Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
S. Dharani ◽  
R. Rakkiyappan ◽  
Jinde Cao
Keyword(s):  
Lyapunov Functional ◽  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sampled Data ◽  
Stiffness Matrices ◽  
Sampling Intervals ◽  
Data Controller ◽  
Wirtinger’S Inequality ◽  
Theoretical Results

This paper considers a class of mechanical systems with uncertainties appearing in all the mass, damping, and stiffness matrices. Two cases, linear fractional and randomly occurring uncertainty formulations, are considered. Since sampled-data controllers have an advantage of implementing with microcontroller or digital computer to lower the implementation cost and time, a robust stochastic sampled-data controller is considered with m sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov functional based on the extended Wirtinger's inequality is constructed with triple integral terms and sufficient conditions that promises the robust mean square asymptotic stability of the concerned system are derived in terms of linear matrix inequalities (LMIs). In an aim to reduce the conservatism, a newly introduced concept called the second-order reciprocally convex approach is employed in deriving the bound for some cross terms that arise while maneuvering the derivative of Lyapunov functional. The obtained LMIs can be easily solved through any of the standard available software. Finally, numerical examples are given to verify the effectiveness of the proposed theoretical results.

Pinning synchronization control of complex networks with partial couplings

2020 ◽  
pp. 095965181989833
Author(s):  
Yanzhou Li ◽  
Yishan Liu ◽  
Yuanqing Wu ◽  
Shenghuang He
Keyword(s):  
Complex Networks ◽  
Linear Matrix ◽  
Sampled Data ◽  
Lower And Upper Bounds ◽  
Target Node ◽  
Decoupling Method ◽  
Synchronization Problem ◽  
Sampling Intervals ◽  
Wirtinger’S Inequality ◽  
Theoretical Results

In this article, the pinning synchronization problem of complex networks with a target node via sampled-data communications is considered. Due to partial couplings among the nodes in complex networks, a decoupling method is adopted to investigate each channel of complex networks independently. By constructing a time-dependent Lyapunov function, it is proved that the pinning synchronization of complex networks with a target node can be achieved if the control parameters are appropriately selected. Furthermore, further study is needed to investigate the pinning synchronization of complex networks in the presence of constant delay. A novel criterion is obtained using Jensen’s inequality and Wirtinger’s inequality. It is worth noting that the lower and upper bounds of the sampling intervals can be calculated by linear matrix inequality box of MATLAB. Theoretical results are well verified through a numerical simulation.

Dissipativity-Based Reliable Sampled-Data Control With Nonlinear Actuator Faults

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
Srimanta Santra ◽  
R. Sakthivel ◽  
B. Kaviarasan
Keyword(s):  
Sufficient Conditions ◽  
Control Design ◽  
Delay Systems ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Actuator Faults ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Data Controller

In this paper, the problem of reliable sampled-data control design with strict dissipativity for a class of linear continuous-time-delay systems against nonlinear actuator faults is studied. The main objective of this paper is to design a reliable sampled-data controller to ensure a strictly dissipative performance for the closed-loop system. Based on the linear matrix inequality (LMI) optimization approach and Wirtinger-based integral inequality, a new set of sufficient conditions is established for reliable dissipativity analysis of the considered system by assuming the mixed actuator fault matrix to be known. Then, the proposed result is extended to unknown fault matrix case. Also, the reliable sampled-data controller with strict dissipativity is designed by solving a convex optimization problem which can be easily solved by using standard numerical algorithms. Finally, a numerical example based on liquid propellant rocket motor with a pressure feeding system model is presented to illustrate the effectiveness of the developed control design technique.

Reliable Robust Control Design for Uncertain Mechanical Systems

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
R. Sakthivel ◽  
Srimanta Santra ◽  
K. Mathiyalagan ◽  
A. Arunkumar
Keyword(s):  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Linear Matrix ◽  
Actuator Failure ◽  
Time Varying Delay ◽  
Stiffness Matrices ◽  
Control Scheme ◽  
Robust Control Design ◽  
Varying Delay

In this article, we consider the problem of reliable H∞ control for a class of uncertain mechanical systems with input time-varying delay and possible occurrence of actuator faults. In particular, we assume that linear fractional transformation (LFT) uncertainty formulations appear in the mass, damping, and stiffness matrices. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable while satisfying a prescribed H∞ performance constraint. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived in terms of LMIs for the existence of robust reliable H∞ controller. Further, Schur complement and Jenson's integral inequality are used to substantially simplify the derivation in the main results. The obtained results are formulated in terms of LMIs which can be easily verified by the standard numerical softwares. Finally, numerical examples with simulation result are provided to illustrate the applicability and effectiveness of the proposed reliable H∞ control scheme. The numerical results reveal that the proposed theory significantly improves the upper bound of time delays and minimum feasible H∞ performance index over some existing works.

Stochastic Sampled-Data Control for H∞ Stabilization of Transport Reaction Systems

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
R. Rakkiyappan ◽  
S. Dharani
Keyword(s):  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Control Input ◽  
Sampled Data ◽  
Transport Reaction ◽  
Reaction Systems ◽  
Data Control ◽  
Sampled Data Control ◽  
Discontinuous Lyapunov Functional

This paper investigates the problem of stochastic sampled-data H∞ control for a class of parabolic systems governed by one-dimensional semilinear transport reaction systems with external disturbances. A sampled-data controller design is developed by introducing the time-varying delay in the control input signals. The m sampling periods are considered whose occurrence probabilities are known constants and satisfy Bernoulli distribution. Since discontinuous Lyapunov functional copes well with problems of sampled-data control systems, a discontinuous Lyapunov functional is constructed based on the extended Wirtinger’s inequality. With this new approach, sufficient conditions that guarantee the asymptotic mean-square stabilization of the considered systems and the L2-gain analysis are derived in terms of linear matrix inequalities (LMIs), which can be solved by any of the available software.

Exponentially Stable Sampled-Data Control for Uncertain Systems

2014 ◽  
Vol 981 ◽  
pp. 551-554
Author(s):  
Li Ying Fan
Keyword(s):  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Control Input ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Exponentially Stable ◽  
Data Controller ◽  
Continuous Time System

In this paper, the problem of the exponentially stable sampled-data control was investigated for a class of uncertain systems. Based on the input delay approach, the system was modeled as a continuous-time system with the delayed control input. Attention was focused on the design of a state feedback sampled-data controller which guarantees the exponential stability of the closed-loop system for all admissible parametric uncertainties. Using linear matrix inequality (LMI) approach, sufficient conditions are obtained. Simulation example was given to demonstrate the effectiveness and correctness of the proposed method.

scholarly journals H∞ Sampled-Data Control for Singular Neutral System

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Minjie Zheng ◽  
Yujie Zhou ◽  
Shenhua Yang ◽  
Lina Li ◽  
Yongfeng Suo
Keyword(s):  
Singular System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Neutral System ◽  
Sampled Data ◽  
Composite State ◽  
Time Varying Delay ◽  
Data Control ◽  
Conservative Result ◽  
Data Controller

This study is concerned with the H∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed H∞ performance. Then, the H∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective.

scholarly journals Sampled-Data Control of Singular Systems with Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Zheng Minjie ◽  
Zhou Yujie ◽  
Yang Shenhua ◽  
Li Lina
Keyword(s):  
Controller Design ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Linear Matrix ◽  
Sampled Data ◽  
Data Control ◽  
Exponentially Stable ◽  
Data Controller

This paper is concerned with sampled-data controller design for singular systems with time delay. It is assumed that the sampling periods are arbitrarily varying but bounded. A time-dependent Lyapunov function is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Combining input delay approach with Lyapunov method, sufficient conditions are derived which guarante that the singular system is regular, impulse free, and exponentially stable. Then, the existence conditions of desired sampled-data controller can be obtained, which are formulated in terms of strict linear matrix inequality. Finally, numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Robust H∞ control of neutral system for sampled-data dynamic positioning ships

2018 ◽  
Vol 36 (4) ◽  
pp. 1325-1345 ◽  
Author(s):  
Minjie Zheng ◽  
Yujie Zhou ◽  
Shenhua Yang ◽  
Lina Li
Keyword(s):  
Sufficient Conditions ◽  
Control Law ◽  
Dynamic Positioning ◽  
Neutral System ◽  
Time Varying ◽  
Sampled Data ◽  
Stability Theorems ◽  
Data Control ◽  
Conservative Result ◽  
Data Controller

Abstract This study focuses on the robust ${H}_{\infty }$ sampled-data control problem of neutral system for dynamic positioning (DP) ships. Using the input delay approach and a state-derivative control law, the ship DP system is turned into a neutral system with time-varying delays. By incorporating the delay-decomposition technique, Wirtinger-based integral inequality and an augmented Lyapunov–Krasovskii functional, less conservative result is derived for the resulting system. Sufficient conditions are established to determine the system’s asymptotical stability and achieve ${H}_{\infty }$ performance using Lyapunov stability theorems. Then the ${H}_{\infty }$ sampled-data controller is obtained by analyzing the stabilization conditions. Finally, simulation result is shown that the proposed method is effective.

Formation-containment control of sampled-data second-order multi-agent systems with sampling delay

2018 ◽  
Vol 40 (16) ◽  
pp. 4369-4381 ◽  
Author(s):  
Baojie Zheng ◽  
Xiaowu Mu
Keyword(s):  
Matrix Theory ◽  
Sufficient Conditions ◽  
Second Order ◽  
Control Problems ◽  
Sampled Data ◽  
Multi Agent Systems ◽  
Containment Control ◽  
Agent Systems ◽  
Multi Agent ◽  
Theoretical Results

The formation-containment control problems of sampled-data second-order multi-agent systems with sampling delay are studied. In this paper, we assume that there exist interactions among leaders and that the leader’s neighbours are only leaders. Firstly, two different control protocols with sampling delay are presented for followers and leaders, respectively. Then, by utilizing the algebraic graph theory and matrix theory, several sufficient conditions are obtained to ensure that the leaders achieve a desired formation and that the states of the followers converge to the convex hull formed by the states of the leaders, i.e. the multi-agent systems achieve formation containment. Furthermore, an explicit expression of the formation position function is derived for each leader. An algorithm is provided to design the gain parameters in the protocols. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.

scholarly journals Exponential Synchronization for Stochastic Neural Networks with Mixed Time Delays and Markovian Jump Parameters via Sampled Data

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yingwei Li ◽  
Xueqing Guo
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Stochastic Neural Networks ◽  
Sampled Data ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Mixed Time Delays ◽  
Data Controller

The exponential synchronization issue for stochastic neural networks (SNNs) with mixed time delays and Markovian jump parameters using sampled-data controller is investigated. Based on a novel Lyapunov-Krasovskii functional, stochastic analysis theory, and linear matrix inequality (LMI) approach, we derived some novel sufficient conditions that guarantee that the master systems exponentially synchronize with the slave systems. The design method of the desired sampled-data controller is also proposed. To reflect the most dynamical behaviors of the system, both Markovian jump parameters and stochastic disturbance are considered, where stochastic disturbances are given in the form of a Brownian motion. The results obtained in this paper are a little conservative comparing the previous results in the literature. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

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