Robust Adaptive Inverse Optimal Tracking for Strict-Feedback Stochastic Nonlinear System

2010 ◽  
Vol 143-144 ◽  
pp. 984-989 ◽  
Author(s):  
Lu Wang
Keyword(s):  
Reference Signal ◽  
Original System ◽  
Optimal Tracking ◽  
Stochastic Nonlinear System ◽  
Parameters Uncertainty ◽  
Adaptive Laws ◽  
Error System ◽  
Robust Adaptive ◽  
Backstepping Algorithm ◽  
Strict Feedback

For a class of strict-feedback nonlinear systems with unknown constant parameters, uncertainty in the input gains and standard Wiener-noise, combining the system function with the known reference signal, the error system is obtained. The adaptive inverse optimal controller and adaptive laws of parameters are designed using Backstepping algorithm, thus the robust adaptive inverse optimal tracking problem of original system is solved．

scholarly journals Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Xiao Yu ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Tracking Error ◽  
Reference Signal ◽  
Original System ◽  
Linear Matrix ◽  
Preview Control ◽  
Lipschitz Nonlinear Systems ◽  
Error System ◽  
Discrete Integrator

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

Design of an Optimal Preview Controller for Dual-Rate Linear Discrete-Time Systems

2018 ◽  
Vol 6 (2) ◽  
pp. 178-192 ◽  
Author(s):  
Yujian Guo ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Reference Signal ◽  
Sufficient Conditions ◽  
Original System ◽  
Discrete Time System ◽  
Linear Quadratic ◽  
Preview Control ◽  
Time System ◽  
Lifting Technique ◽  
Error System

Abstract A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system is converted into a single-rate augmented system. On this basis, the augmented error system is constructed by introducing a first-order difference operator and the previewable reference signal. Then the tracking problem is transformed into a regulator problem of the augmented error system. The optimal preview control law of the augmented error system is obtained by using standard linear quadratic optimal preview control theory, and then the optimal preview controller of the original system is derived. In addition, the necessary and sufficient conditions for the controller are given. Finally, simulation results show the effectiveness of the proposed method.

scholarly journals Preview tracking control for a class of fractional-order linear systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fucheng Liao ◽  
Hao Xie
Keyword(s):  
Linear System ◽  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Tracking Control ◽  
Reference Signal ◽  
Original System ◽  
State Equation ◽  
Order Linear ◽  
Error System

AbstractThis paper studies the preview tracking control of a class of fractional-order linear systems. Firstly, we use the fractional derivative property to take the fractional derivative of both sides of the state equation several times, and we obtain a formal ordinary linear system. An augmented error system is constructed for the transformed ordinary linear system, the appropriate performance index function is introduced and relevant results of the optimal preview control are applied to design the optimal preview controller for the augmented error system when the reference signal is previewable. Based on the relationship between the original system and the augmented error system, the preview tracking controller of the original system can be obtained. It can guarantee the asymptotic tracking of the output of the original closed-loop system to the reference signal. The validity of the theoretical results is verified by numerical simulation.

scholarly journals Synchronization of Switched Interval Networks and Applications to Chaotic Neural Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jinde Cao ◽  
Abdulaziz Alofi ◽  
Abdullah Al-Mazrooei ◽  
Ahmed Elaiw
Keyword(s):  
Neural Networks ◽  
Matrix Measure ◽  
Chaotic Neural Networks ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Arbitrary Switching ◽  
Parameters Uncertainty ◽  
Inequality Technique ◽  
Error System ◽  
Switched Interval Networks

This paper investigates synchronization problem of switched delay networks with interval parameters uncertainty, based on the theories of the switched systems and drive-response technique, a mathematical model of the switched interval drive-response error system is established. Without constructing Lyapunov-Krasovskii functions, introducing matrix measure method for the first time to switched time-varying delay networks, combining Halanay inequality technique, synchronization criteria are derived for switched interval networks under the arbitrary switching rule, which are easy to verify in practice. Moreover, as an application, the proposed scheme is then applied to chaotic neural networks. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

scholarly journals Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Fucheng Liao ◽  
Yingxue Wu ◽  
Xiao Yu ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Tracking Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Error System ◽  
Finite Time Boundedness ◽  
Boundedness Problem ◽  
Time Systems

A finite-time bounded tracking control problem for a class of linear discrete-time systems subject to disturbances is investigated. Firstly, by applying a difference method to constructing the error system, the problem is transformed into a finite-time boundedness problem of the output vector of the error system. In fact, this is a finite-time boundedness problem with respect to the partial variables. Secondly, based on the partial stability theory and the research methods of finite-time boundedness problem, a state feedback controller formulated in form of linear matrix inequality is proposed. Based on this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is presented to illustrate the effectiveness of the controller.

Modeling and Dynamic Surface Control of Uncertain Strict-Feedback Nonlinear Systems Using Adaptive Fuzzy Wavelet Network

2018 ◽  
pp. 112-133
Author(s):  
Maryam Shahriari-Kahkeshi
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Surface Control ◽  
Wavelet Network ◽  
Dynamic Surface ◽  
Adaptive Fuzzy ◽  
Surface Control ◽  
Control Scheme ◽  
Adaptive Laws ◽  
Dsc Method ◽  
Strict Feedback

This chapter proposes a new modeling and control scheme for uncertain strict-feedback nonlinear systems based on adaptive fuzzy wavelet network (FWN) and dynamic surface control (DSC) approach. It designs adaptive FWN as a nonlinear-in-parameter approximator to approximate the uncertain dynamics of the system. Then, the proposed control scheme is developed by incorporating the DSC method to the adaptive FWN-based model. Stability analysis of the proposed scheme is provided and adaptive laws are designed to learn all linear and nonlinear parameters of the network. It is proven that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can be made arbitrary small. The proposed scheme does not require any prior knowledge about dynamics of the system and offline learning. Furthermore, it eliminates the “explosion of complexity” problems and develops accurate model of the system and simple controller. Simulation results on the numerical example and permanent magnet synchronous motor are provided to show the effectiveness of the proposed scheme.

Output tracking and disturbance rejection for 1-D anti-stable wave equation

2019 ◽  
Vol 25 ◽  
pp. 69 ◽  
Author(s):  
Hua-Cheng Zhou
Keyword(s):  
Wave Equation ◽  
Disturbance Rejection ◽  
External Disturbance ◽  
Reference Signal ◽  
Original System ◽  
Delay Systems ◽  
Transport Systems ◽  
Control Law ◽  
Proportional Control ◽  
Output Tracking

In this paper, we solve the output tracking and disturbance rejection problem for a system described by a one-dimensional anti-stable wave equation, with reference and disturbance signals that belong to W1,∞[0, ∞) and L∞[0, ∞), respectively. Generally, these signals cannot be generated from an exosystem. We explore an approach based on proportional control. It is shown that a proportional gain controller can achieve exponentially the output tracking while rejecting disturbance. Our method consists of three steps: first, we convert the original system without disturbance into two transport equations with an ordinary differential equation by using Riemann variables, then we propose a proportional control law by making use of the properties of transport systems and time delay systems. Second, based on our recent result on disturbance estimator, we apply the estimation/cancellion strategy to cancel to the external disturbance and to track the reference asymptotically. Third, we design a controller using a state observer. Since disturbance does not appear in the observer explicitly (the disturbance is exactly compensated), the controlled output signal is exponentially tracking the reference signal. As a byproduct, we obtain a new output feedback stabilizing control law by which the resulting closed-loop system is exponentially stable using only two displacement output signals.

scholarly journals A Novel Robust Adaptive Backstepping Method Combined with SMC on Strict-Feedback Nonlinear Systems Using Neural Networks

2019 ◽  
Vol 291 ◽  
pp. 01001
Author(s):  
Yahui Li ◽  
Feng Gao ◽  
Franco Bernelli-Zazzera ◽  
Zeyou Tong ◽  
Fugui Li ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode ◽  
Design Method ◽  
The Novel ◽  
Backstepping Method ◽  
Adaptive Backstepping ◽  
Closed Loop Systems ◽  
Robust Adaptive ◽  
Derivatives Of ◽  
Strict Feedback

Adaptive backstepping methodology is a powerful tool for nonlinear systems, especially for strict-feedback ones, but its robustness still needs improvements. In this paper, combined with sliding mode control (SMC), a new backstepping design method is proposed to guarantee the robustness. In this method, based on the novel combining method, the auxiliary controller is introduced only in the final step of the real controller, unlike traditional methods, which usually all include an auxiliary controller in every de-signing step to guarantee the robustness of the closed-loop systems. The novel combing methods can avoid calculating multiple and high-order derivatives of the auxiliary controllers in the intermediate steps, low-ering the computational burden in evaluating the controller. The effectiveness of the proposed approach is illustrated from simulation results.

Sign in / Sign up

Export Citation Format

Share Document