Adaptive Intelligent Controller Design-Based ISS Modular Approach for Uncertain Nonlinear Systems With Time-Varying Full-State Constraints

Abstract

The present article focuses on an input-to-state stability (ISS) problem of nonlinear strict-feedback system with time-varying full-state constraints. The adaptive neural controllers are designed by using backstepping, barrier Lyapunov function (BLF), and ISS small-gain approach. BLF is proved to satisfy the small-gain condition; thus, the conception of input-to-state stable time-varying BLF (ISSTVBLF) is produced. Also, the ISSTVBLF is novel embedded into the back-stepping design for a subsystem, which can prevent the full-state constraints from being violated all the time and avoid the designed difficulties resulting from the requirement of the entire BLF for the time-varying constrained system. The neural network approximate technique is utilized to estimate the unknown nonlinear functions. Then, a systematic procedure is developed to derive new adaptive tracking controllers based on the small-gain theorem. It is proved that all the closed-loop signals are semiglobal, uniform, and ultimate boundedness and the tracking error is driven to a small domain around zero. Finally, simulation study results illustrate the effectiveness of the proposed control schemes. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Impact Statement</i>—There are constraints in various systems. In this paper a strict feedback system with time-varying full-state constraints is studied. Handling the time-varying unknown nonlinearities and high-order coupling terms is a difficult question. It tends to be conservative to choose transformation functions to transform the constrained system to an unconstrained one. The controllers introduced in this paper, which are constructed by applying back-stepping, BLF and ISS small-gain approach, can overcome the difficulty of designing an overall Lyapunov function. Checking ISS small-gain condition is another difficulty, we construct a novel class K function for BLF in the design process, then the subsystem of the imbedded BLF is proved to be ISS. Simulation study results illustrate the effectiveness of proposed control schemes.