Robust adaptive neural control for a class of non-affine nonlinear systems

Abstract

This paper addresses the adaptive neural tracking control problem for a class of uncertain non-affine nonlinear system with non-affine function being semi-bounded and possibly non-differentiable. Compared with traditional control schemes, the proposed scheme can be applied to a more general class of non-affine nonlinear system, and relaxes constraint conditions as follows: firstly, the assumption that non-affine function must be differentiable is canceled, and only a continuous condition for non-affine function is required to guarantee the controllability of the considered system, secondly, the assumption that non-affine function is completely bounded is relaxed, and the non-affine function is constrained by a semi-bounded condition with the bounds being unknown functions. Then, an adaptive neural tracking controller is designed based on an invariant set. In the control design process, minimal learning parameter (MLP) technique is used to reduce the number of adaptive parameters, and a smooth robust compensator is employed to circumvent the influences of approximation error and external disturbance. Furthermore, it is proven that all the closed-loop signals are semi-globally uniformly ultimately bounded. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

“…The approximation curves of x 1 and x 2 are shown in Fig. 2, which implies the effectiveness of approximation method (7). Figs 3 and 4 demonstrate the good tracking performance of system states and r confronted with unknown compound disturbance, actuator faults.…”

“…14, the estimation disturbance changes obviously at t = 15s and then approximates compound disturbance in finite time. From the simulation results (Figs 1-14), it is concluded that non-affiine UAV helicopter with unknown compound disturbance and actuator faults can track not only constant desired signal but also time-varying desired signal in finite time based on the approximation method (7), ATSMDO (8) and controller (30), (40) and (47)). In Figs 5 and 13, it is obvious that actuator faults occurs at t = 15 and last later.…”

“…A non-affine unmanned-aerial-vehicle (UAV) helicopter system [6] is used to prove the effectiveness of the addressed control scheme based on approximation method (7), adaptive terminal sliding mode disturbance observer (8), controllers (30), (40), (47) and robust term (48). The UAV helicopter system is as follows:…”

A DSC method for strict-feedback nonlinear systems with possibly unbounded control gain functions

“…Recent years have witnessed a great amount of research in approximation-based adaptive control for nonlinear uncertain systems due to both the practical need and theoretical challenges [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In these works, neural networks (NNs) or fuzzy-logic systems (FLS) are typically used to approximate nonlinear functions with little knowledge of system to be controlled, which has effectively removed the restrictive matching conditions for system uncertainties.…”

Robust output tracking of a class of non-affine systems

“…There exist many practical systems which are non-affine in the control input. For example: the model of aircraft dynamics (Boškovic, Chen, & Mehra, 2004), underwater vehicles (Geranmehr & Nekoo, 2015), active magnetic bearings (Tombul, Banks, & Akturk, 2009); electromagnetic levitation (Gutierrez & Ro, 2005) and etc (Ríos, Punta, & Fridman, 2017;Shi, Dong, Xue, Chen, & Zhi, 2017;Song & Song, 2014). Because of the complex structure of non-affine systems, the Lyapunov-based controllers have not been fully studied for these systems and most of the designed controllers for the non-affine systems are based on the non-model based methods like fuzzy or neural network controllers (Chien, Wang, Leu, & Lee, 2011Gao, 2017;Labiod & Guerra, 2010).…”