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Robust H_∞ control for time-delay networked control systems with probability constraints

IET CONTROL THEORY AND APPLICATIONS 2015年第16期9卷 2482-2489页

作者： Wang, Shuo Yu, Mei Sun, Ximing North China Elect Power Univ Sch Control & Comp Engn Beijing 102206 Peoples R China Dalian Univ Technol Sch Control Sci & Engn Dalian 116024 Peoples R China

In this study, the probability-guaranteed H control of networked control systems (NCSs) with time-varying networked-induced delays is addressed. The time-varying delays are modelled as polytopic uncertainty by a new approximation method based on real Jordan form. The system uncertainty lies in a parameter hyper-rectangle box which can shrink, i.e. the probability can be less than one with a better disturbance attenuation level. By the uniformity principle and the one-to-one correspondence between the time delays and the vertices of polytopic system, a sufficient condition for the NCS to achieve prescribed performance with a given probability is derived. The controller synthesis problem is also proposed to meet the probabilistic requirement by solving a set of bilinear matrix inequalities iteratively. A uniform distribution is assumed for all the delays and thus the maximal probability guaranteeing the given performance can be calculated.

关键词： robust control H control delay systems delays networked control systems distributed parameter systems uncertain systems approximation theory control system synthesis probability linear matrix inequalities robust H control time-delay networked control systems NCS probability constraints probability-guaranteed H control time-varying networked-induced delays polytopic uncertainty approximation method real Jordan form system uncertainty parameter hyper-rectangle box disturbance attenuation level uniformity principle controller synthesis problem probabilistic requirement bilinear matrix inequalities uniform distribution

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Control of 2 x 2 linear hyperbolic systems: Backstepping-based trajectory generation and PI-based tracking

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systems & CONTROL LETTERS 2015年 86卷 24-33页

作者： Lamare, Pierre-Olivier Bekiaris-Liberis, Nikolaos Univ Grenoble Lab Jean Kuntzmann F-38041 Grenoble France Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94704 USA Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94704 USA

We consider the problems of trajectory generation and tracking for general 2 x 2 systems of first-order linear hyperbolic PDEs with anti-collocated boundary input and output. We solve the trajectory generation problem via backstepping. The reference input, which generates the desired output, incorporates integral operators acting on advanced and delayed versions of the reference output with kernels which were derived by Vazquez, Krstic, and Coron for the backstepping stabilization of 2 x 2 linear hyperbolic systems. We apply our approach to a wave PDE with indefinite in-domain and boundary damping. For tracking the desired trajectory we employ a PI control law on the tracking error of the output. We prove exponential stability of the closed-loop system, under the proposed PI control law, when the parameters of the plant and the controller satisfy certain conditions, by constructing a novel "non-diagonal" Lyapunov functional. We demonstrate that the proposed PI control law compensates in the output the effect of in-domain and boundary disturbances. We illustrate our results with numerical examples. (C) 2015 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Hyperbolic systems Backstepping Lyapunov function

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Domain decomposition methods in the distributed estimation of spatially distributed processes with mobile sensors

Domain decomposition methods in the distributed estimation o...

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American Control Conference

作者： Michael A. Demetriou Worcester Polytechnic Institute Dept of Mechanical Engineering MA 01609 USA

ISBN: (纸本)9781467386838

This paper considers the state estimation of spatially distributed processes via the employment of mobile sensors. In order to reduce the computational demands, a domain decomposition method is utilized and which decomposes the spatial domain into two subdomains. The estimator in the inner domain implements a hybrid Kalman filter with a mobile sensor, whereas the outer subdomain implements a naive observer. Coupling conditions at the inner/outer boundary serve as a means to exchange information between the two estimators and which constitute a consensus protocol. The motion of the mobile sensor is based on a spatial gradient scheme and serves as a further means of reducing the computational load associated with the solution to large scale differential Riccati equations. The proposed scheme is further extended to collaborative distributed estimation in which multiple mobile sensors are enforcing another level of consensus protocol in order to penalize the differences between their state estimates. Extensive numerical simulations of a one-dimensional parabolic partial differential equation are presented to further demonstrate the multi-level computational savings associated with the use of domain decomposition in state estimation of spatially distributed processes with mobile sensors.

关键词： distributed state estimation distributed parameter systems scientific computing mobile sensors distributed processing State estimation distributed parameter systems Scientific computing Mobile Sensors decomposition Domain

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Semidiscrete approximation and renorming in control of distributed parameter systems

Semidiscrete approximation and renorming in control of distr...

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American Control Conference

作者： R.H. Fabiano Department of Mathematics and Statistics 140 Petty Building University of North Carolina at Greensboro Greensboro NC 27412 USA

ISBN: (纸本)9781424474264

We consider finite dimensional semidiscrete approximation of an LQR control problem with dynamics governed by a distributed parameter system. We investigate how changing the norm on the state space affects the resulting finite dimensional control problem. Numerical results are given for examples in delay equations and elastic structures.

关键词： distributed control Control systems distributed parameter systems Riccati equations State-space methods Cost function Eigenvalues and eigenfunctions Delay Hilbert space Time of arrival estimation

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Design of decentralized local controllers of spatially distributed systems by approximation of feedback kernels

Design of decentralized local controllers of spatially distr...

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American Control Conference

作者： Michael A. Demetriou Worcester Polytechnic Institute Dept of Mechanical Engineering MA 01609 USA

ISBN: (纸本)9781467386838

This paper considers the problem of decentralized controllers for spatially distributed systems. The spatially distributed systems are assumed to have a network of control units and the decentralized design is solved by approximation of the feedback kernels. By first obtaining the full state feedback controllers corresponding to the centralized design, the individual feedback operators are numerically approximated by the product of static feedback gains with spatial delta functions representing the spatial distribution of the sensing devices. The resulting kernel approximation produces both the interconnection topology between the control units and their interconnection strengths. Since the feedback kernels are themselves based on quadratic control costs, then the kernel approximation method results in a suboptimal controller design with a significantly improved communication costs that reduces the information exchange between the control units. As a special case of a SISO system, the kernel approximation can also provide an optimal sensor location with respect to the energy of the resulting closed loop system. Extensive numerical studies for a diffusion partial differential equation (PDE) in one spatial dimension having four collocated actuator/sensor pairs along with the joint sensor and static gain optimization of a SISO diffusion PDE are included.

关键词： kernel approximation distributed parameter systems distributed local controllers networked systems control unit distributed parameter systems distributed systems Seeds approximation Decentralized Kernel Feedback local controller single input single output systems information exchange static feedback DELTA FUNCTIONS state feedback controller

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Generalized exponential trichotomy for difference equations

Generalized exponential trichotomy for difference equations

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International Symposium on Applied Computational Intelligence and Informatics ( SACI)

作者： Ioan-Lucian Popa Traian Ceauşu Department of Exact Sciences and Engineering “1 Decembrie 1918” University of Alba Iulia Alba Iulia Romania Department of Mathematics West University of Timişoara Timişoara Romania

In this note we address two trichotomy concepts for discrete-time linear time-varying systems. We extend the notion of exponential trichotomy in the sense of Elaydi-Janglajew to the so called notion of generalized exponential trichotomy. This approach is motivated by an example. Also, a characterization for generalized exponential trichotomy in terms of necessary and sufficient conditions is given.

关键词： Difference equations Time-varying systems Frequency modulation Computational intelligence Informatics distributed parameter systems

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Design and analysis of networked non-linear predictive control systems

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IET CONTROL THEORY AND APPLICATIONS 2015年第11期9卷 1740-1745页

作者： Liu, Guo-Ping Univ South Wales Sch Engn Pontypridd CF37 1DL M Glam Wales

This study is concerned with the control problem of networked non-linear systems with communication delay and data dropout. A networked non-linear predictive control scheme is proposed to compensate for communication delay and data dropout actively rather than passively. The stability analysis shows that the stability problem of the closed-loop networked non-linear predictive control system is converted to the one of a conventional non-linear control system without network. The simulations illustrate that the proposed scheme can compensate for communication delay and data dropout, and achieve the same control performance of the local closed-loop control system without network.

关键词： networked control systems distributed parameter systems nonlinear control systems predictive control closed loop systems delays stability compensation control system analysis control system synthesis closed-loop networked nonlinear predictive control system design closed-loop networked nonlinear predictive control system analysis communication delay compensation data dropout compensation stability analysis local closed-loop control system

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Balanced POD Algorithm for Robust Control Design for Linear distributed parameter systems

Balanced POD Algorithm for Robust Control Design for Linear ...

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American Control Conference

作者： John R. Singler Belinda A. Batten Department of Mathematics and Statistics Missouri University of Science and Technology Rolla MO 65409 School of Mechanical Industrial and Manufacturing Engineering Oregon State University Corvallis OR 97331-6001

ISBN: (纸本)9781424474264

A mathematical model of a physical system is never perfect;therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also "nearby" systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale finite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Numerical results are presented for a convection diffusion partial differential equation.

关键词： Robust control Algorithm design and analysis distributed parameter systems Control systems Large-scale systems Mathematical model Centralized control Linear systems Riccati equations Matrix decomposition

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Fault-Tolerant Control of Sampled-Data Nonlinear distributed parameter systems

Fault-Tolerant Control of Sampled-Data Nonlinear Distributed...

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American Control Conference

作者： Sathyendra Ghantasala Nael H. El-Farra Department of Chemical Engineering & Materials Science University of California Davis CA 95616 USA

ISBN: (纸本)9781424474264

This work presents an integrated fault detection and fault-tolerant control architecture for spatially-distributed systems described by highly-dissipative systems of nonlinear partial differential equations with actuator faults and sampled measurements. The architecture consists of a family of nonlinear feedback controllers, observer-based fault detection filters that account for the discrete measurement sampling, and a switching law that reconfigures the control actuators following fault detection. An approximate model that captures the dominant dynamics of the infinite-dimensional system is embedded in the control system to provide the controller and fault detection filter with estimates of the measured output between sampling instances. The model state is then updated using the actual measurements whenever they become available from the sensors. A sufficient condition for stability of the sampled-data nonlinear closed-loop system is derived in terms of the sampling rate, the model accuracy, the controller design parameters and the spatial placement of the control actuators. This characterization is used to derive rules for fault detection and actuator reconfiguration. The results are demonstrated through an application to the problem of stabilizing the zero solution of the Kuramoto-Sivashinsky equation.

关键词： Fault tolerant systems Nonlinear control systems Control systems distributed parameter systems Fault detection Actuators Sampling methods Filters Partial differential equations Adaptive control

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Electromagnetic field theory as system theory

Electromagnetic field theory as system theory

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URSI International Symposium on Electromagnetic Theory (EMTS)

作者： Eike Scholz Sebastian Lange Thomas Eibert Chair of High-Frequency Engineering Technical University of Munich München Germany Bundeswehr Research Institute for Protective Technologies - NBC Protection Munster Germany

ISBN: (纸本)9781509025039

This paper presents a transformation of Maxwell's equations for general nonlinear material operators into a system state equation of an equivalent nonlinear distributed parameter system. The proposed formulation has a fair amount of practical and didactic advantages, with regard to modeling hysteresis and memory effects, understanding causality, control and stability of electromagnetic fields, formulating multiphysics models, as well as computing analytic solutions or constructing numerical solution algorithms.

关键词： Mathematical model Maxwell equations Electromagnetics distributed parameter systems Magnetic hysteresis Numerical models Hysteresis

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