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Controller Synthesis for Periodic, Linear-distributed parameter systems: Channel Flow Application

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2015年第6期38卷 993-1000页

作者： Kang, Sung M. Speyer, Jason L. Kim, John Univ Calif Los Angeles Dept Mech & Aerosp Engn Los Angeles CA 90095 USA

A framework is presented in which temporally periodic, linear, distributed parameter systems can be converted to a time-invariant system. This conversion is key for the control of the secondary instabilities in three-dimensional channel flow induced by an upstream traveling wave of zero-net mass flux of wall transpiration. Linearized dynamical equations derived from Floquet analysis have shown that the instabilities are a direct result of the primary disturbance of the traveling wave but do not provide an analytical framework upon which to design a feedback controller. The necessary observation, although simple but subtle, is that the dynamics of the steady-state flow induced by a traveling wave must be linearized and decomposed in a frame of reference moving with the traveling wave. The resulting linear time-invariant equations are appropriate for system theoretic feedback control synthesis, i.e., H-2 and H-infinity methods. Although the linearization method produces a time-invariant linear system in the moving frame, the controller is periodic from a fixed reference frame. This approach for constructing a time-invariant system with periodic inputs is applicable to any system in which the dynamics are described as a combination of a static base and a periodic primary disturbance.

关键词： Poiseuille Flow distributed parameter system Full State Feedback Mass Flux Direct Numerical Simulation Drag Reduction Kalman Filter Vorticity Navier Stokes Equations Collocation Method

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Modeling of distributed parameter systems for applications-A synthesized review from time-space separation

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JOURNAL OF PROCESS CONTROL 2010年第8期20卷 891-901页

作者： Li, Han-Xiong Qi, Chenkun City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China Shanghai Jiao Tong Univ Sch Mech Engn State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China

Many industrial processes belong to distributed parameter systems (DPS) that have strong spatial-temporal dynamics. Modeling of DPS is difficult but essential to simulation, control and optimization. The first-principle modeling for known DPS often leads to the partial differential equation (PDE). Because it is an infinite-dimensional system, the model reduction (MR) is very necessary for real implementation. The model reduction often works with selection of basis functions (BF). Combination of different BF and MR results in different approaches. For unknown DPS, system identification is usually used to figure out unknown structure and parameters. Using various methods, different approaches are developed. Finally, a novel kernel-based approach is proposed for the complex DPS. This paper provides a brief review of different DPS modeling methods and categorizes them from the view of time-space separation. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： distributed parameter system system modeling Time-space separation system identification Model reduction parameter estimation

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ESTIMATION OF distributed parameter-systemS - SOME CLOSED-FORM SOLUTIONS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1986年第4期9卷 408-412页

作者： SCHAECHTER, DB Lockheed Missiles and Space Co. Inc. Palo Alto CA

The estimation and control of distributed parameter systems has numerous applications in the control of structures. In many cases, obtaining the solutions of estimation and control problems that involve partial differential equations requires the use of numerical methods and yields only approximate answers. In this paper, exact solutions are obtained for several practical estimation problems associated with static systems, solutions that cannot be obtained by any other reasonable approach.

关键词： distributed parameter system Green's Function Kalman Filter Satellites Large Space Structures Attitude Control Digital Computers Flight Vehicle Space Shuttle Astrophysics

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Exponential stability and L_(2) gain analysis of switched distributed parameter systems with time delay

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Journal of Control and Decision 2021年第4期8卷 385-393页

作者： Leping Bao Pu Huang Shumin Fei Department of Automation Taiyuan Institute of TechnologyTaiyuanShanxi 030008People’s Republic of China School of Information Science and Engineering Northeast UniversityShenyangPeople’s Republic of China School of Automation Southeast UniversityNanjingJiangsuPeople’s Republic of China

The present paper is concerned with stability and L_(2) gain analysis of switched distributed parameter system(SDPS)with time ***,exponential stability is discussed,and the state decay estimate of the system is explicitly given by using linear matrix inequalities(LMIs)incorporating with the average dwell time(ADT)***,L_(2) gain analysis is also *** last,illustrative examples are given to show the effectiveness of the proposed *** main contribution of the paper is:some criteria of exponential stability and L_(2) gain for multiple-input multiple-output(MIMO)switched PDE are developed in the form of LMIs and ADT signal for the first *** advantage of the work is we generalize the application range of the related *** proposed method is expected to provide an effective tool for stability and H∞control analysis of SDPS.

关键词： Switched system distributed parameter system multiple-input multiple-output(MIMO) time delay average dwell time(ADT)

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Controllability of distributed parameter systems

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2024年第6期64卷 1211-1223页

作者： Tolstykh, V. K. Donetsk State Univ Doneck 283001 Russia

The problem of controllability for problems of optimal control and optimization of distributed parameter systems governed by partial differential equations is considered. The concept of controllability understood as Tikhonov correctness for solving optimization problems is introduced. A theorem formulating controllability conditions for directly solving optimization problems (direct minimization of the objective functional) is presented. A test example of the numerical solution of the optimization problem for a nonlinear hyperbolic system describing the unsteady flow of water in an open channel is considered. The analysis of controllability is demonstrated that ensures the correctness of the problem solution and high accuracy of optimization of the distributed friction coefficient in the flow equations.

关键词： controllability distributed parameter system optimization optimal control identification gradient optimization methods

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Sliding mode observer-based synthesis of state derivative-free model reference adaptive control of distributed parameter systems

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JOURNAL OF DYNAMIC systemS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME 2000年第4期122卷 725-731页

作者： Orlov, YV CICESE Res Ctr Dept Elect & Telecommun San Diego CA 92143 USA

This paper presents control laws for distributed parameter systems of parabolic and hyperbolic types which, on the one hand ensure robustness with respect to small dynamic uncertainties and disturbances, and on the other hand, permit on-line plant parameter estimation. The novelty of the algorithms proposed is (a) in the construction of a sliding mode-based state derivative observer and (b) in the inclusion of this observer into a model reference adaptive controller which thereby regularizes the ill-posed identification problem itself. Apart from this, the controllers constructed do not suffer from on-line computation of spatial derivatives of the measurement data, and hence they are of reduced sensitivity with respect to the measurement noise. [S0022-0434(00)02104-3].

关键词： distributed parameter system adaptive control reference model sliding mode observer

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An approximation approach to H^∞ control problems for distributed parameter systems

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AUTOMATICA 1997年第11期33卷 2049-2052页

作者： Yoon, MG Lee, BH Samsung Adv Inst Technol Syst & Control Sector Electro Mech Lab Suwon 440600 South Korea Seoul Natl Univ Dept Elect Engn Seoul 151742 South Korea

A new approximation approach is presented for H-infinity control problems involving distributed parameter systems. Related approximation error bound is provided. Using Frostman's theorem, we approximate a general inner function with a finite Blaschke product and then apply known finite dimensional solution techniques. This simple method can give an approximate solution of various infinite dimensional H-infinity control problems with great generality. (C) 1997 Elsevier Science Ltd.

关键词： H-infinity control problem distributed parameter system approximation approach Frostman's theorem Blaschke product

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Mobile sensor networks for sampled-data control of a class of distributed parameter systems

Mobile sensor networks for sampled-data control of a class o...

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26th Chinese Control and Decision Conference (CCDC)

作者： Qian, Xueming Cui, Baotong Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China

ISBN: (纸本)9781479937066

This paper develop the sampled-data control problem of a class of distributed parameter systems. A novel sampled-data control scheme is presented using mobile sensor networks. By utilizing a Lyapunov functional which depend on spatial parameter, a controller combine to decentralized static output feedback control scheme and the point measurement of the mobile sensor is designed to derive several sufficient criteria ensuring the distributed parameter systems to be globally asymptotically stable. The criteria are given in the form of linear operator inequalities and the velocity law of each mobile sensor. It is also shown that static sampled-data control of distributed parameter systems is just a special case of our main results. A numerical simulations illustrate the effectiveness of the proposed control scheme in enhancing system performance.

关键词： distributed parameter system Sampled-data control Mobile sensor networks

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A NONQUADRATIC BOLZA PROBLEM AND A QUASI-RICCATI EQUATION FOR distributed parameter-systemS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1987年第4期25卷 905-920页

作者： YOU, YC FUDAN UNIV INST MATHSHANGHAIPEOPLES R CHINA

Closed-loop optimal control of a nonquadratic Bolza problem for linear distributed parameter systems and normal solution of an associated quasi-Riccati operator equation are studied by the approach of a nonlinear inte... 详细信息

关键词： 49A27 Bolza problem nonquadratic cost function quasi-Riccati equation closed-loop optimal control nonlinear integral equation distributed parameter system

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D-Optimal Trajectories of Mobile Sensors with Fractional Dynamics for parameter Estimation of distributed parameter systems

D-Optimal Trajectories of Mobile Sensors with Fractional Dyn...

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8th World Congress on Intelligent Control and Automation (WCICA)

作者： Tricaud, Christophe Chen, YangQuan Utah State Univ Dept Elect & Comp Engn Ctr Self Organizing & Intelligent Syst Logan UT 84322 USA

ISBN: (纸本)9781424467129

In this paper, we propose a methodology to optimize the trajectory of mobile sensors whose dynamics contains fractional derivatives to find parameter estimates of a distributed parameter system. The problem is to maximize the determinant of the Fischer information matrix representing the amount of information gathered on parameters by the sensors. The introduced method transforms the problem to a fractional optimal control one in which both the steering of the sensors and their initial positions are optimized. The resulting fractional optimal control problem is reformulated into an integer order optimal control one which is then solved using the Matlab PDE toolbox and the RIOTS optimal control toolbox which handles various constraints imposed on the sensor motions. The effectiveness of the method is illustrated with a two-dimensional diffusion equation for different numbers of sensors and different orders.

关键词： distributed parameter system sensor trajectory fractional dynamics motion planning optimal control

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