Unified prescribed-time performance control for HONSs with input saturation

This article is concerned with the issue of unified prescribed-time performance control(UPTPC) for high-order nonlinear systems(HONSs) subject to input saturation. The “unified performance” means that multiple performance of output tracking error can be achieved by choosing different arguments, such as global performance, asymmetric performance and semi-global performance(Case 1-3 in Remark 4), which makes the control algorithm more flexible and the control application easier. A class of prescribed-time performance functions(PTPFs) is constructed to guarantee the unified performance, and the error transformation is introduced to convert the issue of ensuring the unified performance into the stability problem of the error variable. Furthermore, the proposed UPTPC algorithm can ensure that the output tracking error converges to a prescribed steady-state accuracy within a prescribed time, and the settling time is irrelevant to the initial states and system parameters. Meanwhile, the singularity problem can be avoided by the proposed algorithm when the tracking error approaches performance boundaries. Additionally, due to the consideration of input saturation and HONSs, it is difficult to isolate the control input as an independent quantity, which increases the difficulty of control design. To solve this problem, a novel Lyapunov function(LF) is constructed in the final step of the backstepping technique, incorporating the properties of hyperbolic tangent function and the mean value theorem, not only the effect of input saturation is eliminated, but also the closed-loop system is stable. Simulations confirm the validity of the developed control.