Adaptive multi-dimensional Taylor network control for nonlinear stochastic systems with time-delay

2021 ◽  
pp. 095965182110402
Author(s):  
Shan-Liang Zhu ◽  
Ming-Xin Wang ◽  
Yu-Qun Han
Keyword(s):  
Time Delay ◽  
Stochastic Systems ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Network Control ◽  
Closed Loop System ◽  
Integral Type ◽  
Nonlinear Stochastic Systems ◽  
Network Controller ◽  
Control Scheme

In this article, the problem of adaptive multi-dimensional Taylor network control for strict-feedback nonlinear stochastic systems with time-delay is investigated. To overcome the control degradation resulting from the delay terms, the appropriate integral-type Lyapunov–Krasovskii functions are introduced. A novel adaptive multi-dimensional Taylor network control scheme is provided via backstepping technique. The proposed adaptive multi-dimensional Taylor network controller can ensure that all signals in the closed-loop system are bounded in probability and the tracking error eventually converges to a small neighborhood of the origin. Three simulation examples are given to demonstrate the effectiveness of the proposed control scheme.

Recurrent Higher Order Neural Network Control for Output Trajectory Tracking with Neural Observers and Constrained Inputs

2010 ◽  
pp. 286-311 ◽  
Author(s):  
Luis J. Ricalde ◽  
Edgar N. Sanchez ◽  
Alma Y. Alanis
Keyword(s):  
Neural Network ◽  
Tracking Error ◽  
Network Control ◽  
Design Parameters ◽  
The Neural Network ◽  
Control Scheme ◽  
Output Trajectory ◽  
Error Dynamics ◽  
Adaptation Law ◽  
Constrained Inputs

This Chapter presents the design of an adaptive recurrent neural observer-controller scheme for nonlinear systems whose model is assumed to be unknown and with constrained inputs. The control scheme is composed of a neural observer based on Recurrent High Order Neural Networks which builds the state vector of the unknown plant dynamics and a learning adaptation law for the neural network weights for both the observer and identifier. These laws are obtained via control Lyapunov functions. Then, a control law, which stabilizes the tracking error dynamics is developed using the Lyapunov and the inverse optimal control methodologies . Tracking error boundedness is established as a function of design parameters.

A New Controller of Stochastic Delay Systems

2011 ◽  
Vol 63-64 ◽  
pp. 974-977
Author(s):  
Yun Chen ◽  
Qing Qing Li
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Stochastic Systems ◽  
Delay Systems ◽  
Mean Square ◽  
Closed Loop System ◽  
Stochastic Delay ◽  
Numerical Example ◽  
Mean Square Stability ◽  
Delay Dependent

By introducing an additional vector, a new delay-dependent controller is designed for stochastic systems with time delay in this paper. The presented controller is formulated by means of LMI, and it guarantees robust asymptotical mean-square stability of the resulting closed-loop system. Our result shows advantage over some existing ones, which is demonstrated by a numerical example.

scholarly journals Robust adaptive tracking for Markovian jump nonlinear systems with unknown nonlinearities

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Jin Zhu ◽  
Hong-Sheng Xi ◽  
Hai-Bo Ji ◽  
Bing Wang
Keyword(s):  
Tracking Error ◽  
Small Neighborhood ◽  
Parametric Uncertainty ◽  
Control Law ◽  
Fourth Moment ◽  
Closed Loop System ◽  
Markovian Jump ◽  
Adaptive Tracking ◽  
Adaptive Law ◽  
Robust Adaptive

Robust adaptive tracking problems for a class of Markovian jump parametric-strict-feed-back systems with both parametric uncertainty and unknown nonlinearity are investigated. The unknown nonlinearities considered herein lie within some “bounding functions,” which are assumed to be partially known. By using a stochastic Lyapunov method and backstepping techniques, a parameter adaptive law and a control law were obtained, which guarantee that the tracking error could be within a small neighborhood around the origin in the sense of the fourth moment. Moreover, all signals of the closed-loop system could be globally uniformly ultimately bounded.

Composite hierarchical anti-disturbance control for stochastic systems with multiple disturbances

2017 ◽  
Vol 40 (6) ◽  
pp. 1950-1955 ◽  
Author(s):  
Shixiang Sun ◽  
Xinjiang Wei ◽  
Huifeng Zhang
Keyword(s):  
Disturbance Observer ◽  
Closed Loop ◽  
Stochastic Systems ◽  
Time Derivative ◽  
Closed Loop System ◽  
Stochastic Disturbance ◽  
Multiple Disturbances ◽  
Control Scheme ◽  
Bounded Disturbance ◽  
White Noises

A class of stochastic systems with multiple disturbances, which includes white noises and disturbances whose time derivative is bounded, is considered in this paper. To estimate the unknown bounded disturbance, a stochastic disturbance observer is proposed. Based on the observer, a disturbance observer-based disturbance control scheme is constructed such that the composite closed-loop system is asymptotically bounded. Finally, a simulation example is given to demonstrate the feasibility and effectiveness of the proposed scheme.

Robust Control for a Class of Nonlinear Systems Based on Backstepping

2011 ◽  
Vol 50-51 ◽  
pp. 110-114
Author(s):  
Nai Bao He ◽  
Qian Gao
Keyword(s):  
Robust Control ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Control Law ◽  
Closed Loop System ◽  
Unknown Parameters ◽  
Feedback Form ◽  
Output Tracking ◽  
Adaptive Parameter ◽  
Adaptive Parameter Control

Based on coordinate transform, the paper deduced the principle with which Chua’s chaotic system can be translated into the so-called general strict-feedback form. Combining the backstepping method with robust control technology, an adaptive parameter control law is developed and thus the output tracking is successfully accomplished for the system with unknown parameters and dynamic uncertainties. It is proved that all states of the closed-loop system are globally uniformly　ultimately bounded, and lead the system tracking error to a small neighborhood. Finally simulation results are provided to show the effectiveness of the proposed approach.

scholarly journals Asymptotic Stability of Delay-Controlled Nonlinear Stochastic Systems with Actuator Failures

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
N. Zhou ◽  
R. H. Huan
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Original System ◽  
Stochastic Averaging ◽  
Largest Lyapunov Exponent ◽  
Control Force ◽  
Nonlinear Stochastic Systems ◽  
Actuator Failures

The problem of asymptotic stability of delay-controlled nonlinear stochastic systems with actuator failures is investigated in this paper. Such a system is formulated as a continuous-discrete hybrid system based on the random switch model of failure-prone actuator. Time delay control force is converted into delay-free one by randomly periodic characteristic of the system. Using limit theorem and stochastic averaging, an approximate formula for the largest Lyapunov exponent of the original system is then derived, from which necessary and sufficient conditions for asymptotic stability are obtained. The validity and utility of the proposed procedure are demonstrated by using a stochastically driven nonlinear two-degree system with time delay feedback and actuator failure.

scholarly journals H∞Control for Nonlinear Stochastic Systems with Time-Delay and Multiplicative Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Ming Gao ◽  
Weihai Zhang ◽  
Zhengmao Zhu
Keyword(s):  
Time Delay ◽  
General Class ◽  
Multiplicative Noise ◽  
Stochastic Systems ◽  
Design Method ◽  
Infinite Horizon ◽  
Control Design ◽  
Mean Square ◽  
Nonlinear Stochastic Systems ◽  
Numerical Examples

This paper studies the infinite horizonH∞control problem for a general class of nonlinear stochastic systems with time-delay and multiplicative noise. The exponential/asymptotic mean squareH∞control design of delayed nonlinear stochastic systems is presented by solving Hamilton-Jacobi inequalities. Two numerical examples are provided to show the effectiveness of the proposed design method.

Neural Network Control for Uncertain Nonlinear Time-Delay Systems

2014 ◽  
Vol 898 ◽  
pp. 705-708
Author(s):  
Hong Yu Gao ◽  
Xiu Ming Wang ◽  
Yuan Gao ◽  
Ke Yong Shao
Keyword(s):  
Neural Network ◽  
Time Delay ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Nonlinear Function ◽  
Network Control ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Neural Network Controller ◽  
Network Controller

Based on stability theory, a class of neural network controller design of uncertain nonlinear time-delay systems is studied. Using the ability that neural network can approximate any nonlinear function, a kind of weights correction law based on radial basis function (RBF) neural network (NN) and the adaptive controller design scheme are proposed. According to Lyapunov stability analysis method, this paper gives the sufficient conditions that neural network controller can make this kind of uncertain nonlinear time-delay systems stable in the sense of Lyapunov. At last, the proposed neural network controller is verified to be correct and effective by the simulation examples.

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