Adaptive fixed time tracking performance control of stochastic nonlinearly parameterized systems with unknown trajectory

Abstract

A fixed-time tracking performance control strategy is devised for stochastic nonlinear systems with tracking error constraints to come true the tracking control under the uncertain desired trajectory. Primarily, bonding the Fourier series and the radial basis function neural network (RBFNN), the unknown ideal tracking target is reconstructed, and the controller is designed on this basis. Subsequently, a modified error transformation technique with the fixed-time performance function (FPF) is formulated to dispose of the tracking error constraint. Then, by introducing an improved first-order filter, the problem of differential explosion is avoided. Moreover, the Lyapunov stability theorem proves that the whole system states remain bounded and the tracking error is kept in the preset limits in fixed time despite of the ideal trajectory is unknown. Definitively, the simulation example is designed to confirm the feasibility.