Fixed-time prescribed performance control method for nonlinear systems with unknown time-varying parameters

Abstract

In this study, it is considered that the question of adaptive tracking control of nonlinear systems containing unknown time-varying parameters. To optimize the control effect, a fixed-time control strategy is adopted, in which the upper bound of the settling time is connected with the designed parameters, but not to the initial conditions. In the design, the unknown time-varying parameters are treated as the multiplication of known and unknown vectors, and the adaptive laws are constructed to estimate the mean value of the components in the unknown ones, which availably solve the difficulty of unknown control gains. Besides, the application of command filtered technique, which combined with the compensation signals containing the adaptive parameters, effectively avoids the “complexity explosion” problem. Further, Lyapunov stability theory verifies that the tracking error can always be kept within the boundaries of the performance functions, and converges to a designated neighbourhood of the origin within a fixed time, beyond that all signals of the closed-loop system are bounded. Finally, the simulation results prove the effectiveness of the proposed control scheme.