Saturation-Tolerant Prescribed Control for Nonlinear Time-Delay Systems

This article studies the problem of saturation-tolerant prescribed control (SPC) for a class of nonlinear time-delay systems with unknown control directions. We propose a unified finite-time tunnel prescribed performance (FTPP), which not only provides more tight allowable set leading to smaller overshoot, but also drives the tracking error into the prescribed set within a known time. To remove the implicit assumption that both input and performance constraints need to be satisfied simultaneously, an auxiliary system is developed to establish a balance between these two constraints instead of ignoring their interconnection and conflict. With aid of its generated nonnegative signals, the developed saturation-tolerant prescribed performance (SPP) possesses flexible performance. Namely, SPP can temporarily enlarge the performance boundaries to guarantee both constraints when input saturation occurs, and fast recover back to the prescribed boundaries when input saturation disappears. Consequently, a low-complexity SPC for uncertain nonlinear systems is developed, which can always guarantee both input and performance constraints even under unknown time delay and unknown control directions. Finally, comparative simulation is provided to illustrate the merits of the presented control strategy.