Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

Abstract

This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

Adaptive second-order backstepping control for a class of 2DoF underactuated systems with input saturation and uncertain disturbances

“…( 11 ), every backstepping step is designed for a second-order subsystem. Compared with first-order backstepping 9 , 21 , 22 , 24 , the proposed second-order backstepping has the following advantages: firstly, the number of backstepping design steps is the same as the number of system DoFs, which can reduce the number of design steps and simplify the design process; secondly, the dynamic performance of the each subsystem can be adjusted by changing parameters ( for the first subsystem and for the second subsystem) according to the idea of classic linear system control theory.…”

“…To handle the EoC problems, the dynamic surface control (DSC) 20 is proposed, in which a first-order filter is applied in each step to allow a design where the model is not differentiated. There have been reports on DSC schemes 21 , 22 , and some DSC solutions 17 , 23 are designed for the underactuated systems. However, the uncompensated filtering errors may affect the control performance.…”

Observer-Based Adaptive Fuzzy Quantized Control for Fractional-Order Nonlinear Time-Delay Systems with Unknown Control Gains

“…The Nussbaum gain technique (originally proposed in [19]) has been widely used to address the adaptive control problem for nonlinear systems with unknown control gains, and many remarkable results have been obtained [20][21][22][23]. In [21], a composite adaptive neural control approach was developed to guarantee the convergence of the tracking error to an arbitrarily small neighborhood, even if the sign of the control gain was unavailable.…”

Adaptive Neural Network Command Filtered Backstepping Control for the Underactuated TORA System

“…The dynamic surface control (DSC) concept introduced by Swaroop [19] resolves the EoC by using first-order filters. Many adaptive, fuzzy and NN-based DSC solutions [20], [21] have also been reported. Some DSC solutions are designed for the TORA system [22], [23].…”

“…In recent several decades, NN-based techniques have gained great attention. The NNs are used as observers in [27], [28], adaptive NN is used to approximate unknown uncertainties in the system's dynamics [7], [21], [29], [30], and a variety of different types of nonlinear systems have been explored by using NNs-based adaptive backstepping techniques to deal with unknown nonlinearities [31]- [35].…”