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Control of networked systems with packet loss and channel uncertainty

IET CONTROL THEORY AND APPLICATIONS 2016年第17期10卷 2251-2259页

作者： Na, Xitai Zhan, Yufeng Xia, Yuanqing Dong, Jianjun Beijing Inst Technol Key Lab Intelligent Control & Decis Complex Syst Sch Automat Beijing 100081 Peoples R China

This study considers the control problem of networked control systems (NCSs) concerning both bounded channel uncertainty and packet loss. First, the authors deal with the problems of state feedback control for NCSs concerning both bounded random packet loss and channel uncertainty. Based on a previous work which copes with packet loss only, a classic model is used to describe the NCS with both packet loss and channel uncertainty in an unified framework. The stability conditions of NCSs are given by a common quadratic Lyapunov function and an approach is given to design the dynamic feedback controller via solving linear matrix inequalities. Second, the problems of output feedback control for NCSs concerned both bounded random packet loss and channel uncertainty are considered. A new sufficient condition is developed to guarantee the exponentially mean square stability of closed-loop networked systems and by using the stability theory, the controller and observer design problem is solved. Finally, numerical simulations and practical experiments are given to show the effectiveness of both approaches.

关键词： networked control systems distributed parameter systems uncertain systems state feedback asymptotic stability Lyapunov methods control system synthesis closed loop systems linear matrix inequalities observers numerical simulations observer design problem closed-loop networked systems exponentially mean square stability output feedback control problem linear matrix inequalities dynamic feedback controller design common quadratic Lyapunov function state feedback control bounded channel uncertainty bounded random packet loss NCS networked control systems

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A heat equation for freezing processes with phase change: stability analysis and applications

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INTERNATIONAL JOURNAL OF CONTROL 2016年第4期89卷 833-849页

作者： Backi, C. J. Bendtsen, J. D. Leth, J. Gravdahl, J. T. Norwegian Univ Sci & Technol Dept Engn Cybernet N-7034 Trondheim Norway Aalborg Univ Dept Elect Syst Aalborg Denmark

In this work, the stability properties as well as possible applications of a partial differential equation (PDE) with state-dependent parameters are investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (potential) Burgers' equation. We show that for certain forms of coefficient functions, the PDE converges to a stationary solution given by (fixed) boundary conditions that make physical sense. These boundary conditions are either symmetric or asymmetric of Dirichlet type. Furthermore, we present an observer design based on the PDE model for estimation of inner-domain temperatures in block-frozen fish and for monitoring freezing time. We illustrate the results with numerical simulations.

关键词： freezing process observer design distributed parameter systems stability analysis

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Robust Regulation Theory for Transfer Functions With a Coprime Factorization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第10期61卷 3109-3114页

作者： Laakkonen, Petteri Tampere Univ Technol Dept Math FIN-33101 Tampere Finland

Classical frequency domain results of robust regulation are extended by requiring only a right or a left coprime factorization of a plant, but not both. The famous internal model principle is generalized first, which leads to a necessary and sufficient solvability condition of the robust regulation problem and to a parametrization of all robustly regulating controllers. In addition, a procedure for constructing robustly regulating controllers is proposed.

关键词： distributed parameter systems linear systems parametrization robust control

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Singular perturbation approximation by means of a H² Lyapunov function for linear hyperbolic systems

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systems & CONTROL LETTERS 2016年 88卷 24-31页

作者： Tang, Ying Prieur, Christophe Girard, Antoine Ctr Rech Automat Nancy 2 Ave Foret Haye F-54516 Vandoeuvre Les Nancy France Gipsa Lab Grenoble Campus11 Rue MathBP 46 F-38402 St Martin Dheres France Univ Paris Saclay Univ Paris 11 CNRS L2SCent Supelec 3 Rue Joliot Curie F-91192 Gif Sur Yvette France

A linear hyperbolic system of two conservation laws with two time scales is considered in this paper. The fast time scale is modeled by a small perturbation parameter. By formally setting the perturbation parameter to zero, the full system is decomposed into two subsystems, the reduced subsystem (representing the slow dynamics) and the boundary-layer subsystem (standing for the fast dynamics). The solution of the full system can be approximated by the solution of the reduced subsystem. This result is obtained by using a H-2 Lyapunov function. The estimate of the errors is the order of the perturbation parameter for all initial conditions belonging to H-2 and satisfying suitable compatibility conditions. Moreover, for a particular subset of initial conditions, more precise estimates are obtained. The main result is illustrated by means of numerical simulations. (C) 2015 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Singular perturbation Lyapunov methods

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New stability and exact observability conditions for semilinear wave equations

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AUTOMATICA 2016年 63卷 1-10页

作者： Fridman, Emilia Terushkin, Maria Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

The problem of estimating the initial state of 1-D wave equations with globally Lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers, and deriving the upper bound for exact observability time in terms of Linear Matrix Inequalities (LMIs) (Fridman, 2013). In the present paper, we generalize this result to n-D wave equations on a hypercube. This extension includes new LMI-based exponential stability conditions for n-D wave equations, as well as an upper bound on the minimum exact observability time in terms of LMIs. For 1-D wave equations with locally Lipschitz nonlinearities, we find an estimate on the region of initial conditions that are guaranteed to be uniquely recovered from the measurements. The efficiency of the results is illustrated by numerical examples. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Wave equation Lyapunov method LMIs Exact observability

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Interconnected Observers for Robust Decentralized Estimation With Performance Guarantees and Optimized Connectivity Graph

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IEEE TRANSACTIONS ON CONTROL OF NETWORK systems 2016年第1期3卷 1-11页

作者： Li, Yuchun Sanfelice, Ricardo G. Univ Calif Santa Cruz Dept Comp Engn Santa Cruz CA 95064 USA

Motivated by the need for observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems with a noisy output that consists of a combination of N-coupled observers over a connectivity graph. At each node of the graph, the output of these interconnected observers is defined as the average of the estimates obtained using local information. The convergence rate and the robustness to measurement noise of the proposed observer's output are characterized in terms of KL bounds. Several optimization problems are formulated to design the proposed observer in order to satisfy a given rate of convergence specification while minimizing the H-infinity gain from noise to estimates or the size of the connectivity graph. It is shown that the interconnected observers relax the well-known tradeoff between the rate of convergence and noise amplification, which is a property attributed to the proposed innovation term, that over the graph, couples the estimates between the individual observers. Sufficient conditions involving information of the plant only, ensuring that the estimate obtained at each node of the graph outperforms the one obtained with a single, standard Luenberger observer are given. The results are illustrated in several examples throughout this paper.

关键词： distributed parameter systems observers for linear systems optimization

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Stability Analysis for a Class of Partial Differential Equations via Semidefinite Programming

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第6期61卷 1649-1654页

作者： Valmorbida, Giorgio Ahmadi, Mohamadreza Papachristodoulou, Antonis Univ Oxford Dept Engn Sci Parks Rd Oxford OX1 3PJ England Univ Oxford Somerville Coll Oxford OX2 6HD England

This paper studies scalar integral inequalities in one-dimensional bounded domains with polynomial integrands. We propose conditions to verify the integral inequalities in terms of differential matrix inequalities. These conditions allow for the verification of the inequalities in subspaces defined by boundary values of the dependent variables. The results are applied to solve integral inequalities arising from the Lyapunov stability analysis of partial differential equations. Examples illustrate the results.

关键词： distributed parameter systems partial differential equations (PDEs) stability analysis sum of squares

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A Novel Boundary Control Solution for Unstable Heat Conduction systems Based on Active Disturbance Rejection Control

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ASIAN JOURNAL OF CONTROL 2016年第2期18卷 595-608页

作者： Zhao, Dong Li, Donghai Wang, Youqing Beijing Univ Chem Technol Coll Informat Sci & Technol Beijing 100029 Peoples R China Tsinghua Univ Dept Thermal Engn State Key Lab Power Syst Beijing 100084 Peoples R China

In this study, a new boundary control scheme is proposed for a class of unstable heat conduction systems based on active disturbance rejection control and frequency domain analysis methods. The unstable heat conduction systems studied here corresponds to a thin rod with surface heat loss and internal heat generation. An active disturbance rejection boundary controller is designed to stabilize the unstable heat conduction systems. Using the frequency domain analysis method, the Nyquist stability criterion for distributed parameter systems, the relative stability indices (gain margin, phase margin, and exponential stability speed) can be obtained for performance evaluation, and a constructive parameter-tuning method for controller is proposed. Finally, it is proved that an active disturbance rejection boundary controller can stabilize the unstable heat conduction systems with one unstable pole, and the simulation results demonstrate that the temperature profile of the whole rod has good convergence properties under both Dirichlet and Neumann boundary control.

关键词： Unstable heat conduction system distributed parameter systems active disturbance rejection control parameter tuning Nyquist stability criterion

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Sliding mode control of Schrodinger equation-ODE in the presence of unmatched disturbances

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systems & CONTROL LETTERS 2016年 98卷 65-73页

作者： Kang, Wen Fridman, Emilia Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel Harbin Inst Technol Dept Math Harbin 150001 Peoples R China

In this paper, we consider boundary stabilization for a cascade of Schrodinger equation-ODE system with both, matched and unmatched disturbances. The backstepping method is first applied to transform the system into an equivalent target system where the target system is input-to-state stable. To reject the matched disturbance, the sliding mode control (SMC) law is designed for the target system. The well-posedness of the closed-loop system is proved, and the reachability of the sliding manifold in finite time is justified by infinite-dimensional system theory. It is shown that the resulting closed-loop system is input to -state stable. A Numerical example illustrates the efficiency of the sliding mode design that reduces the ultimate bound of the closed-loop system by rejecting the matched disturbance. (C) 2016 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Schrodinger equation Backstepping Sliding mode control Input-to-state stability

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Worst-case analysis of distributed parameter systems with application to the 2D reaction-diffusion equation

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OPTIMAL CONTROL APPLICATIONS & METHODS 2010年第5期31卷 433-449页

作者： Kishida, Masako Braatz, Richard D. Univ Illinois Urbana IL 61801 USA

It is well known that optimal control trajectories can be highly sensitive to perturbations in the model parameters. Computationally efficient numerical algorithms are presented for the worst-case analysis of the effects of parametric uncertainties on boundary control problems for finite-time distributed parameter systems. The approach is based on replacing the full-order model of the system with a power series expansion that is analyzed by linear matrix inequalities or power iteration, which are polynomial-time algorithms. Theory and algorithms are provided for computing the most positive and most negative worst-case deviation in a state or output, in contrast to the 'two-sided' deviations normally computed in worst-case analyses. Application to the Dirichlet boundary control of the reaction diffusion equation to track a desired two-dimensional concentration field illustrates the promise of the approach. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： distributed parameter systems boundary control robustness analysis partial differential equations

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