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.
Highlights
The approximation-based adaptive control of uncertain nonlinear systems is a significant theoretical challenge that has garnered a great deal of research interest in recent years [1,2,3]
We developed a novel adaptive neural prescribed performance control (PPC) scheme for a large class of nonlinear nonstrict-feedback systems with both prescribed performance and input saturation constraints
(1) Unlike other strategies [27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43], this is the first instance in which an adaptive control problem of a large class of nonstrict-feedback systems with continuous, possibly unbounded control gain functions fall under both prescribed performance and input saturation constraints
Summary
The approximation-based adaptive control of uncertain nonlinear systems is a significant theoretical challenge that has garnered a great deal of research interest in recent years [1,2,3]. To the best of our knowledge, there are extremely few extant schemes applicable to the control of large classes of nonstrict-feedback systems under both prescribed performance and input saturation constraints where the control gain functions are possibly unbounded This is yet an open problem with theoretical and practical significance. (1) Unlike other strategies [27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43], this is the first instance in which an adaptive control problem of a large class of nonstrict-feedback systems with continuous, possibly unbounded control gain functions fall under both prescribed performance and input saturation constraints.
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