scholarly journals Adaptive Fuzzy Tracking Control for a Class of Uncertain Nonlinear Time-Delayed Systems with Saturation Constrains

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Yu-Jun Zhang ◽  
Li-Bing Wu ◽  
Hong-Yang Zhao ◽  
Xiao-Dong Hu ◽  
Wen-Yu Zhang ◽  
...  
Keyword(s):  
Tracking Control ◽  
Mean Value ◽  
Van Der Pol Oscillator ◽  
Mean Value Theorem ◽  
Approximation Technique ◽  
Multiple Time ◽  
Tracking Errors ◽  
Delayed Systems ◽  
Input Nonlinearity ◽  
Adaptive Fuzzy

In this paper, the problem of adaptive fuzzy tracking control is considered for a class of uncertain nonaffine nonlinear systems with external disturbances, multiple time delays, and nonsymmetric saturation constrains. First, the mean value theorem is employed to deal with the nonaffine term with input nonlinearity. Then, a new adaptive fuzzy tracking controller with parameter updating laws is designed by using fuzzy approximation technique. Moreover, it is shown that all the closed-loop signals are bounded and the tracking errors can asymptotically converge to zero via the Lyapunov stability analysis. Finally, the simulation example for van der Pol oscillator system is worked out to verify the effectiveness of the proposed adaptive fuzzy design approach.

Adaptive decentralized fault-tolerant tracking control of a class of uncertain large-scale nonlinear systems with actuator faults

2016 ◽  
Vol 40 (3) ◽  
pp. 831-842 ◽  
Author(s):  
Yang Yang ◽  
Dong Yue
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Large Scale ◽  
Fault Tolerant ◽  
Dynamic Surface Control ◽  
Mean Value ◽  
Value Theory ◽  
Tracking Errors ◽  
Dynamic Surface ◽  
The Stability

We are concerned with the fault-tolerant tracking control affair for a class of large-scale multi-input and multi-output (MIMO) nonlinear systems suffering from actuator failures. Taking advantage of the mean-value theory and the implicit function theorem, the non-affine subsystems are transformed into affine forms. Neural networks (NNs) are utilized to approximate unknown virtual control signals, and then an adaptive NN-based decentralized tracking control strategy is exploited recursively by combining backstepping methods as well as the dynamic surface control (DSC) methodology. In theory, the stability of the resulting whole system is rigorously analysed, where it is proven that all signals remain uniformly ultimately bounded (UUB) and the designed strategy can guarantee the convergence of tracking errors via a suitable choice of control parameters. Finally, two simulation examples, both practical and numerical examples, are illustrated to verify the feasibility of the theoretical claims.

scholarly journals Adaptive fuzzy tracking control for a constrained flexible air-breathing hypersonic vehicle based on actuator compensation

2016 ◽  
Vol 13 (6) ◽  
pp. 172988141667111 ◽  
Author(s):  
Peng Fei Wang ◽  
Jie Wang ◽  
Xiang Wei Bu ◽  
Ying Jie Jia
Keyword(s):  
Tracking Control ◽  
Hypersonic Vehicle ◽  
Reference Trajectory ◽  
Fuzzy Logic Systems ◽  
Tracking Errors ◽  
Control Laws ◽  
Air Breathing ◽  
Adaptive Fuzzy ◽  
Adaptive Parameter ◽  
Actuator Constraints

The design of an adaptive fuzzy tracking control for a flexible air-breathing hypersonic vehicle with actuator constraints is discussed. Based on functional decomposition methodology, velocity and altitude controllers are designed. Fuzzy logic systems are applied to approximate the lumped uncertainty of each subsystem of air-breathing hypersonic vehicle model. Every controllers contain only one adaptive parameter that needs to be updated online with a minimal-learning-parameter scheme. The back-stepping design is not demanded by converting the altitude subsystem into the normal output-feedback formulation, which predigests the design of a controller. The special contribution is that novel auxiliary systems are developed to compensate both the tracking errors and desired control laws, based on which the explored controller can still provide effective tracking of velocity and altitude commands when the inputs are saturated. Finally, reference trajectory tracking simulation shows the effectiveness of the proposed method in its application to air-breathing hypersonic vehicle control.

scholarly journals On determinism and well-posedness in multiple time dimensions

2009 ◽  
Vol 465 (2110) ◽  
pp. 3023-3046 ◽  
Author(s):  
Walter Craig ◽  
Steven Weinstein
Keyword(s):  
Initial Value Problem ◽  
Mean Value ◽  
Uniqueness Result ◽  
Mean Value Theorem ◽  
Multiple Time ◽  
Fourier Synthesis ◽  
Initial Value ◽  
Codimension One ◽  
The Cauchy Problem ◽  
Arbitrary Space

We study the initial value problem for the wave equation and the ultrahyperbolic equation for data posed on initial hypersurfaces surface of arbitrary space–time signature. We show that, under a non-local constraint, the initial value problem posed on codimension-one hypersurfaces—the Cauchy problem—has global unique solutions in the Sobolev spaces H m . Thus, it is well-posed. However, we show that the initial value problem on higher codimension hypersurfaces is ill-posed due to failure of uniqueness, at least when specifying a finite number of derivatives of the data. This failure is in contrast to a uniqueness result for data given in an arbitrary neighbourhood of such initial hypersurfaces, which Courant deduces from Asgeirsson’s mean value theorem. We give a generalization of Courant’s theorem that extends to a broader class of equations. The proofs use Fourier synthesis and the Holmgren–John uniqueness theorem.

scholarly journals Approximation-Based Fixed-Time Adaptive Tracking Control for a Class of Uncertain Nonlinear Pure-Feedback Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Cheng He ◽  
Jian Wu ◽  
Jiyang Dai ◽  
Zhe Zhang ◽  
Libin Xu ◽  
...  
Keyword(s):  
Tracking Control ◽  
Tracking Error ◽  
Fixed Time ◽  
Mean Value ◽  
Design Parameters ◽  
Mean Value Theorem ◽  
Feedback Systems ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking ◽  
Time Control

This paper examines approximation-based fixed-time adaptive tracking control for a class of uncertain nonlinear pure-feedback systems. Novel virtual and actual controllers are designed that resolve the meaninglessness of virtual and actual controllers at the origin and in the negative domain, and the sufficient condition for the system to have semiglobal fixed-time stability is also provided. Radial basis function neural networks are introduced to approximate unknown functions for solving the fixed-time control problem of unknown nonlinear pure-feedback systems, and the mean value theorem is used to solve the problem of nonaffine structure in nonlinear pure-feedback systems. The controllers designed in this paper ensure that all signals in the closed-loop system are semiglobally uniform and ultimately bounded in a fixed time. Two simulation results show that appropriate design parameters can limit the tracking error within a region of the origin in a fixed time.

scholarly journals Adaptive Fuzzy Fast Finite-Time Tracking Control for Nonlinear Systems in Pure-Feedback Form with Unknown Disturbance

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Ke Xu ◽  
Huanqing Wang ◽  
Xiaoping Liu ◽  
Ming Chen
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Tracking Control ◽  
Tracking Error ◽  
Adaptive Fuzzy Control ◽  
Small Neighborhood ◽  
Mean Value Theorem ◽  
Feedback Form ◽  
Adaptive Fuzzy ◽  
Unknown Disturbance

In this paper, based on the fast finite-time stability theorem, an adaptive fuzzy control problem is considered for a class of nonlinear systems in pure-feedback form with unknown disturbance. In the controller design process, the mean value theorem is applied to address the nonaffine structure of the pure-feedback plant, the universal approximation capability of the fuzzy logic system (FLS) is utilized to compensate the unknown uncertainties, and the adaptive backstepping technique is used to design the controller model. Combined with the selection of the appropriate Lyapunov function at each step, a fuzzy-based adaptive tracking control scheme is proposed, which ensures that all signals in the closed-loop system are bounded and tracking error converges to a small neighborhood of the origin in fast finite-time. Finally, simulation results illustrate the validity of the proposed approach.

Quasi sliding mode control for chaotic symmetric gyros with linear-plus-cubic damping and input nonlinearity

2011 ◽  
Vol 18 (9) ◽  
pp. 1330-1335 ◽  
Author(s):  
Cheng-Fang Huang ◽  
Jui-Sheng Lin ◽  
Teh-Lu Liao ◽  
Jun-Juh Yan
Keyword(s):  
Sliding Mode Control ◽  
Numerical Simulations ◽  
Tracking Control ◽  
Sliding Mode ◽  
Design Method ◽  
Tracking Errors ◽  
Input Nonlinearity ◽  
Mode Control ◽  
Gyro System ◽  
Chattering Phenomenon

In this paper, a new concept of quasi sliding mode control (QSMC) is introduced for the tracking control of chaotic symmetric gyros with linear-plus-cubic damping. In contrast to previous works on sliding mode control, based on the proposed QSMC, the chattering phenomenon can be eliminated. Furthermore, the controlled gyro system can track desired trajectories and tracking errors can be driven into a predictable neighborhood of zero, even when the input nonlinearity is present. Numerical simulations are provided to demonstrate the effectiveness of the proposed QSMC design method.

Finite-time tracking control of hypersonic aircrafts with input saturation

2017 ◽  
Vol 232 (7) ◽  
pp. 1373-1389 ◽  
Author(s):  
Jing-Guang Sun ◽  
Shen-Min Song ◽  
Hai-Tao Chen ◽  
Xue-Hui Li
Keyword(s):  
Finite Time ◽  
Tracking Control ◽  
Sliding Mode ◽  
Digital Simulation ◽  
Input Saturation ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Parameter Uncertainties ◽  
Integral Sliding Mode ◽  
Sliding Mode Controllers

In this paper, the related research and analysis are made on the finite-time tracking control of hypersonic aircrafts. Two finite-time anti-saturation integral sliding mode controllers are designed with the consideration of external disturbances, coupling responses, model parameter uncertainties, and input saturation. Firstly, based on the mean value theorem, the control problem with input saturation constraints is transformed into the one without input constraints, which overcomes the assumption of the input boundedness. Secondly, two adaptive finite-time integral sliding mode controllers are designed: the first controller is finite-time stable, while the second controller is practical finite-time stable which utilizes the adaptive algorithms with low-pass filtering properties to ensure the boundedness of adaptive parameters. Finally, the digital simulation is carried out on different types of signals to further verify the validity and robustness of the proposed finite-time anti-saturation controllers.

Tracking Control System Design Based on Adaptive Neural Network

2014 ◽  
Vol 536-537 ◽  
pp. 1236-1239
Author(s):  
Liang Cheng
Keyword(s):  
Neural Network ◽  
Tracking Control ◽  
Rbf Neural Network ◽  
Gain Control ◽  
High Gain ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Affine Function ◽  
Control Scheme ◽  
Practical Engineering

The implicit function theorem and the mean value theorem non-affine function of the system into an affine form, and then RBF neural network approximation virtual control and actual control signals desired. Finally Lyapunov functional theory and backstepping method are used to design a self-adapt tracking control scheme. The proposed control scheme can guaranteed to achieve better tracking performance, thus avoiding the problems caused by the high-gain control affine term sector caused by design problems and overcome loop controller. In order to solve practical engineering control problems provides a theoretical basis and can learn from the ideas, and finally through numerical examples to demonstrate the effectiveness of the proposed method.

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