Extended grey wolf optimization–based adaptive fast nonsingular terminal sliding mode control of a robotic manipulator

This article proposes a novel hybrid metaheuristic technique based on nonsingular terminal sliding mode controller, time delay estimation method, an extended grey wolf optimization algorithm and adaptive super twisting control law. The fast convergence is assured by nonsingular terminal sliding mode controller owing to its inherent nonlinear property and no prior knowledge of the robot dynamics is required due to time delay estimation. The proposed extended grey wolf optimization algorithm determines an optimal approximation of the inertial matrix of the robot. Moreover, adaptive super twisting control based on the Lyapunov approach overcomes the disturbances and compensate the higher dynamics not achievable by the time delay estimation method. First, the fast nonsingular terminal sliding mode controller relying on time delay estimation is designed and is combined with super twisting control for chattering attenuation. The constant gain matrix of the time delay is determined by the proposed extended grey wolf optimization algorithm. Second, an adaptive law based on Lyapunov stability theorem is designed for improving tracking performance in the presence of uncertainties and disturbances. The novelty of the proposed method lies in the adaptive law where the prior knowledge of parametric uncertainties and disturbances is not needed. Moreover, the constant gain matrix of time delay estimation method is obtained using the proposed algorithm. The control method has been tested in simulation on a 3-degrees of freedom robotic manipulator in trajectory tracking mode in the presence of control disturbances and uncertainties. The results obtained confirmed the effectiveness, robustness and the superior precision of the proposed control method compared to the classical ones

Finite-time control for uncertain systems and application to flight control

In this paper, the finite-time control design problem for a class of nonlinear systems with matched and mismatched uncertainty is addressed. The finite-time control scheme is designed by integrating multi power reaching (MPR) law and finite-time disturbance observer (FTDO) into integral sliding mode control, where a novel sliding surface is designed, and the FTDO is applied to estimate the uncertainty. Then the fixed-time reachability of the MPR law is analyzed, and the finite-time stability of the closed-loop system is proven in the framework of Lyapunov stability theory. Finally, numerical simulation and the application to the flight control of hypersonic vehicle (HSV) are provided to show the effectiveness of the designed controller

Terminal Sliding Mode Control with Adaptive Law for Uncertain Nonlinear System

A novel nonsingular terminal sliding mode controller is proposed for a second-order system with unmodeled dynamics uncertainties and external disturbances. We need not achieve the knowledge for boundaries of uncertainties and external disturbances in advance. The adaptive control gains are obtained to estimate the uncertain parameters and external disturbances which are unknown but bounded. The closed loop system stability is ensured with robustness and adaptation by the Lyapunov stability theorem in finite time. An illustrative example of second-order nonlinear system with unmodeled dynamics and external disturbances is given to demonstrate the effectiveness of the presented scheme

On Continuous Full-Order Integral-Terminal Sliding Mode Control with Unknown Apriori Bound on Uncertainty

This study aims at providing a solution to the problem of designing a continuous and finite-time control for a class of nonlinear systems in the presence of matched uncertainty with an unknown apriori bound. First, we propose a Full-Order Integral-Terminal Sliding Manifold (FOITSM) with a conventional (discontinuous) sliding mode to show that it provides the combined attributes of the nonsingular terminal and integral sliding mode algorithms. Secondly, an Adaptive Disturbance Observer (ADO) has been designed to alleviate the effect of the uncertainty acting on the system. On application of the ADO-based Full-Order Integral-Terminal Sliding Mode Control (FOITSMC), the chattering phenomenon in control input has been reduced substantially in the presence of conditionally known matched disturbances. Moreover, the adaptive gains of ADO are updated non-monotonically without over-bounding the acting disturbance, yet sustain the global boundedness of state trajectories within a specific bound. %Finally, an application of the proposed algorithm for attitude stabilization of a rigid spacecraft has been successively shown.Comment: 14 pages, 9 figure

Intelligent nonsingular terminal sliding-mode control via perturbed fuzzy neural network

[[abstract]]In this paper, an intelligent nonsingular terminal sliding-mode control (INTSMC) system, which is composed of a terminal neural controller and a robust compensator, is proposed for an unknown nonlinear system. The terminal neural controller including a perturbed fuzzy neural network (PFNN) is the main controller and the robust compensator is designed to eliminate the effect of the approximation error introduced by the PFNN upon the system stability. The PFNN is used to approximate an unknown nonlinear term of the system dynamics and perturbed asymmetric membership functions are used to handle rule uncertainties when it is hard to exactly determine the grade of membership functions. In additional, Lyapunov stability theory is used to discuss the parameter learning and system stability of the INTSMC system. Finally, the proposed INTSMC system is applied to an inverted pendulum and a voice coil motor actuator. The simulation and experimental results show that the proposed INTSMC system can achieve favorable tracking performance and is robust against parameter variations in the plant

Stochastic stability and stabilization of discrete-time singular Markovian jump systems with partially unknown transition probabilities

This paper considers the stochastic stability and stabilization of discrete-time singular Markovian jump systems with partially unknown transition probabilities. Firstly, a set of necessary and sufficient conditions for the stochastic stability is proposed in terms of LMIs, then a set of sufficient conditions is proposed for the design of a state feedback controller to guarantee that the corresponding closed-loop systems are regular, causal, and stochastically stable by employing the LMI technique. Finally, some examples are provided to demonstrate the effectiveness of the proposed approaches

Control and synchronization of the generalized Lorenz system with mismatched uncertainties using backstepping technique and time‐delay estimation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140007/1/cta2353.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/140007/2/cta2353_am.pd

Terminal sliding mode control for continuous stirred tank reactor

© 2014 The Institution of Chemical Engineers. A continuous stirred tank reactor (CSTR) is a typical example of chemical industrial equipment, whose dynamics represent an extensive class of second order nonlinear systems. It has been witnessed that designing a good control algorithm for the CSTR is very challenging due to the high complexity. The two difficult issues in CSTR control are state estimation and external disturbance attenuation. In general, in industrial process control a fast and robust response is essential. Driven by these challenging issues and desired performance, this paper proposes an output feedback terminal sliding mode control (TSMC) framework which is developed for CSTR, and can estimate the system states and stabilize the system output tracking error to zero in a finite time. The corresponding stability analysis is presented in terms of the Lyapunov method. Illustrative examples are demonstrated by using Matlab simulations to validate the effectiveness of the proposed approach

Terminal Sliding Mode Control of Mobile Wheeled Inverted Pendulum System with Nonlinear Disturbance Observer

A terminal sliding mode controller with nonlinear disturbance observer is investigated to control mobile wheeled inverted pendulum system. In order to eliminate the main drawback of the sliding mode control, “chattering” phenomenon, and for compensation of the model uncertainties and external disturbance, we designed a nonlinear disturbance observer of the mobile wheeled inverted pendulum system. Based on the nonlinear disturbance observer, a terminal sliding mode controller is also proposed. The stability of the closed-loop mobile wheeled inverted pendulum system is proved by Lyapunov theorem. Simulation results show that the terminal sliding mode controller with nonlinear disturbance observer can eliminate the “chattering” phenomenon, improve the control precision, and suppress the effects of external disturbance and model uncertainties effectively