Sliding mode control for underactuated system with input constraint based on RBF neural network and Hurwitz stability analysis

Abstract

The sliding mode control method is proposed for a class of underactuated systems with input constraint in this paper. The properties of hyperbolic tangent function are used to deal with input constraint. Furthermore, a radial basis function (RBF) neural network is adopted to achieve the approximation of the unknown function and the projection mapping operator is used to further guarantee the bounded approximation. The control law is designed by using the Lyapunov's direct method, and the stability is conducted by using Hurwitz stability analysis. In the simulation part, two examples are listed, including a simple underactuated system and an underactuated inverted pendulum system, which can all be transformed into the model style studied in this paper to illustrate the effectiveness of the proposed control law. At last, the conclusion is summarized.

Adaptive neural control with fast approximation for uncertain nonlinear systems: A novel composite learning approach

“…Remark 5. Among the existing adaptive neural control schemes, most of them adopt the traditional direct adaptive approach, such as in earlier studies [2,3,8,9]. For the closed-loop system (1) driven by the control low ( 7) with ( 6), according to the traditional direct adaptive approach with 𝜎-modification, the adaptive law can be designed as follows:…”

“…Neural network (NN) can accurately approximate arbitrary nonlinear functions, due to its fast learning ability. Therefore, it is often used to deal with uncertainties of the system models, such as in earlier studies [1][2][3][4][5][6][7].…”

“…In Yang et al [9], a novel disturbance observer-based adaptive NN control for a hydraulic knee exoskeleton with valve deadband and output constraint is presented; the unknown nonlinearities of the hydraulic actuator are approximated by NN. In Ji and Liu [2], when studying a class of underactuated systems with input constraints, NN is adopted to achieve the approximation of the unknown functions, and the projection mapping operator is used to further guarantee the bounded approximation. In the above-mentioned application cases where NN is adopted to approximate unknown functions, the learning strategies of NN are all based on the traditional direct adaptive approach.…”

“…• Compared with the traditional direct adaptive approach adopted by earlier studies [2,3,8,9], the approach proposed in this paper introduces the prediction error generated by the regressor filtering scheme to the NN weights update law based on the tracking error, so as to ensure that the uncertainty in the nonlinear system can be approximated more quickly and smoothly, which will improve the approximation performance and tracking performance of the controller. • Compared with other composite learning approaches:…”

“…Motivated by the works [10, 19], a novel composite learning approach based on adaptive neural control is proposed for a class of strict‐feedback nonlinear systems with uncertainties. Compared with the existing NN learning control approaches, the novelty and advantages of this approach mainly rely on the following three points: Compared with the traditional direct adaptive approach adopted by earlier studies [2, 3, 8, 9], the approach proposed in this paper introduces the prediction error generated by the regressor filtering scheme to the NN weights update law based on the tracking error, so as to ensure that the uncertainty in the nonlinear system can be approximated more quickly and smoothly, which will improve the approximation performance and tracking performance of the controller. Compared with other composite learning approaches: (1) The model prediction error in [18, 22] is related to the system states, and their approaches can only ensure that the tracking error and the approximation error are uniformly ultimately bounded. The prediction error in this paper is generated by the regressor filtering scheme, which is directly related to the uncertainty of the system.…”