Adaptive finite-time control for stochastic nonlinear systems using multi-dimensional Taylor network

2021 ◽  
pp. 014233122110396
Author(s):  
Shan-Liang Zhu ◽  
Ming-Xin Wang ◽  
Yu-Qun Han
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Lyapunov Stability Theory ◽  
Loop System ◽  
Stochastic Nonlinear Systems ◽  
Time Control ◽  
Control Scheme ◽  
The Stability

In this paper, the problem of adaptive finite-time multi-dimensional Taylor network (MTN) control for a class of stochastic nonlinear systems is investigated. By combining the MTN-based approximate method and adaptive backstepping technique, a novel adaptive finite-time MTN control scheme is proposed. In this scheme, the MTNs are used to approximate the unknown nonlinear functions of the systems. The finite-time Lyapunov stability theory is utilized to prove the stability of the close-loop system. The proposed scheme can ensure that all signals in the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood of the origin in a finite time. Three simulation examples are presented to show the effectiveness of the control scheme. It should be pointed that the adaptive MTN controller proposed in this paper has the advantages of fast computational speed and good real-time performance thanks to the simple structure of the MTN.

Finite-time backstepping control with command filter for a class of nonlinear systems with parametric uncertainties

2020 ◽  
Vol 42 (12) ◽  
pp. 2297-2307 ◽  
Author(s):  
Cong Feng ◽  
Qing Wang ◽  
Changhua Hu ◽  
Shen Zhang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Error Compensation ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Backstepping Control ◽  
Parametric Uncertainties ◽  
Compensation Mechanism ◽  
Time Control ◽  
Command Filter

In this paper, the problem of adaptive finite-time control is considered for a class of nonlinear systems with parametric uncertainties. A novel adaptive command filtered backstepping control method is proposed, and the adverse impact caused by the command filter is eliminated by introducing modified error compensation mechanism with consideration of parametric uncertainties. Combined with the designed adaptation laws, the error compensation mechanism can be finite-time stable. Rigorous proof is achieved to show that the tracking error converges to a small neighborhood of zero in finite time with online parameters adaptation and error compensation. Finally, numeral simulations are presented to validate the effectiveness of the proposed adaptive finite-time control scheme.

scholarly journals Adaptive Fixed-time Control for Nonlinear Systems Against Time-varying Actuator Faults

2021 ◽  
Author(s):  
Yu Mei ◽  
Jing Wang ◽  
Ju H. Park ◽  
Kaibo Shi ◽  
Hao Shen
Keyword(s):  
Nonlinear Systems ◽  
Fault Tolerant ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Fixed Time ◽  
Time Interval ◽  
Time Varying ◽  
Actuator Faults ◽  
Time Control ◽  
Control Scheme

Abstract The adaptive fixed-time control problem for nonlinear systems with time-varying actuator faults is investigated in this paper. A novel adaptive fixed-time controller is designed via combining the Lyapunov stability theory with the backstepping method. It can be adapted to both system uncertainties and unknown actuator faults. Compared with the existing fault-tolerant control schemes subject to actuator faults, the adaptive fixed-time neural networks control scheme can make sure that the tracking error is convergent in a small neighborhood of the origin within a fixed-time interval, and it does not depend on the original states of the system and actuator faults. In light of the control scheme proposed in this paper, the fixed-time stability of the closed-loop system can be guaranteed by theoretical analysis, and a numerical example is provided to verify the effectiveness of obtained theoretical results.

scholarly journals Stabilization of a Class of Stochastic Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Valiollah Ghaffari ◽  
Hamid Reza Karimi ◽  
Navid Noroozi ◽  
S. Vahid Naghavi
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Systems ◽  
Adaptive Controller ◽  
Stochastic Nonlinear Systems ◽  
Nonlinear Stochastic Systems ◽  
Closed Loop Systems ◽  
Time Control ◽  
Control Scheme ◽  
Control Schemes ◽  
The Stability

This paper addresses two control schemes for stochastic nonlinear systems. Firstly, an adaptive controller is designed for a class of motion equations. Then, a robust finite-time control scheme is proposed to stabilize a class of nonlinear stochastic systems. The stability of the closed-loop systems is established based on stochastic Lyapunov stability theorems. Links between these two methods are given. The efficiency of the control schemes is evaluated using numerical simulations.

scholarly journals Finite Time Inverse Optimal Stabilization for Stochastic Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiushan Cai ◽  
Yuhang Lin ◽  
Wei Zhang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Loop System ◽  
Stochastic Nonlinear Systems ◽  
Control Law ◽  
Closed Loop System ◽  
Control Lyapunov Function ◽  
Optimal Stabilization ◽  
Time Control

This paper deals with finite time inverse optimal stabilization for stochastic nonlinear systems. A concept of the stochastic finite time control Lyapunov function (SFT-CLF) is presented, and a control law for finite time stabilization for the closed-loop system is obtained. Furthermore, a sufficient condition is developed for finite time inverse optimal stabilization in probability, and a control law is designed to ensure that the equilibrium of the closed-loop system is finite time inverse optimal stable. Finally, an example is given to illustrate the applications of theorems established in this paper.

scholarly journals Underactuated AUV Nonlinear Finite-Time Tracking Control Based on Command Filter and Disturbance Observer

Sensors ◽  
2019 ◽  
Vol 19 (22) ◽  
pp. 4987 ◽  
Author(s):  
Xu ◽  
Zhang ◽  
Cao ◽  
Pang ◽  
Sun
Keyword(s):  
Finite Time ◽  
Autonomous Underwater Vehicle ◽  
Tracking Error ◽  
Three Dimensional ◽  
Path Following ◽  
Lyapunov Stability Theory ◽  
Ocean Currents ◽  
3D Tracking ◽  
Time Control ◽  
Underactuated Auv

The three-dimensional (3D) path following problem of an underactuated autonomous underwater vehicle with ocean currents disturbances is addressed in this paper. Firstly, the motion equation under the ocean currents disturbance is established, and the dynamic model of 3D tracking error is constructed based on virtual guidance method. Then, a finite-time control scheme based on super-twisting observer and command filtered backstepping technology is proposed. We adopt super-twisting observer based on finite-time theory to observe the ocean currents disturbances for improving the system robust. A command filtered backstepping is proposed to replace the differential process in the conventional backstepping method for avoiding the differential expansion problem. The filter compensation loop is designed to ensure the accuracy of the filtered signal, and the anti-integration saturation link is designed considering the influence of integral saturation. Lyapunov stability theory is used to prove the stability of the underactuated AUV. Simulation studies are conducted to show the effectiveness and robustness of the controller.

Neural network-based finite-time control of quantized stochastic nonlinear systems

2019 ◽  
Vol 362 ◽  
pp. 195-202 ◽  
Author(s):  
Fang Wang ◽  
LiLi Zhang ◽  
Shaowei Zhou ◽  
Yuanyuan Huang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Stochastic Nonlinear Systems ◽  
Time Control

scholarly journals Direct Adaptive Tracking Control for a Class of Pure-Feedback Stochastic Nonlinear Systems Based on Fuzzy-Approximation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Huanqing Wang ◽  
Xiaoping Liu ◽  
Qi Zhou ◽  
Hamid Reza Karimi
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Controller Design ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Adaptive Controller ◽  
Stochastic Nonlinear Systems ◽  
Fuzzy Logic Systems ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

The problem of fuzzy-based direct adaptive tracking control is considered for a class of pure-feedback stochastic nonlinear systems. During the controller design, fuzzy logic systems are used to approximate the packaged unknown nonlinearities, and then a novel direct adaptive controller is constructed via backstepping technique. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error eventually converges to a small neighborhood around the origin in the sense of mean quartic value. The main advantages lie in that the proposed controller structure is simpler and only one adaptive parameter needs to be updated online. Simulation results are used to illustrate the effectiveness of the proposed approach.

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