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

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.