scholarly journals RobustH∞Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Cheng-Dong Yang ◽  
Jianlong Qiu ◽  
Jun-Wei Wang
Keyword(s):  
Decay Rate ◽  
Design Method ◽  
Direct Method ◽  
Distributed Parameter Systems ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Spatial Derivative ◽  
Control Approach ◽  
Exponentially Stable

This paper addresses the problem of robustH∞control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robustH∞P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribedH∞performance of disturbance attenuation. Moreover, a suboptimalH∞controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.

scholarly journals RobustH∞Filtering for Networked Control Systems with Random Sensor Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shenping Xiao ◽  
Liyan Wang ◽  
Hongbing Zeng ◽  
Lingshuang Kong ◽  
Bin Qin
Keyword(s):  
Networked Control Systems ◽  
Filter Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Attenuation Level ◽  
Exponentially Stable ◽  
Disturbance Attenuation Level ◽  
Filter Design Method

The robustH∞filtering problem for a class of network-based systems with random sensor delay is investigated. The sensor delay is supposed to be a stochastic variable satisfying Bernoulli binary distribution. Using the Lyapunov function and Wirtinger’s inequality approach, the sufficient conditions are derived to ensure that the filtering error systems are exponentially stable with a prescribedH∞disturbance attenuation level and the filter design method is proposed in terms of linear matrix inequalities. The effectiveness of the proposed method is illustrated by a numerical example.

scholarly journals Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Chengdong Yang ◽  
Jianlong Qiu ◽  
Kejia Yi ◽  
Xiangyong Chen ◽  
Ancai Zhang ◽  
...  
Keyword(s):  
Direct Method ◽  
Variable Coefficients ◽  
Distributed Parameter Systems ◽  
Exponential Synchronization ◽  
Nonlinear Perturbation ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Synchronization Problem ◽  
Time Space ◽  
Pde Systems

This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.

scholarly journals Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaona Song ◽  
Mi Wang ◽  
Shuai Song ◽  
Jingtao Man
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Control Gain

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

H 2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach

2011 ◽  
Author(s):  
Xin Wang ◽  
Edwin E. Yaz ◽  
Susan C. Schneider ◽  
Yvonne I. Yaz
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Time Step ◽  
Control Approach ◽  
The Difference

A novel H2–H∞ State Dependent Riccati Equation control approach is presented for providing a generalized control framework to discrete time nonlinear system. By solving a generalized Riccati Equation at each time step, the nonlinear state feedback control solution is found to satisfy mixed performance criteria guaranteeing quadratic optimality with inherent stability property in combination with H∞ type of disturbance attenuation. Two numerical techniques to compute the solution of the resulting Riccati equation are presented: The first one is based on finding the steady state solution of the difference equation at every step and the second one is based on finding the minimum solution of a linear matrix inequality. The effectiveness of the proposed techniques is demonstrated by simulations involving the control of an inverted pendulum on a cart, a benchmark mechanical system.

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

2020 ◽  
pp. 095965182096689
Author(s):  
Xingyu Zhou ◽  
Haoping Wang ◽  
Yang Tian
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Parabolic Type ◽  
Distributed Parameter Systems ◽  
Temperature Control System ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Stability ◽  
Finite Time Stability ◽  
L2 Norm

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

scholarly journals Robust Control for Autonomous Spacecraft Evacuation with Model Uncertainty and Upper Bound of Performance with Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Dian Sheng ◽  
Xuebo Yang ◽  
Hamid Reza Karimi
Keyword(s):  
Upper Bound ◽  
Controller Design ◽  
Design Method ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Fuel Cost ◽  
Convex Optimization Problem ◽  
Output Tracking ◽  
Guaranteed Cost ◽  
Initial States

This paper studies the problem of guaranteed cost control for spacecraft evacuation. The relative dynamic model is established based on Clohessy-Wiltshire (C-W) equations. The paper has taken parameter uncertainty, output tracking, disturbance attenuation, and fuel cost into consideration. The paper introduces a new Lyapunov approach, so the controller design problem can be transferred into a convex optimization problem subject to linear matrix inequality (LMI) constraints. By using the controller, the spacecraft evacuation can be completed in a safe extent. Meanwhile, the fuel cost also has an upper bound. Then the paper analyzes the approach of evacuation and discusses possible initial states of the spacecraft for the controller design. An illustrative example is applied to show the effectiveness of the proposed control design method, and different performances caused by different initial states of spacecraft (-V-bar, -R-bar, and +H-bar) are simulated.

scholarly journals Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Kun Yuan ◽  
Abdulaziz Alofi ◽  
Jinde Cao ◽  
Abdullah Al-Mazrooei ◽  
Ahmed Elaiw
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Coupled System ◽  
Parabolic Partial Differential Equation ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Sufficient Condition ◽  
Spatial Derivative ◽  
Parameter System ◽  
System With Time Delay

By combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. First, based on Kronecker product and Lyapunov functional, some easy-to-test sufficient condition is given to ensure the synchronization of coupled DPS with time delay. Secondly, in the case that the whole coupled system cannot synchronize by itself, the proportional-spatial derivative (P-sD) state feedback controller is designed and applied to force the network to synchronize. The sufficient condition on the existence of synchronization controller is given in terms of a set of linear matrix inequalities. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.

scholarly journals Design of a Preview Controller for Discrete-Time Systems Based on LMI

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Reference Signal ◽  
Original System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Time Systems

A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.

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