Adaptive prescribed performance control with selected transient response for a class of nonlinear systems with uncertainties

Abstract

This article proposes a novel adaptive prescribed performance control method.Featured with a selected transient performance, the proposed control method can achieve prescribed performance control by a new error transformation method. With the proposed control strategy, the closed-loop system can follow the prescribed performance with a predefined curve. An adaptive controller is constructed based on the adaptive backstepping technique. By utilizing the Lyapunov stability, asymptotic stability is achieved for the closed-loop system. Two examples with simulation results are provided to illustrate the proficiency of the proposed control strategy. To make comparisons, the same second-order transient response is adopted as the performance function for both examples. The selection of gains and parameters are investigated by tests. The expected prescribed performance and the asymptotic stability are achieved in both examples, which verifies the proposed control strategy. Some discussions and comparisons are made accordingly as well.