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Ensemble Controllability of Cellular Oscillators

IEEE CONTROL systems LETTERS 2019年第2期3卷 296-307页

作者： Kuritz, Karsten Zeng, Shen Allgoewer, Frank Univ Stuttgart Inst Syst Theory & Automat Control D-70550 Stuttgart Germany Washington Univ Dept Elect & Syst Engn St Louis MO 63130 USA

Many diseases including cancer, Parkinson's disease and heart diseases are caused by loss or malfunction of regulatory mechanism of an oscillatory system. Successful treatment of these diseases might involve recovering the healthy behavior of the oscillators in the system, i.e., achieving synchrony or a desired distribution of the oscillators on their periodic orbit. In this letter, we consider the problem of controlling the distribution of a population of cellular oscillators described in terms of phase models. Different practical limitations on the observability and controllability of cellular states naturally lead to an ensemble control formulation in which a populationlevel feedback law for achieving a desired distribution is sought. A systems theoretic approach to this problem leads to Lyapunov- and LaSalle-like arguments, from which we develop our main contribution, novel necessary and sufficient conditions for the controllability of phase distributions in terms of the Fourier coefficients of the phase response curve. Since our treatment is based on a rather universal formulation of phase models, the results and methods proposed in this letter are readily applicable to the control of a wide range of other types of oscillating populations, such as circadian clocks, and spiking neurons.

关键词： systems biology emerging control applications distributed parameter systems cellular dynamics biological systems

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Adaptive estimation for nonlinear systems using reproducing kernel Hilbert spaces

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2019年第2期45卷 869-896页

作者： Bobade, Parag Majumdar, Suprotim Pereira, Savio Kurdila, Andrew J. Ferris, John B. Virginia Tech Dept Engn Sci & Mech Blacksburg VA 24061 USA Virginia Tech Dept Elect & Comp Engn Blacksburg VA 24061 USA Virginia Tech Dept Mech Engn Blacksburg VA 24061 USA

This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown or uncertain nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS) and defines a distributed parameter system (DPS) that governs state estimates and estimates of the unknown function. Under the assumption that full state measurements are available, this paper (1) derives sufficient conditions for the existence and stability of the infinite dimensional online estimation problem, (2) derives existence and stability of finite dimensional approximations of the infinite dimensional approximations, and (3) determines sufficient conditions for the convergence of finite dimensional approximations to the infinite dimensional online estimates. A new condition for persistency of excitation in a RKHS in terms of its evaluation functionals is introduced in the paper that enables proof of convergence of the finite dimensional approximations of the unknown function in the RKHS. This paper studies two particular choices of the RKHS, those that are generated by exponential functions and those that are generated by multiscale kernels defined from a multiresolution analysis.

关键词： Adaptive estimation Reproducing kernel Hilbert spaces distributed parameter systems

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Control Law Realification for the Feedback Stabilization of a Class of Diagonal Infinite-Dimensional systems With Delay Boundary Control

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IEEE CONTROL systems LETTERS 2019年第4期3卷 930-935页

作者： Lhachemi, Hugo Shorten, Robert Prieur, Christophe Univ Coll Dublin Sch Elect & Elect Engn Dublin D04 V1W8 4 Ireland Imperial Coll London Dyson Sch Design Engn London England Univ Grenoble Alpes CNRS Grenoble INP GIPSA Lab F-38000 Grenoble France

Recently, a predictor feedback control strategy has been reported for the feedback stabilization of a class of infinite-dimensional Riesz-spectral boundary control systems exhibiting a finite number of unstable modes by means of a delay boundary control. Nevertheless, for real abstract boundary control systems exhibiting eigenstructures defined over the complex field, the direct application of such a control strategy requires the embedding of the control problem into a complexified state-space which yields a complex-valued control law. This letter discusses the realification of the control law, i.e., the modification of the design procedure for obtaining a real-valued control law for the original real abstract boundary control system. The obtained results are applied to the feedback stabilization of an unstable Euler-Bernoulli beam by means of a delay boundary control.

关键词： distributed parameter systems boundary feedback stabilization predictor feedback Euler-Bernoulli beam

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Solution of Time-Variant Fractional Differential Equations With a Generalized Peano-Baker Series

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IEEE CONTROL systems LETTERS 2019年第1期3卷 79-84页

作者： Eckert, Marius Nagatou, Kaori Rey, Felix Stark, Oliver Hohmann, Soren Karlsruhe Inst Technol Inst Control Syst D-76131 Karlsruhe Germany Karlsruhe Inst Technol Dept Math D-76131 Karlsruhe Germany Swiss Fed Inst Technol Automat Control Lab CH-8092 Zurich Switzerland

Time-variant fractional systems have many applications. For example, they can be used for system identification of lithium-ion batteries. However, the analytical solution of the time-variant fractional pseudo state space equation is missing so far. To overcome this limitation, this letter introduces a novel matrix approach, namely the generalized Peano-Baker series, which is comparable to the transition matrix in the case of ordinary systems. Using this matrix, the solution of the time-variant fractional pseudo state space equation is derived. The initialization process is taken into account, which has been proven to be a crucial part for fractional operator calculus. Following this initialization, a modified definition of a fractional pseudo state is presented.

关键词： Linear systems time-variant systems distributed parameter systems

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Dynamic Density Estimation in Heterogeneous Cell Populations

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IEEE CONTROL systems LETTERS 2019年第2期3卷 242-247页

作者： Kuper, Armin Durr, Robert Waldherr, Steffen Katholieke Univ Leuven Dept Chem Engn Bio & Chem Syst Technol Reactor Engn & Safety B-3001 Leuven Belgium

Multicellular systems play a key role in bioprocess and biomedical engineering. Cell ensembles encountered in these setups show phenotypic variability like size and biochemical composition. As this variability may result in undesired effects in bioreactors, close monitoring of the cell population heterogeneity is important for maximum production output, and accurate control. However, direct measurements are mostly restricted to a few cellular properties. This motivates the application of model-based online estimation techniques for the reconstruction of non-measurable cellular properties. Population balance modeling allows for a natural description of cell-to-cell variability. In this contribution, we present an estimation approach that, in contrast to existing ones, does not rely on a finite-dimensional approximation through grid based discretization of the underlying population balance model. Instead, our so-called characteristics based density estimator employs sample approximations. With two and three-dimensional benchmark examples we demonstrate that our approach is superior to the grid based designs in terms of accuracy and computational demand.

关键词： Biological systems estimation distributed parameter systems

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Multi-Layer Adaptive Finite Time Super Twisting Control for Quaternion-Based Quadrotor Formation With Obstacle Avoidance

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IEEE ACCESS 2020年 8卷 213062-213077页

作者： Zhang, Guowei Shang, Wei Jing, Guohao Chen, Tianlong Liang, Qihang Hubei Univ Technol Sch Mech Engn Wuhan 430068 Peoples R China

This article investigates the trajectory tracking problem of quadrotor formation with collision avoiding. The safety distributed control strategy is introduced for quaternion-based multiple quadrotors formation to avoid collision. Then, based on super-twisting and adaptive control method, a multiple adaptive finite time super-twisting control method (MAFTSTC) is proposed, which rarely relies on the information of the formation model. The purpose of the robust controller designed in the position loop and the attitude loop is to ensure that quadrotor formation tracks the desired trajectory and maintains formation configuration in finite time. The closed-loop system stability of the novel control method is verified through Lyapunov theory. Finally, compared with traditional finite time convergence (FTC) method and non-robustness control (NRC) method, the simulation results illustrate the effectiveness of the proposed control method.

关键词： Stability analysis Collision avoidance Uncertainty Trajectory Licenses Attitude control Convergence Position control attitude control distributed parameter systems nonlinear control systems control design angular velocity control optimal control

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Stability by the First Approximation of a Water Hammer Model

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IFAC-PapersOnLine 2020年第2期53卷 4339-4344页

作者： Daniela Danciu Vladimir Răsvan Department of Automation and Electronics University of Craiova A.I.Cuza 13 Craiova RO-200585 Romania

Usually the water hammer models in hydroelectric engineering are described by the adapted Saint-Venant Partial Differential Equations with linear and nonlinear boundary conditions. If the dynamic head and the Darcy-Weisbach losses are neglected the PDEs are linear hyperbolic and can be tackled by associating a system of Neutral Functional Differential Equations with two delays - there are two conduits (the tunnel and the penstock). The time scale analysis shows that in certain cases arising from practice the dynamics of the penstock can be considered as described by ordinary differential equations. Consequently the water hammer dynamics has now a single time delay. The stability is then discussed by analyzing the characteristic equation: frequency domain methods combined with algebraic ones are implied. In this way stability by the first approximation is obtained. From the engineering point of view the results display the stabilizing role of the surge tank.

关键词： distributed parameter systems Linear systems Time delay Stability

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Constrained control of 1-D parabolic PDEs using sampled in space sensing and actuation

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systems & CONTROL LETTERS 2020年 140卷 104698-104698页

作者： Kang, Wen Fridman, Emilia Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Peoples R China Tel Aviv Univ Dept Elect Engn Syst Tel Aviv Israel

We consider distributed control of a class of 1-D parabolic PDEs under distributed in-domain point actuation and measurements in the presence of control constraints. This class includes unstable diffusion-reaction equations as well as stable Burgers' equations, where we aim to locally improve the convergence. We suggest an observer-based control law that employs the averaged values of the observer state. This allows to regionally stabilize the system. We derive linear matrix inequalities (LMIs) conditions that provide an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example validates the efficiency of the method. (C) 2020 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Parabolic systems Burgers' equation Point actuation Constrained control

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Shape memory alloy tube actuators inherently enable internal fluidic cooling for a robotic finger under force control

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SMART MATERIALS AND STRUCTURES 2020年第11期29卷 115009-115009页

作者： Ades, Craig J. Dilibal, Savas Engeberg, Erik D. Florida Atlantic Univ Boca Raton FL 33431 USA Instanbul Gedik Univ Istanbul Turkey

This paper presents the design, control and evaluation of a novel robotic finger actuated by shape memory alloy (SMA) tubes which intrinsically afford an internal conduit for fluidic cooling. The SMA tubes are thermomechanically programmed to flex the robotic finger when Joule heated. A superelastic SMA plate provides a spring return motion to extend the finger when cooling liquid is pumped through the internal channel of the SMA tube actuators. The mechanical design and nonlinear force controller are presented for this unique robotic finger. Sinusoidal and step response experiments demonstrate excellent error minimization when operated below the bandwidth which was empirically determined to be 6 rad s(-1). Disturbance rejection experiments are also performed to demonstrate the potential to minimize externally applied forces. This method of internal liquid cooling of Joule heated SMA tubes simultaneously increases the system bandwidth and expands the potential uses of SMA actuators for robotic applications. The results show that this novel robotic finger is capable of precise force control and has a high strength to weight ratio. The finger can apply a force of 4.35 N and has a mass of 30 g. Implementing this design into wearable prosthetic devices could enable lightweight, high strength applications previously not achievable.

关键词： distributed parameter systems nonlinear control robotic finger shape memory alloy

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Network-based deployment of the second-order multi agents: a PDE approach

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IFAC-PapersOnLine 2020年第2期53卷 7617-7622页

作者： Maria Terushkin Emilia Fridman School of Electrical Engineering Tel Aviv University Israel

Deployment of a second-order nonlinear multi agent system over a desired open smooth curve in 2D or 3D space is considered. We assume that the agents have access to their velocities and to the local information of the desired curve and their displacements with respect to their closest neighbors, whereas in addition a leader is able to measure his absolute position. We assume that a small number of leaders transmit their measurements to other agents through a communication network. We take into account the following network imperfections: the variable sampling, transmission delay and quantization. We propose a static output-feedback controller and model the resulting closed-loop system as a disturbed (due to quantization) nonlinear damped wave equation with delayed point state measurements, where the state is the relative position of the agents with respect to the desired curve. To manage with the open curve we consider Neumann boundary conditions. We derive linear matrix inequalities (LMIs) that guarantee the input-to-state stability (ISS) of the system. The advantage of our approach is in the simplicity of the control law and the conditions. Numerical example illustrates the efficiency of the method.

关键词： distributed parameter systems multi-agent systems network-based control time-delay

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