scholarly journals Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
J. Humberto Pérez-Cruz ◽  
José de Jesús Rubio ◽  
E. Ruiz-Velázquez ◽  
G. Solís-Perales
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Exponential Convergence ◽  
Broad Class ◽  
Tracking Error ◽  
The State ◽  
Control Law ◽  
Reference Trajectory ◽  
Uncertain Dynamics ◽  
The Difference

This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

Practical Tracking Control of a Class of Uncertain Surface Vessels Under Weak Assumptions on Uncertainties and Reference Trajectories

2021 ◽  
Author(s):  
Jian Li ◽  
Wenqing Xu ◽  
Zhaojing Wu ◽  
Yungang Liu
Keyword(s):  
Tracking Control ◽  
Broad Class ◽  
Tracking Error ◽  
Reference Trajectory ◽  
Unknown Parameters ◽  
Related Literature ◽  
Surface Vessels ◽  
Control Scheme ◽  
Reference Trajectories ◽  
Theoretical Results

Abstract This paper is devoted to the tracking control of a class of uncertain surface vessels. The main contributions focus on the considerable relaxation of the severe restrictions on system uncertainties and reference trajectory in the related literature. Specifically, all the system parameters are unknown and the disturbance is not necessarily to be differentiable in the paper, but either unknown parameters or disturbance is considered but the other one is excluded in the related literature, or both of them are considered but the disturbance must be continuously differentiable. Moreover, the reference trajectories in the related literature must be at least twice continuously differentiable and themselves as well as their time derivatives must be known for feedback, which are generalized to a more broad class ones that are unknown and only one time continuously differentiable in the paper. To solve the control problem, a novel practical tracking control scheme is presented by using backstepping scheme and adaptive technique, and in turn to derive an adaptive state-feedback controller which guarantees that all the states of the resulting closed-loop system are bounded while the tracking error arrives at and then stay within an arbitrary neighborhood of the origin. Finally, simulation is provided to validate the effectiveness of the proposed theoretical results.

scholarly journals Adaptive output regulation for a class of nonlinear systems with guaranteed transient performance

2019 ◽  
Vol 42 (6) ◽  
pp. 1180-1190
Author(s):  
Weijie Sun ◽  
Zhenhua Zhu ◽  
Jianglin Lan ◽  
Yunjian Peng
Keyword(s):  
Nonlinear Systems ◽  
Tracking Error ◽  
High Gain ◽  
Output Regulation ◽  
Control Law ◽  
Stabilization Problem ◽  
Transient Performance ◽  
Adaptive Stabilization ◽  
Output Tracking ◽  
Output Constraints

This paper is dedicated to adaptive output regulation for a class of nonlinear systems with asymptotic output tracking and guarantee of prescribed transient performance. With the employment of internal model principle, we first transform this problem into a specific adaptive stabilization problem with output constraints. Then, by integrating the time-varying Barrier Lyapunov Function (BLF) technique together with the high gain feedback method, we develop an output-based control law to solve the constrained stabilization problem and consequently confine the output tracking error to a predefined arbitrary region. The output-based control law enables adaptive output regulation in the sense that, under unknown exosystem dynamics, all the closed-loop system signals are bounded whilst the controlled output constraints are not violated. Finally, efficacy of the proposed design is illustrated through a simulation example.

scholarly journals Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
J. Humberto Pérez-Cruz ◽  
José de Jesús Rubio ◽  
Rodrigo Encinas ◽  
Ricardo Balcazar
Keyword(s):  
Neural Network ◽  
Trajectory Tracking ◽  
Feedback Linearization ◽  
Neural Control ◽  
Tracking Error ◽  
Uncertain System ◽  
Reference Trajectory ◽  
System A ◽  
Multiple Input ◽  
Feedback Linearization Control

The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.

scholarly journals A Novel Data-Driven Terminal Iterative Learning Control with Iteration Prediction Algorithm for a Class of Discrete-Time Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shangtai Jin ◽  
Zhongsheng Hou ◽  
Ronghu Chi
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Data Driven ◽  
Prediction Algorithm ◽  
Control Law ◽  
Control Input

A data-driven predictive terminal iterative learning control (DDPTILC) approach is proposed for discrete-time nonlinear systems with terminal tracking tasks, where only the terminal output tracking error instead of entire output trajectory tracking error is available. The proposed DDPTILC scheme consists of an iterative learning control law, an iterative parameter estimation law, and an iterative parameter prediction law. If the partial derivative of the controlled system with respect to control input is bounded, then the proposed control approach guarantees the terminal tracking error convergence. Furthermore, the control performance is improved by using more information of predictive terminal outputs, which are predicted along the iteration axis and used to update the control law and estimation law. Rigorous analysis shows the monotonic convergence and bounded input and bounded output (BIBO) stability of the DDPTILC. In addition, extensive simulations are provided to show the applicability and effectiveness of the proposed approach.

A Note on a Reduced-Order Observer Based Controller for a Class of Lipschitz Nonlinear Systems

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Mohamadreza Homayounzade ◽  
Mehdi Keshmiri
Keyword(s):  
Nonlinear Systems ◽  
Global Exponential Stability ◽  
Degrees Of Freedom ◽  
Large Range ◽  
Robot Manipulator ◽  
Tracking Error ◽  
Control Law ◽  
Reduced Order ◽  
Lipschitz Nonlinear Systems ◽  
Reduced Order Observer

This paper presents a novel reduced-order observer based controller for a class of Lipschitz nonlinear systems, described by a set of second order ordinary differential equations. The control law is designed based on the measured output and estimated states. The main features are: (1) The computation cost is reduced noticeably, since the observer is a reduced-order one; (2) The controller guarantees semi-global exponential stability for both estimation and tracking error; and (3) The proposed method can be used in a large range of applications, especially in mechanical systems. The effectiveness of the proposed method is investigated through the numerical simulation for a two-degrees-of-freedom robot manipulator acting on a horizontal worktable.

NEURAL NETWORK-BASED DIGITAL REDESIGN APPROACH FOR CONTROL OF UNKNOWN CONTINUOUS-TIME CHAOTIC SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2433-2455
Author(s):  
JOSE I. CANELON ◽  
LEANG S. SHIEH ◽  
SHU M. GUO ◽  
HEIDAR A. MALKI
Keyword(s):  
Neural Network ◽  
State Space ◽  
Continuous Time ◽  
Digital Control ◽  
Chaotic Systems ◽  
Linear Time ◽  
The State ◽  
Control Law ◽  
Analog Control ◽  
Digital Redesign

This paper presents a neural network-based digital redesign approach for digital control of continuous-time chaotic systems with unknown structures and parameters. Important features of the method are that: (i) it generalizes the existing optimal linearization approach for the class of state-space models which are nonlinear in the state but linear in the input, to models which are nonlinear in both the state and the input; (ii) it develops a neural network-based universal optimal linear state-space model for unknown chaotic systems; (iii) it develops an anti-digital redesign approach for indirectly estimating an analog control law from a fast-rate digital control law without utilizing the analog models. The estimated analog control law is then converted to a slow-rate digital control law via the prediction-based digital redesign method; (iv) it develops a linear time-varying piecewise-constant low-gain tracker which can be implemented using microprocessors. Illustrative examples are presented to demonstrate the effectiveness of the proposed methodology.

scholarly journals Novel semiactive suspension using a magnetorheological elastomer (MRE)-based absorber and adaptive neural network controller for systems with input constraints

2020 ◽  
Vol 11 (2) ◽  
pp. 465-479
Author(s):  
Xuan Bao Nguyen ◽  
Toshihiko Komatsuzaki ◽  
Hoa Thi Truong
Keyword(s):  
Neural Network ◽  
Active Region ◽  
The State ◽  
Design System ◽  
Input Constraints ◽  
Magnetorheological Elastomer ◽  
Adaptive Neural Network ◽  
Neural Network Controller ◽  
Uncertain Dynamics ◽  
Quarter Car

Abstract. For most existing semiactive systems, it is commonly known that the stability and tracking performance will deteriorate in a real application due to the input constraints and nonlinearity in the system. In this study, in order to overcome the above shortcomings, a novel bench-scale suspension plant using a magnetorheological elastomer (MRE)-based absorber accompanied with an adaptive and global neural-network-based tracking controller is introduced. The adaptive neural network (ANN) is used to estimate the uncertain dynamics of the quarter-car model. The novel scheme consists of three parts, including a conventional ANN controller dominating the active region of neurons, a robust controller serving as a temporary controller to pull back the state into the active region when the neural approximation falls outside, and a switch to be used to monitor the activation of the neural part and switch the control authority between the above two controllers. The controller ensures that a globally uniform ultimate boundedness can be achieved. Furthermore, an auxiliary design system was added to the controller in order to deal with the effects of input constraints, and the state was analyzed for the tracking of the stabilization. The control scheme ensures that the output of the system converges to the vicinity of a reference trajectory and all the signals are globally, uniformly, and ultimately bounded. The simulation and experimental results demonstrate that the proposed controller can effectively suppress the vibrations of the semiactive quarter car.

Multi-dimensional Taylor network modelling and optimal control of SISO nonlinear systems for tracking by output feedback

2019 ◽  
Vol 37 (3) ◽  
pp. 699-717 ◽  
Author(s):  
Qi-Ming Sun ◽  
Hong-Sen Yan
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Nonlinear Systems ◽  
Real Time ◽  
Output Feedback ◽  
Tracking Error ◽  
Real Time Control ◽  
Network Modelling ◽  
Single Input Single Output ◽  
Time Control

Abstract In this paper, a multi-dimensional Taylor network (MTN) output feedback tracking control of nonlinear single-input single-output (SISO) systems in discrete-time form is studied. To date, neural networks are generally used to identify unknown nonlinear systems. However, the neuron of neural networks includes the exponential function, which contributes to the complexity of calculation, making the neural network control unable to meet the real-time requirements. In order to identify the controlled object whose model is unknown, the MTN, which requires only addition and multiplication, is utilized for successful real-time control of the SISO nonlinear system based on only its output feedback. Lyapunov analysis proves that output signals in the closed-loop system remain bounded and the tracking error converges to an arbitrarily small neighbourhood around the origin. In contrast to the back propagation (BP) neural network self-adaption reconstitution controller, the edge of the scheme is that the MTN optimal controller promises desirable response speed, robustness and real-time control.

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