Sliding Flexible Prescribed Performance Control for Input Saturated Nonlinear Systems

Abstract

The issue of sliding flexible prescribed performance control (SFPPC) of input saturated nonlinear systems (ISNSs) is first studied in this article. Compared to the traditional PPC and the finite-time PPC algorithms for ISNSs, under which the performance constraint boundaries (PCBs) present the symmetrical or asymmetric “horn” shape, which leads to a large jitter in the tracking error before the system reaches steady state; and once the parameters are selected, the PCBs are fixed, when the initial state (or reference signal) changes, it is necessary to reverify whether the initial error still satisfies the initial constraint condition. By designing a new pair of sliding flexible PCBs (SFPCBs) associated with the initial error, a novel SFPPC algorithm is presented in this article, which presents two main advantages: 1) the SFPCBs can slide adaptively with the initial tracking error without increasing the measure of the initial PCBs, implying that the proposed SFPPC algorithm can be applied to ISNSs with arbitrary initial errors without sacrificing the initial control performance; 2) the proposed SFPPC algorithm achieves a tradeoff between performance constraint and input saturation, i.e., the SFPCBs can adaptively increase when the control input exceeds the maximum allowable threshold, effectively avoiding singularity, and when the control input is within the saturation threshold range, the SFPCBs can adaptively revert back to the original PCBs. The results demonstrate that the proposed SFPPC approach can guarantee that the system output tracks the desired signal, and the tracking error always kept within the SFPCBs that depend on initial error, input, and output constraints. The developed algorithm is exemplified by means of simulation instances.