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Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

INTERNATIONAL JOURNAL OF systems SCIENCE 2018年第5期49卷 897-907页

作者： Aksikas, I. Moghadam, A. Alizadeh Forbes, J. F. Qatar Univ Dept Math Stat & Phys Doha Qatar Sherritt Int Corp Dept Technol Toronto ON Canada Univ Alberta Dept Chem & Mat Engn Edmonton AB Canada

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

关键词： Optimal control partial differential equations distributed parameter systems time-varying system chemical process systems

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Boundary control design for a vibrating flexible string system with input nonlinearities

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NONLINEAR DYNAMICS 2018年第2期93卷 323-333页

作者： He, Xiuyu Zhao, Zhijia Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Guangzhou Univ Sch Mech & Elect Engn Guangzhou 510006 Guangdong Peoples R China

In this paper, the main concern lies in developing a vibration control scheme for globally stabilizing the string system under the influence of input nonlinearities and external disturbance. To that end, an antidisturbance boundary control is presented by merging Lyapunov approach and disturbance observer control theory. Besides, the auxiliary system and auxiliary function are introduced to compensate for the input nonlinearities effects. Using the rigorous analysis without simplifying or discretizing the infinite-dimensional dynamics, the designed control laws can be proven to ensure the uniformly bounded stability of the controlled system. In the end, simulation results are presented for control performance verification.

关键词： distributed parameter systems Vibration control Input nonlinearities Disturbance observer Antidisturbance control

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Design of distributed sampled-data fuzzy controller for a class of non-linear hyperbolic PDE systems: input delay approach

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IET CONTROL THEORY AND APPLICATIONS 2018年第6期12卷 728-737页

作者： Mardani, Mohammad Mehdi Shasadeghi, Mokhtar Safarinejadian, Behrouz Shiraz Univ Technol Dept Elect & Elect Engn Modarres Blvd Shiraz Iran

This study addresses the problem of distributed sampled-data fuzzy controller design for a class of non-linear distributed parameter systems which are described by first-order hyperbolic partial differential equations (PDEs). To achieve this goal, first, the non-linear system is modelled by a continuous-time Takagi-Sugeno first-order hyperbolic PDE fuzzy model. Subsequently, the authors design a new distributed sampled-data fuzzy controller that generates a zero-order hold sampled-data control signal appropriate for the PDE systems. Then, a new Lyapunov-Krasovskii functional is suggested to provide the stability analysis conditions of the closed-loop control system. Moreover, the stabilisation conditions are obtained and converted to linear matrix inequalities using some new null terms. The proposed technique has removed the structural constraints on the convection and Lyapunov matrices. Finally, the proposed approach is applied on a biological system and a non-isothermal plug flow reactor .

关键词： distributed control sampled data systems fuzzy control nonlinear control systems hyperbolic equations partial differential equations delays control system synthesis distributed parameter systems continuous time systems Lyapunov methods stability criteria closed loop systems linear matrix inequalities chemical reactors flow control biology nonisothermal plug flow reactor biological system Lyapunov matrices convection structural constraints null terms linear matrix inequalities stabilisation conditions closed-loop control system stability analysis conditions Lyapunov-Krasovskii functional zero-order hold sampled-data control signal distributed sampled-data fuzzy controller design continuous-time Takagi-Sugeno first-order hyperbolic PDE fuzzy model first-order hyperbolic partial differential equations nonlinear distributed parameter systems input delay approach nonlinear hyperbolic PDE systems

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On Homogeneous Finite-Time Control for Linear Evolution Equation in Hilbert Space

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2018年第9期63卷 3143-3150页

作者： Polyakov, Andrey Coron, Jean-Michel Rosier, Lionel Inria Lille F-59650 Villeneuve Dascq France ITMO Univ St Petersburg 197101 Russia Univ Paris 06 Lab Jacques Louis Lions F-75252 Paris France Ecole Mines Paris Ctr Automat & Syst F-75272 Paris France

Based on the notion of generalized homogeneity, a new algorithm of feedback control design is developed for a plant modeled by a linear evolution equation in a Hilbert space with a possibly unbounded operator. The designed control law steers any solution of the closed-loop system to zero in a finite time. A method of homogeneous extension is presented in order to make the developed control design principles to be applicable for evolution systems with nonhomogeneous operators. The design scheme is demonstrated for the heat equation with the control input distributed on the segment [0,1].

关键词： distributed parameter systems nonlinear control systems hilbert space

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Boundary Constrained Control of Delayed Nonlinear Schrodinger Equation

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2018年第11期63卷 3873-3880页

作者： Kang, Wen Fridman, Emilia Tel Aviv Univ Sch Elect Engn IL-6997801 Tel Aviv Israel Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100081 Peoples R China Tel Aviv Univ Sch Elect Engn IL-6997801 Tel Aviv Israel

This paper studies regional boundary stabilization of nonlinear Schrodinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-to-state stability of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay's inequality. Estimates on the set of initial conditions are found starting from which the solutions are exponentially attracted to a bounded set. A numerical example demonstrates the efficiency of the results.

关键词： Boundary control constrained control law distributed parameter systems nonlinear systems time delay

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Modeling and simulating the thermoelastic deformation of mirrors using transient multilayer models

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MECHATRONICS 2018年 53卷 168-180页

作者： Schmidt, Kevin Wittmuess, Philipp Piehler, Stefan Ahmed, Marwan Abdou Graf, Thomas Sawodny, Oliver Univ Stuttgart Inst Syst Dynam ISYS Waldburgstr 17-19 D-70563 Stuttgart Germany Univ Stuttgart Inst Strahlwerkzeuge IFSW Pfaffenwaldring 43 D-70569 Stuttgart Germany

We present a dynamic model with distributed parameters for the thermoelastic transfer behavior in multilayer structures, which are motivated by optically addressed deformable mirrors (OADMs). These are encountered in adaptive optics and utilized for correcting wavefront disturbances of high-power radiation. Our modeling approach is based on a continuum-mechanic multilayer model which distinguishes between an addressing heat load - the control input - and a boundary disturbance evoked by the high-power primary radiation. Thus, the model without control action can be used for passive mirrors as well. The relevant transient effects are investigated with physically motivated assumptions, the plate-like geometry, and parametric rheological analogue models. Furthermore, an efficient simulation scheme is established using Fourier methods in conjunction with model order reduction. The model's accuracy and the validity of all assumptions is demonstrated by means of an experimental setup. The parametric model is a first step towards feedback and feedforward control designs and disturbance compensation algorithms for OADMs.

关键词： Thermoelastic deformation Adaptive optics Deformable mirror Parametric modeling distributed parameter systems Numerical simulation

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Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING systems 2018年第4期29卷 1213-1225页

作者： Talaei, Behzad Jagannathan, Sarangapani Singler, John Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA Amer Axle & Mfg Rochester Hills MI 48309 USA Missouri Univ Sci & Technol Dept Math & Stat Rolla MO 65409 USA

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

关键词： distributed parameter systems dynamic programming partial differential equations PDE Identifier

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Robust compensation of a chattering time-varying input delay with jumps

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AUTOMATICA 2018年 92卷 225-234页

作者： Bresch-Pietri, Delphine Mazenc, Frederic Petit, Nicolas PSL Res Univ CAS MINES ParisTech 60 Bd St Michel F-75006 Paris France CNRS Cent Supelec L2S EPI DISCO Inria Saclay 3 Rue Joliot Curie F-91192 Gif Sur Yvette France

We investigate the design of a prediction-based controller for a linear system subject to a time-varying input delay, not necessarily First-In/First-Out (FIFO). This means that the input signals can be reordered. The feedback law uses the current delay value in the prediction. It does not exactly compensate for the delay in the closed-loop dynamics but does not require to predict future delay values, contrary to the standard prediction technique. Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic stabilization of the system state, that is, robust delay compensation, providing that the average L-2-norm of the delay time-derivative over some time-window is sufficiently small and that the average time between two discontinuities (average dwell time) is sufficiently large. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Delay systems distributed parameter systems Reduction method Prediction-based control Time-varying delay Hybrid systems

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Revisiting APOD accuracy for nonlinear control of transport reaction processes: A spatially discrete approach

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CHEMICAL ENGINEERING SCIENCE 2018年 181卷 146-158页

作者： Yang, Manda Armaou, Antonios Penn State Univ Dept Chem Engn University Pk PA 16802 USA Wenzhou Univ Dept Mech & Automat Engn Chashan Univ Town Zhejiang Peoples R China

This article addresses the problem of output feedback control of dissipative distributed parameter systems. The reduced order model used for controller and observer synthesis is recursively updated using a revised version of adaptive proper orthogonal decomposition (APOD), based on decomposing spatially discrete solution profiles. This approach eliminates the basis size oscillation resulting from the inaccuracy of estimation of energy in APOD when the sampling speed is too slow. The performance of this method is illustrated by applying it to regulate a diffusion-reaction process and a fluid flow system described by the Kuramoto-Sivashinsky equation. (C) 2017 Published by Elsevier Ltd.

关键词： Adaptive proper orthogonal decomposition distributed parameter systems Process control Nonlinear control Model order reduction

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Stabilization of a linear hyperbolic PDE with actuator and sensor dynamics

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AUTOMATICA 2018年 95卷 104-111页

作者： Anfinsen, Henrik Aamo, Ole Morten Norwegian Univ Sci & Technol NTNU Dept Engn Cybernet N-7491 Trondheim Norway

We consider a scalar 1-D linear hyperbolic partial differential equation (PDE) for which infinite dimensional backstepping controllers have previously been designed based on boundary actuation and sensing, and incorporate first order actuator and sensor dynamics into the design. Two observer designs are proposed, and combined with a state-feedback into output-feedback control laws which render the origin of the closed-loop system exponentially stable with arbitrary convergence rate. The theory is verified in simulations. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Hyperbolic systems Linear systems Boundary control

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