A Nearly Optimal Chattering Reduction Method of Sliding Mode Control With an Application to a Two-wheeled Mobile Robot

Abstract

The problem we focus on in this paper is to find a nearly optimal sliding mode controller of continuous-time nonlinear multiple-input multiple-output (MIMO) systems that can both reduce chattering and minimize the cost function, which is a measure of the performance index of dynamics systems. First, the deficiency of chattering in traditional SMC and the quasi-SMC method are analyzed in this paper. In quasi-SMC, the signum function of the traditional SMC is replaced with a continuous saturation function. Then, a chattering reduction algorithm based on integral reinforcement learning (IRL) is proposed. Under an initial sliding mode controller, the proposed method can learn the nearly optimal saturation function using policy iteration. To satisfy the requirement of the learned saturation function, we treat the problem of training the saturation function as the constraint of an optimization problem. The online neural network implementation of the proposed algorithm is presented based on symmetric radius basis functions and a regularized batch least-squares (BLS) algorithm to train the control law in this paper. Finally, two examples are simulated to verify the effectiveness of the proposed method. The second example is an application to a real-world dynamics model-a two-wheeled variable structure robot.

Chattering Reduction of Sliding Mode Control for Quadrotor UAVs Based on Reinforcement Learning

“…This section verifies the proposed method with the comparison methods in the MAT-LAB environment, considering the system (1), setting the attitude target of 0.3 rad based on the existing equivalent control (14), combined with the switching control calculated based on the proposed RL-based ( 16), the improved Class A method (30), and the improved Class B method (32), for target tracking. The system's initial state X = [0, 0, 0] T .…”

“…In class D, ref. [23] replaced the sign function with the smooth function (32) to alleviate chattering.…”

“…Their study is based on the saturation function and uses RL to realize adaptive control; however, the selected saturation function limits the final effect. Another study [32] proposed a method to solve the optimal control under constraints by applying the hyperbolic tangent and symmetry radial basis functions to design the saturating function. Subsequently, integral Q-learning was used to approximate it to reduce chattering.…”

“…Based on the above discussion, to avoid the problems of state dimension limitation [32] and auxiliary function limitation [31] in the existing works, this study combines a policybased RL method to solve the chattering problem in SMC. Specifically, a reference modelbased SMC was adopted as the base controller.…”

Adaptive Sliding Mode Control Based on Fuzzy Logic and Low Pass Filter for Two-Tank Interacting System

“…Chattering phenomenon due to imperfections and time delays in Volume 13, Number 6, 2022 switching, due to small time constant actuators, power circuits are prone to overheating leading to damage [10,11]. Many research have provided solutions to overcome chattering phenomenon in the SMC, such as a signum function of the SMC is replaced by saturation function and a Recurrent Elman Neural Network was developed for optimal determination of the switching gain of the Smoothed Sliding Mode Control was given in [8], the feed forward neural network was used [12], an adaptive terminal sliding mode control was given [13], a Smooth Hyperbolic Tangent Function was utilized to replace the discontinuous signum function [14,15] was used a nearly optimal sliding mode controller, a robust multichannel control system based on SMC was given [16], and an adaptive finite time robust control methods were employed [17] based on SMC method.…”