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13
Realtime control under clock offsets between sensors and controllers
"... This paper studies the impact of clock mismatches in spatially distributed realtime control systems. We consider a con guration in which sensor measurements are collected by one processor that transmits the measurements to another control/actuation processor through a network, but the two processo ..."
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This paper studies the impact of clock mismatches in spatially distributed realtime control systems. We consider a con guration in which sensor measurements are collected by one processor that transmits the measurements to another control/actuation processor through a network, but the two processors do not have a common clock. Due to the clock mismatch, there will be an offset between the actual time at which a measurement is taken and the time reported by the sensor. Our goal is to discover fundamental limitations to the ability to stabilize the control loop arising from the clocks mismatch. We consider timevarying bounded offsets and derive limitations on the offset bound for the stability of the feedback system. For the case of a scalar linear process, there exists a critical limitation, which depends on the level of instability of the plant and the nominal sampling period. In contrast, for the vector linear processes, if the process dynamics has at least two distinct real eigenvalues, then there is no fundamental limitation on the offset bound.
Synchronization of Heterogeneous Kuramoto Oscillators with Arbitrary Topology
"... Abstract—We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a Positively Invariant Set (PIS) and lead to synchroni ..."
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Abstract—We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a Positively Invariant Set (PIS) and lead to synchronization. We also introduce an optimization approach that further improves our bounds by employing the topology features of a particular system. Examples are provided to illustrate our results as well as the improvement over previous existing bounds. I.
1Distributed Synchronization of Heterogeneous Oscillators on Networks with Arbitrary Topology
"... Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted messages. In this paper, we study the problem of using distribute ..."
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Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted messages. In this paper, we study the problem of using distributed control to achieve both phase and frequency synchronization of a network of coupled heterogeneous nonlinear oscillators. Not only do our controllers guarantee zero phase error in steady state under arbitrary frequency heterogeneity, but they also require little knowledge of the oscillator nonlinearities and network topology. Furthermore, we provide a global convergence analysis, in the absence of noise and propagation delay, for the resulting nonlinear system whose phase vector evolves on the ntorus.
Construction of power flow feasibility sets
"... Abstract—We develop a new approach for construction of convex analytically simple regions where the AC power flow equations are guaranteed to have a feasible solutions. Construction of these regions is based on efficient semidefinite programming techniques accelerated via sparsity exploiting algori ..."
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Abstract—We develop a new approach for construction of convex analytically simple regions where the AC power flow equations are guaranteed to have a feasible solutions. Construction of these regions is based on efficient semidefinite programming techniques accelerated via sparsity exploiting algorithms. Resulting regions have a simple geometric shape in the space of power injections (polytope or ellipsoid) and can be efficiently used for assessment of system security in the presence of uncertainty. Efficiency and tightness of the approach is validated on a number of test networks. I.
f n i, r
"... specific correlation with note that our method tor networks, provided rm. Moreover, because s have served as a paranchronization in various hed light more generally d could potentially give he termination of cardiac We consider the famous Kuramoto m ..."
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specific correlation with note that our method tor networks, provided rm. Moreover, because s have served as a paranchronization in various hed light more generally d could potentially give he termination of cardiac We consider the famous Kuramoto m
RESEARCH ARTICLE Timescales of Massive Human Entrainment
"... The past two decades have seen an upsurge of interest in the collective behaviors of complex systems composed of many agents entrained to each other and to external events. In this paper, we extend the concept of entrainment to the dynamics of human collective attention. We conducted a detailed in ..."
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The past two decades have seen an upsurge of interest in the collective behaviors of complex systems composed of many agents entrained to each other and to external events. In this paper, we extend the concept of entrainment to the dynamics of human collective attention. We conducted a detailed investigation of the unfolding of human entrainment—as expressed by the content and patterns of hundreds of thousands of messages on Twitter— during the 2012 US presidential debates. By timelocking these data sources, we quantify the impact of the unfolding debate on human attention at three time scales. We show that collective social behavior covaries secondbysecond to the interactional dynamics of the debates: A candidate speaking induces rapid increases in mentions of his name on social media and decreases in mentions of the other candidate. Moreover, interruptions by an interlocutor increase the attention received. We also highlight a distinct time scale for the impact of salient content during the debates: Across wellknown remarks in each debate, mentions in social media start within 5–10 seconds after it occurs; peak at approximately one minute; and slowly decay in a consistent fashion across wellknown events during the debates. Finally, we show that public attention after an initial burst slowly decays through the course of the debates. Thus we demonstrate that largescale human entrainment may hold across a number of distinct scales, in an exquisitely timelocked fashion. The methods and results pave the way for careful study of the dynamics and mechanisms of largescale human entrainment.
Synchronization of Phasecoupled Oscillators with Plastic Coupling Strength
"... Abstract—In this article we study synchronization of systems of homogeneous phasecoupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of a coupling strength between two oscillators is governed by the phase difference between these oscillators. We show ..."
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Abstract—In this article we study synchronization of systems of homogeneous phasecoupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of a coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that such systems are gradient and always achieve frequency synchronization. Moreover, for these systems we provide sufficient stability and instability conditions that are based on results from algebraic graph theory. For a special case when underlying topology is a tree, we formulate a criterion of stability for equilibria. Several examples are used to demonstrate variety of equilibria the system has, and to illustrate differences in behavior of systems with constant and plastic coupling strengths. I.
ReducedState Synchronization of Quantum Networks: Convergence, Graphical Information Hierarchy, and the Missing Symmetry
"... We establish a thorough treatment of reducedstate synchronization for qubit networks with the aim of driving the qubits ’ reduced states to a common trajectory. The evolution of the quantum network’s state is described by a master equation, where the network Hamiltonian is either a direct sum or a ..."
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We establish a thorough treatment of reducedstate synchronization for qubit networks with the aim of driving the qubits ’ reduced states to a common trajectory. The evolution of the quantum network’s state is described by a master equation, where the network Hamiltonian is either a direct sum or a tensor product of identical qubit Hamiltonians, and the coupling terms are given by a set of permutation operators over the network. The permutations introduce naturally quantum directed interactions. We show that reducedstate synchronization is achieved if and only if the quantum interaction graphs corresponding to the permutation operators form a strongly connected union graph. The proof is based on an algebraic analysis making use of the PerronFrobenius theorem for nonnegative matrices. The convergence rate and the limiting orbit are explicitly characterized. Numerical examples are provided illustrating the obtained results. Further, we investigate the missing symmetry in the reducedstate synchronization from a graphical point of view. The informationflow hierarchy in quantum permutation operators is characterized by different layers of informationinduced graphs. We show that the quantum synchronization equation is by nature equivalent to several parallel cutbalanced consensus processes, and a necessary and sufficient condition is obtained for quantum reducedstate synchronization under switching interactions applying recent work of Hendrickx and Tsitsiklis.
Control of coupled oscillator netw gies m r f n
"... specific correlation with note that our method tor networks, provided rm. Moreover, because s have served as a paranchronization in various hed light more generally d could potentially give he termination of cardiac We consider the famous Kuramoto m ..."
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specific correlation with note that our method tor networks, provided rm. Moreover, because s have served as a paranchronization in various hed light more generally d could potentially give he termination of cardiac We consider the famous Kuramoto m
Decentralized Convergence to Nash Equilibria in Constrained Mean Field Control
, 2014
"... This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior of the overall population. For such largescale systems, the ..."
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This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior of the overall population. For such largescale systems, the theory of “mean field” games and control has been successfully applied in various scientific disciplines. While the existing mean field control literature is limited to unconstrained problems, we formulate mean field problems in the presence of heterogeneous convex constraints at the level of individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several iterative solution methods and show that, even in the presence of constraints, the mean field solution gets arbitrarily close to a mean field Nash equilibrium as the population size grows. We apply our methods to the constrained linear quadratic mean field control problem and to the constrained mean field charging control problem for large populations of plugin electric vehicles.