Sliding Flexible Performance Preset Boundary-Based Fuzzy Control for Input Saturated Discrete-Time Nonlinear Systems

This article first proposes a discrete-time sliding flexible performance preset boundary (DT-SFPPB)-based control algorithm for input saturated discrete-time nonlinear systems (IS-DTNSs). Compared to the existing discrete-time prescribed performance control (DT-PPC) algorithms, the PPB of them present a “trumpet” shape, resulting in fundamental conservation of the transient performance, and whenever the initial error is altered, it is essential to recheck whether the new error meets the original constraint condition, if not, a new PPB with a larger measure has to be reselected. By designing a novel DT-SFPPB associated with the initial error, which can always envelope the initial error with an arbitrarily preset initial measure, indicating that the proposed approach can be utilized for IS-DTNSs with arbitrary initial error without compromising the initial transient performance. Furthermore, the coupling effect between performance preset and input saturation is also considered, by designing a novel equilibrium boundary related to saturation, so that the proposed approach can achieve the synergy between performance preset and input security, i.e., the designed DT-SFPPB can flexibly expand when input saturation occurs to avoid vulnerability, and when the control input is within the safe boundary, it rapidly reverts to the original PPB to guarantee the specified performance metrics. The findings demonstrate that the developed approach guarantees that the system output tracks the desired signal with the specified performance metrics, and all of the tracking errors are always enveloped within their corresponding DT-SFPPBs. The devised approach is exemplified by means of simulation examples.