246 research outputs found

    Fourth SIAM Conference on Applications of Dynamical Systems

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    Optimal Control and Synchronization of Dynamic Ensemble Systems

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    Ensemble control involves the manipulation of an uncountably infinite collection of structurally identical or similar dynamical systems, which are indexed by a parameter set, by applying a common control without using feedback. This subject is motivated by compelling problems in quantum control, sensorless robotic manipulation, and neural engineering, which involve ensembles of linear, bilinear, or nonlinear oscillating systems, for which analytical control laws are infeasible or absent. The focus of this dissertation is on novel analytical paradigms and constructive control design methods for practical ensemble control problems. The first result is a computational method %based on the singular value decomposition (SVD) for the synthesis of minimum-norm ensemble controls for time-varying linear systems. This method is extended to iterative techniques to accommodate bounds on the control amplitude, and to synthesize ensemble controls for bilinear systems. Example ensemble systems include harmonic oscillators, quantum transport, and quantum spin transfers on the Bloch system. To move towards the control of complex ensembles of nonlinear oscillators, which occur in neuroscience, circadian biology, electrochemistry, and many other fields, ideas from synchronization engineering are incorporated. The focus is placed on the phenomenon of entrainment, which refers to the dynamic synchronization of an oscillating system to a periodic input. Phase coordinate transformation, formal averaging, and the calculus of variations are used to derive minimum energy and minimum mean time controls that entrain ensembles of non-interacting oscillators to a harmonic or subharmonic target frequency. In addition, a novel technique for taking advantage of nonlinearity and heterogeneity to establish desired dynamical structures in collections of inhomogeneous rhythmic systems is derived

    5th EUROMECH nonlinear dynamics conference, August 7-12, 2005 Eindhoven : book of abstracts

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    5th EUROMECH nonlinear dynamics conference, August 7-12, 2005 Eindhoven : book of abstracts

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    Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]

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    An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u

    Robust Engineering of Dynamic Structures in Complex Networks

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    Populations of nearly identical dynamical systems are ubiquitous in natural and engineered systems, in which each unit plays a crucial role in determining the functioning of the ensemble. Robust and optimal control of such large collections of dynamical units remains a grand challenge, especially, when these units interact and form a complex network. Motivated by compelling practical problems in power systems, neural engineering and quantum control, where individual units often have to work in tandem to achieve a desired dynamic behavior, e.g., maintaining synchronization of generators in a power grid or conveying information in a neuronal network; in this dissertation, we focus on developing novel analytical tools and optimal control policies for large-scale ensembles and networks. To this end, we first formulate and solve an optimal tracking control problem for bilinear systems. We developed an iterative algorithm that synthesizes the optimal control input by solving a sequence of state-dependent differential equations that characterize the optimal solution. This iterative scheme is then extended to treat isolated population or networked systems. We demonstrate the robustness and versatility of the iterative control algorithm through diverse applications from different fields, involving nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI), electrochemistry, neuroscience, and neural engineering. For example, we design synchronization controls for optimal manipulation of spatiotemporal spike patterns in neuron ensembles. Such a task plays an important role in neural systems. Furthermore, we show that the formation of such spatiotemporal patterns is restricted when the network of neurons is only partially controllable. In neural circuitry, for instance, loss of controllability could imply loss of neural functions. In addition, we employ the phase reduction theory to leverage the development of novel control paradigms for cyclic deferrable loads, e.g., air conditioners, that are used to support grid stability through demand response (DR) programs. More importantly, we introduce novel theoretical tools for evaluating DR capacity and bandwidth. We also study pinning control of complex networks, where we establish a control-theoretic approach to identifying the most influential nodes in both undirected and directed complex networks. Such pinning strategies have extensive practical implications, e.g., identifying the most influential spreaders in epidemic and social networks, and lead to the discovery of degenerate networks, where the most influential node relocates depending on the coupling strength. This phenomenon had not been discovered until our recent study

    Robust reconstruction of sparse network dynamics

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    Reconstruction of the network interaction structure from multivariate time series is an important problem in multiple fields of science. This problem is ill-posed for large networks leading to the reconstruction of false interactions. We put forward the Ergodic Basis Pursuit (EBP) method that uses the network dynamics' statistical properties to ensure the exact reconstruction of sparse networks when a minimum length of time series is attained. We show that this minimum time series length scales quadratically with the node degree being probed and logarithmic with the network size. Our approach is robust against noise and allows us to treat the noise level as a parameter. We show the reconstruction power of the EBP in experimental multivariate time series from optoelectronic networks.Comment: 48 pages, 6 figure

    Formation control of nonholonomic mobile robots: the virtual structure approach

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    PhDIn recent years, there has been a considerable growth in applications of multi-robot systems as opposed to single-robot systems. This thesis presents our proposed solutions to a formation control problem in which mobile robots are required to create a desired formation shape and track a desired trajectory as a whole. In the first instance, we study the formation control problem for unicycle mobile robots. We propose two control algorithms based on a cascaded approach: one based on a kinematic model of a robot and the other based on a dynamic model. We also propose a saturated controller in which actuator limitations are explicitly accounted for. To demonstrate how the control algorithms work, we present an extensive simulation and experimental study. Thereafter we move on to formation control algorithms in which the coordination error is explicitly defined. Thus, we are able to give conditions for robots keeping their desired formation shape without necessarily tracking the desired trajectory. We also introduce a controller in which both trajectory tracking and formation shape maintenance are achieved as well as a saturated algorithm. We validate the applicability of the introduced controllers in simulations and experiments. Lastly, we study the formation control problem for car-like robots. In this case we develop a controller using the backstepping technique. We give conditions for robots keeping their desired formation shape while failing to track their desired trajectories and present simulation results to demonstrate the applicability of the proposed controlle
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