Dual Flexible Prescribed Performance Control of Input Saturated High-Order Nonlinear Systems

Abstract

This article first presents a dual flexible prescribed performance control (DFPPC) approach of input saturated high-order nonlinear systems (IS-HONSs). Compared to the existing PPC approaches of IS-HONSs, under which the performance constraint boundaries (PCBs) are usually fixed and bounded, resulting in a restriction of the initial error in the algorithm implementation; in addition, the coupling relationship between performance constraints and input saturation is usually ignored, resulting in the methods are very fragile when input saturation occurs. By designing the novel tensile model-based PCBs that depend on output and input constraints, the proposed DFPPC method provides sufficient resilience for both the initial conditions and the input saturation, so that the proposed DFPPC method can not only be suitable for multiple types of initial errors by adjusting the parameters, including $e_{1}(0)\in (\underline {\mathcal {B}}(0),\bar {\mathcal {B}}(0))$ , $e_{1}(0)\in (-\infty,\bar {\mathcal {B}}(0))$ , $e_{1}(0)\in (\underline {\mathcal {B}}(0),+\infty)$ and $e_{1}(0)\in (-\infty,\infty)$ , where $\underline {\mathcal {B}}(0)$ , and $\bar {\mathcal {B}}(0)$ denote the initial PCBs; but also can achieve a good balance between input saturation and performance constraints, i.e., when the control input reaches or exceeds the saturation threshold, the PCBs can adaptively extend to avoid the singularity, and when the control input returns to the saturation threshold range, the PCBs are then adaptively restored to the original PCBs. The results show that the proposed DFPPC algorithm guarantees semi-global boundedness for all closed-loop signals, while ensuring that the system output accurately tracks the desired signal, and it consistently maintains the tracking error within the PCBs. The developed algorithm is illustrated by means of simulation instances.