Adaptive Neural Control Of Pure-feedback Nonlinear Time-varying Delays Systems

This paper is concerned with robust stabilization problem for a class of non-affine pure-feedback systems with unknown time-varying delays functions and perturbed uncer-tainties. Novel continuous packaged functions are introduced in advance to remove un-known nonlinear terms deduced from perturbed uncertainties and unknown time-varying delays functions, which avoids the functions with control law to be approximated by radial basis function (RBF) neural networks. This technique combining implicit function and mean value theorems overcomes the difficulty in controlling the non-affine pure-feedback systems. Dynamic surface control (DSC) is used to avoid "the explosion of complexity" in the back-stepping design. Design difficulties from unknown time-varying delays functions are overcome using the function separation technique, the Lyapunov-Krasovskii func-tionals, and the desirable property of hyperbolic tangent functions. RBF neural networks are employed to approximate desired virtual controls and desired practical control. Un-der the proposed adaptive neural DSC, the number of adaptive parameters required is reduced significantly, and semi-global uniform ultimate boundedness of all of the signals in the closed-loop system is guaranteed. Simulation studies are given to demonstrate the effectiveness of the proposed design scheme.