scholarly journals Adaptive Constrained Control for Uncertain Nonlinear Time-Delay System with Application to Unmanned Helicopter

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Rong Li ◽  
Qingxian Wu ◽  
Qingyun Yang ◽  
Hui Ye
Keyword(s):  
Time Delay ◽  
External Disturbance ◽  
Good Control ◽  
Delay System ◽  
Unmanned Helicopter ◽  
Robust Controller ◽  
Delayed Systems ◽  
Prescribed Performance ◽  
The Neural Network ◽  
The Stability

This paper investigates a class of nonlinear time-delayed systems with output prescribed performance constraint. The neural network and DOB (disturbance observer) are designed to tackle the uncertainties and external disturbance, and prescribed performance function is constructed for the output prescribed performance constrained problem. Then the robust controller is designed by using adaptive backstepping method, and the stability analysis is considered by using Lyapunov-Krasovskii. Furthermore, the proposed method is employed into the unmanned helicopter system with time-delay aerodynamic uncertainty. Finally, the simulation results illustrate that the proposed robust prescribed performance control system achieved a good control performance.

scholarly journals Weighted Multiple-Model Neural Network Adaptive Control for Robotic Manipulators with Jumping Parameters

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Jiazhi Li ◽  
Weicun Zhang ◽  
Quanmin Zhu
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Robotic Manipulators ◽  
Adaptive Observer ◽  
Multiple Model ◽  
Neural Network Controller ◽  
The Neural Network ◽  
The Stability

This study addresses the tracking control issue for n-link robotic manipulators with largely jumping parameters. Based on radial basis function neural networks (RBFNNs), we propose weighted multiple-model neural network adaptive control (WMNNAC) approach. To cover the variation ranges of the parameters, different models of robotic are constructed. Then, the corresponding local neural network controller is constructed, in which the neural network has been used to approximate the uncertainty part of the control law, and an adaptive observer is implemented to estimate the true external disturbance. The WMNNAC strategy with improved weighting algorithm is adopted to ensure the tracking performance of the robotic manipulator system when parameters jump largely. Through the Lyapunov stability theory and the method of virtual equivalent system (VES), the stability of the closed-loop system is proved. Finally, the simulation results of a two-link manipulator verify the feasibility and efficiency of the proposed WMNNAC strategy.

On the stability bifurcation of a nonlinear time delay system

Automatica ◽  
1998 ◽  
Vol 34 (3) ◽  
pp. 375-378 ◽  
Author(s):  
Mustapha S. Fofana ◽  
David J. Lamb
Keyword(s):  
Time Delay ◽  
Delay System ◽  
Time Delay System ◽  
The Stability

Active Vibration Suppression With Time Delayed Feedback

2003 ◽  
Vol 125 (3) ◽  
pp. 384-388 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Vibration Suppression ◽  
Linear Time ◽  
Direct Method ◽  
System Stability ◽  
Delayed Systems ◽  
Active Vibration Suppression ◽  
Active Vibration ◽  
The Stability

Various active vibration suppression techniques, which use feedback control, are implemented on the structures. In real application, time delay can not be avoided especially in the feedback line of the actively controlled systems. The effects of the delay have to be thoroughly understood from the perspective of system stability and the performance of the controlled system. Often used control laws are developed without taking the delay into account. They fulfill the design requirements when free of delay. As unavoidable delay appears, however, the performance of the control changes. This work addresses the stability analysis of such dynamics as the control law remains unchanged but carries the effect of feedback time-delay, which can be varied. For this stability analysis along the delay axis, we follow up a recent methodology of the authors, the Direct Method (DM), which offers a unique and unprecedented treatment of a general class of linear time invariant time delayed systems (LTI-TDS). We discuss the underlying features and the highlights of the method briefly. Over an example vibration suppression setting we declare the stability intervals of the dynamics in time delay space using the DM. Having assessed the stability, we then look at the frequency response characteristics of the system as performance indications.

The Stability Analysis and Planning for Multivariable Linear Time-Delay Systems and its Application in Supervision Oilfield

2013 ◽  
Vol 709 ◽  
pp. 727-730
Author(s):  
Ren Wang ◽  
Xue Kun Qi ◽  
Long Xing
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Linear Time ◽  
Control Process ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Water Separation ◽  
Delayed Systems ◽  
Delayed System ◽  
The Stability

Based on Lyapunovs theory of stability, analyze on a control process of oil-water separation with time-delay, coupling and uncertainty in the unite station. a equation of sufficient condition for multi-variable Linear Delayed Systems with delayed independent stabilization is derived and another forms are also given. Based on this, several simple criterions for judging independent stabilization from linear delayed system are presented. We also discuss the exponential stability for delayed system and also provide the sufficient condition of exponential stability with any appointed convergent rate and its corresponding deductions. Using these conditions, we can choose a set of suitable parameters to reduce the conservation. By calculating and being compared with methods of the literature, the results show that our methods have less conservation.

scholarly journals Synchronization approach for chaotic time-varying delay system based on Wirtinger inequality

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668902
Author(s):  
Zhanshan Zhao ◽  
Meili He ◽  
Jing Zhang ◽  
Guowei Xu
Keyword(s):  
Time Delay ◽  
Stability Criterion ◽  
Delay System ◽  
Jensen Inequality ◽  
Time Delay System ◽  
Control Approach ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
The Stability ◽  
Varying Delay

A novel control approach based on Wirtinger inequality is designed for nonlinear chaos synchronization time delay system. In order to reduce the conservatism for the stability criterion, a Lyapunov–Krasovskii functional with triple-integral term is constructed. The improved Wirtinger inequality is used to reduce the conservative which is caused by Jensen inequality, and a stability criterion is proposed by reciprocally convex method. Furthermore, a state feedback controller is designed to synchronize the master-slave systems based on the proposed criteria through cone complementary linearization approach. Finally, a simulation for Lorenz chaos time delay system is given to prove the validity based on the proposed synchronization control approach.

On Stability Analysis of Switched Linear Time-Delay Systems under Arbitrary Switching

2015 ◽  
pp. 480-515 ◽  
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Lyapunov Function ◽  
Continuous Time ◽  
Delay System ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Arbitrary Switching ◽  
The Stability

This chapter focuses on the stability analysis problem for a class of continuous-time switched time-delay systems modelled by delay differential equations under arbitrary switching. Then, a transformation under the arrow form is employed. Indeed, by using a constructed Lyapunov function, the aggregation techniques, the Kotelyanski lemma associated with the M-matrix properties, new delay-dependent sufficient stability conditions are derived. The obtained results provide a solution to one of the basic problems in continuous-time switched time-delay systems. This problem ensures asymptotic stability of the switched time-delay system under arbitrary switching signals. In addition, these stability conditions are extended to be generalized for switched systems with multiple delays. Noted that, these obtained results are explicit, simple to use, and allow us to avoid the problem of searching a common Lyapunov function. Finally, two examples are provided, with numerical simulations, to demonstrate the effectiveness of the proposed method.

scholarly journals H∞ Control of Coronary Artery Input Time-Delay System via the Free-Matrix-Based Integral Inequality

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Sha-sha Li ◽  
Zhan-shan Zhao ◽  
Jing Zhang ◽  
Jie Sun ◽  
Lian-kun Sun
Keyword(s):  
Coronary Artery ◽  
Time Delay ◽  
Integral Inequality ◽  
Controller Design ◽  
Convex Combination ◽  
External Disturbance ◽  
Delay System ◽  
Linear Matrix ◽  
Time Delay System ◽  
Input Time

The issue of H∞ control for the coronary artery input time-delay system with external disturbance is of concern. To further reduce conservation, we utilize the free-matrix-based integral inequality, Wirtinger-based integral inequality, and reciprocal convex combination approach to construct Lyapunov-Krasovskii function (LKF). Then a sufficient condition for controller design which can guarantee robust synchronization the coronary artery system is represented in terms of linear matrix inequality (LMI). Finally, a numerical example is exploited to show the effectiveness of the proposed methods.

scholarly journals Stochastic stability of linear time-delay system with Markovian jumping parameters

1997 ◽  
Vol 3 (3) ◽  
pp. 187-201 ◽  
Author(s):  
K. Benjelloun ◽  
E. K. Boukas
Keyword(s):  
Time Delay ◽  
Stochastic Stability ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay System ◽  
Delay Systems ◽  
Necessary Condition ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
The Stability

This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP). We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.

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