Abstract
In this paper, finite time adaptive neural network (NN) tracking control is investigated for a class of uncertain nonstrict feedback systems with unknown dead-zone and unmodeled dynamics as well as full state restrictions. Using the linearized representation of dead-zone, finite-time adaptive control is presented by the aid of dynamic surface control (DSC) technique and the property of Gaussian function. By introducing logarithmic function as invertible nonlinear mapping, the full state restriction problem is solved. The dynamic signal generated by the low-pass filter is used to handle unmodeled dynamics. Through finite-time stability theory and introducing the bounded closed set in the proof, all the signals in the closed-loop system are proved to be semi-globally practical finite time stable (SGPFS). The restriction conditions are not triggered for all the states. Finally, two numerical examples are used to illustrate the feasiability of the finite time adaptive control strategy.
Highlights
As we know, backstepping method is often used to design all kinds of feedback control strategies for nonlinear systems in [1]–[5]
Using linearly parameterized neural networks (LPNNs) to approximate the unknown continuous function, the asymptotical tracking problem was discussed for strict-feedback nonlinear systems vai dynamic surface control (DSC) in [7]
By using Barrier Lyapunov function (BLF), adaptive finite time tracking control was discussed for parameterized strict-feedback nonlinear systems including dead-zone and without unmodeled dynamics in [38]
Summary
As we know, backstepping method is often used to design all kinds of feedback control strategies for nonlinear systems in [1]–[5]. Zhang: Finite Time Adaptive Neural DSC of Nonstrict Feedback Nonlinear Systems in the presence of dead-zone. By means of BLF method, observer-based adaptive output feedback control was studied for nonlinear systems with unmeasurable states as well as output constraints in [14]. Another control method was proposed for constrained systems by using the good properties of logarithmic functions. By using BLF, adaptive finite time tracking control was discussed for parameterized strict-feedback nonlinear systems including dead-zone and without unmodeled dynamics in [38]. Inspired by the previous work, this article studies the finite time control for constrained nonstrict-feedback systems including dead-zone and unmodeled dynamics via DSC. Using nonlinear mapping to deal with full state constraints overcomes the drawback which using BLF to handle full state constraints requires the known upper bounds of all virtual control signals in [38]
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