Finite-Time Extended State Observer-Based Performance-Critical Control for Uncertain MIMO Nonlinear Systems

This paper studies a prescribed performance control (PPC) problem of uncertain nonlinear systems in a multi-input multi-output Brunovsky form. An observer-based performance-critical control method is proposed, which is different from existing PPC methods using error transformation functions (ETFs). At first, a finite-time extended state observer (FTESO) is designed to identify the nonlinear term. Then, based on the proposed FTESO, a nominal integral sliding mode controller is devised without considering user-specified performance indexes. Next, we construct the input-to-state safe high-order control barrier functions (ISSf-HOCBFs) for tracking error systems with unknown disturbances. The performance-critical input constraints are devised by using PPC constraint-based ISSf-HOCBFs. Later, a modified controller is solved by the quadratic program unifying nominal controller with performance-critical input constraints. Finally, it is proved that the closed-loop system is input-to-state safe by forward invariance analysis, and tracking errors evolve within prescribed constraints. Finally, a simulation example of an unmanned surface vehicle is conducted to demonstrate the effectiveness of the proposed observer-based performance-critical control method.