Deterministic learning from ISS-modular adaptive NN control of nonlinear strict-feedback systems

Abstract

This paper studies deterministic learning from adaptive neural control for a class of strict-feedback nonlinear systems with unknown affine terms. Firstly, an ISS-modular approach is presented to ensure uniformly ultimate boundedness of all the signals in the closed-loop system and the convergence of tracking errors in a finite time. The proposed ISS-modular approach avoids the possible control singularity without the restriction of the derivative of affine terms. Secondly, it will be shown the proposed stable ISS-modular adaptive neural controller is able to learn closed-loop system dynamics. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using previous methods. To overcome these difficulties, the stable closedloop system in control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation (PE) condition for radial basis function (RBF) neural networks (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop control system dynamics is achieved in a local region along a recurrent orbit of closed-loop signals, and a learning ability is implemented during a closed-loop feedback control process. The learned knowledge can be reused in the same or similar control tasks, and avoid the tremendous repeated training process of NNs.

Dynamic Learning from Adaptive Neural Control of Uncertain Robots with Guaranteed Full-State Tracking Precision

“…In the simulation studies, the RBF network given in Figure 6 full-state tracking performance constraints, the simulation comparison is given between the proposed method and the existing method without prescribed performances [30]. For comparison purpose, the existing method [30] is also used to control the same 2-link robot manipulator with the same initial condition (0) = [−0.6, 1] ,(0) = [1.5, −1] and the same reference trajectory (50). For clarity, the existing method without prescribed performance proposed in [30] is recalled as follows: the control law is = − 1 − 2 2 −̂( ) and neural weight updated lawṡ= Γ[ ( ) 2 −̂] and 1 = − 1 1 + 2 .…”

“…For comparison purpose, the existing method [30] is also used to control the same 2-link robot manipulator with the same initial condition (0) = [−0.6, 1] ,(0) = [1.5, −1] and the same reference trajectory (50). For clarity, the existing method without prescribed performance proposed in [30] is recalled as follows: the control law is = − 1 − 2 2 −̂( ) and neural weight updated lawṡ= Γ[ ( ) 2 −̂] and 1 = − 1 1 + 2 . By choosing the appropriate control parameters 1 = 1, 2 = 18, = 0.001, and Γ = 10, to be fair, both control input signals of the two methods are Remark 11.…”

“…Moreover, from (17), (25), (30), and (33), we can obtain the convergence region of the transformed error 1 , 2 as follows:…”

“…The deterministic learning method was further extended to thorder Brunovsky systems with an unknown affine/nonaffine term [28,29], where the derivative of unknown affine terms was assumed to be bounded. By combining backstepping with a system decomposition strategy, an elegant dynamic learning method was proposed to cope with the learning and control problem of third-order strict-feedback systems [30]. By combining dynamic surface control technology [31], the result in [30] was further extended to th-order strictfeedback systems.…”

“…By combining backstepping with a system decomposition strategy, an elegant dynamic learning method was proposed to cope with the learning and control problem of third-order strict-feedback systems [30]. By combining dynamic surface control technology [31], the result in [30] was further extended to th-order strictfeedback systems. The deterministic learning method was also applied in many physical systems such as marine surface vessels [32,33] and robot manipulators [34].…”