A regularly referred example is simulated to demonstrate the effectiveness of the proposed method and the results are compared with the existing investigations.