Approximation‐Based Robust Adaptive Backstepping Prescribed Performance Control for a Huger Class of Nonlinear Systems

Abstract

This paper proposes an innovative adaptive neural prescribed performance control (PPC) scheme for large classes of nonlinear, nonstrict-feedback systems under input saturation constraint. A restrictive hypothesis under which the upper and lower bounds of control gain functions exist a priori is first relieved by constructing appropriate compact sets within which all state trajectories are held. A novel asymmetry error transformed variable is then introduced to cope with the nondifferentiable obstacle and complex deductions corresponding to traditional PPC schemes. To efficiently manage the input saturation constraint, a new auxiliary dynamic system with a bounded compensation tangent function term is established as the strictly bounded assumption of the dynamic system is canceled. It is rigorously proven that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded under both Lyapunov and invariant set theories. The tracking errors converge to a small tunable residual set with prescribed performance under the effect of the input saturation constraint. The effectiveness of the proposed control scheme is thoroughly verified by two simulation examples.

A Neural Network-Based Adaptive Backstepping Control Law With Covariance Resetting for Asymptotic Output Tracking of a CSTR Plant

“…On the other hand, several works have been dedicated to backstepping control design for parametric uncertain nonlinear models [29], [30]. This latter approach can be efficiently implemented to linearize hard system nonlinearities in the existence of modeling uncertainties [31], [32]. Its basic concept consists of selecting recursive proper functions for a state variable subcontrol law for subsets of reduced dimension regarding the global system.…”