arXiv subjects

S. Emre Tuna

Publications and source records attributed to S. Emre Tuna.

At least 19 recordsLinked to original sources

arXiv2023

Synchronization via impulsive deadbeat coupling

For linear networks, where the coupling between the agents takes place through periodic impulses, a simple method is proposed for synchronization. It is shown that closing the loop by (normalized) deadbeat feedback gain produces synchronous behavior if the coupling strength $μ$ is large enough. With such choice of control law, in the limiting case ($μ\to\infty$) exact synchronization is achieved after $n$ periods, where $n$ is the order of individual agent dynamics.

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arXiv2022

Synchronization of oscillators not sharing a common ground

Networks of coupled LC oscillators that do not share a common ground node are studied. Both resistive coupling and inductive coupling are considered. For networks under resistive coupling, it is shown that the oscillator-coupler interconnection has to be bilayer if the oscillator voltages are to asymptotically synchronize. Also, for bilayer architecture (when both resistive and inductive couplers are present) a method is proposed to compute a complex-valued effective Laplacian matrix that represents the overall coupling. It is proved that the oscillators display synchronous behavior if and only if the effective Laplacian has a single eigenvalue on the imaginary axis.

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arXiv2020

Harmonic synchronization under all three types of coupling: position, velocity, and acceleration

Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the oscillators asymptotically synchronize if and only if this matrix has a single eigenvalue on the imaginary axis. This result generalizes some of the known spectral tests for synchronization. Some simpler Laplacian constructions are also proved to work provided that certain structural conditions are satisfied by the coupling graphs.

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arXiv2019

Structural analysis of synchronization in networks of linear oscillators

In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization and coupling structure is studied. Conditions on the interconnection under which synchronization can be achieved for some selection of coupling strengths are established. How to strengthen those conditions so that synchronization is guaranteed for all admissible parameter values is also presented.

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arXiv2019

Synchronization of linear oscillators coupled through dynamic networks with interior nodes

Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network is allowed to contain interior nodes, i.e., those that are not directly connected to an oscillator. It is shown that the oscillators asymptotically synchronize if and only if the Schur complement (with respect to the boundary nodes) of the complex-valued Laplacian matrix representing the coupling has a single eigenvalue on the imaginary axis.

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arXiv2018

Synchronization of small oscillations

Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative connectors. A construction is proposed to combine these two real matrices in a single complex matrix. It is shown that whether the oscillators synchronize in the steady state or not depends on the number of eigenvalues of this complex matrix on the imaginary axis. Certain refinements of this condition for the special cases, where the restorative coupling is either weak or absent, are also presented.

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arXiv2017

Synchronization of linear systems via relative actuation

Synchronization in networks of discrete-time linear time-invariant systems is considered under relative actuation. Neither input nor output matrices are assumed to be commensurable. A distributed algorithm that ensures synchronization via dynamic relative output feedback is presented.

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arXiv2017

Positive controllability of networks under relative actuation

For arrays of identical linear systems coupled through relative actuation four problems are studied: controllability, positive controllability, pairwise controllability, and positive pairwise controllability. To this end, related to the eigenvalues of the system matrix, certain graphs with possibly vector-valued edge weights are constructed. It is shown that array controllability and graph connectivity are equivalent. Similar equivalences are established also between positive controllability and strong connectivity, pairwise controllability and pairwise connectivity, and positive pairwise controllability and strong pairwise connectivity.

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arXiv2016

Observability through matrix-weighted graph

Observability of an array of identical LTI systems with incommensurable output matrices is studied, where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems. It is shown that the observability of an array is equivalent to the connectivity of its interconnection graph, whose edges are assigned matrix weights. The interconnection graph is studied by means of a collection of simpler graphs, each of which is associated to an eigenvalue of the system matrix of individual dynamics. It is reported that the interconnection graph is connected if and only if no member of this collection is disconnected. Moreover, to better understand the relative behavior of distant units, pairwise observability which concerns with the synchronization of a certain pair of individual systems in the array is studied. This milder version of observability is shown to be closely related to certain connectivity properties of the interconnection graph as well. Pairwise observability is also analyzed using the circuit theoretic tool effective conductance. The observability of a certain pair of units is proved to be equivalent to the nonsingularity of the (matrix-valued) effective conductance between the associated pair of nodes of a resistive network (with matrix-valued parameters) whose node admittance matrix is the Laplacian of the array's interconnection graph.

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arXiv2016

Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks

The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented. Through simple physical examples, the meaning and limitations of the theorems are expounded. Also, to demonstrate their versatility, the results are extended to cover LTI passive electrical networks. One of the extensions generalizes the well-known link between the asymptotic stability of the synchronization subspace and the second smallest eigenvalue of the Laplacian matrix.

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arXiv2015

Synchronization under matrix-weighted Laplacian

Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix. Simple methods are proposed to generate a (separate) linear coupling gain for each pair of systems, which ensures that all the solutions converge to a common trajectory. Both continuous-time and discrete-time cases are considered.

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arXiv2013

A dual pair of optimization-based formulations for estimation and control

A finite-horizon optimal estimation problem for discrete-time linear systems is formulated and solved. The formulation is a natural extension of that which yields a deadbeat observer. The resultant observer is the dual of the controller produced by the finite-horizon minimum energy control problem with terminal equality constraint. Nonlinear extensions of this dual pair are also considered and sufficient conditions are provided for stability and convergence.

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arXiv2012

Geometry of deadbeat synchronization

The deadbeat synchronization of identical discrete-time nonlinear systems is studied from a geometric point of view. An array of deadbeat observers coupled via a deadbeat interconnection is shown to achieve synchronization in finite number of steps provided that a compatibility condition is satisfied between the observer and the interconnection. As an illustration to the theory, an example is provided where an array of third order observers achieves deadbeat synchronization.

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arXiv2011

Deadbeat observer: construction via sets

A geometric generalization of discrete-time linear deadbeat observer is presented. The proposed method to generate a deadbeat observer for a given nonlinear system is constructive and makes use of sets that can be computed iteratively. For demonstration, derivations of observer dynamics are provided for various example systems. Based on the method, a simple algorithm that computes the deadbeat gain for a linear system with scalar output is given.

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arXiv2011

Deadbeat control: construction via sets

A geometric generalization of the discrete-time linear deadbeat control problem is studied. The proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively. For demonstration, derivations of deadbeat feedback law and tracker dynamics are provided for various example systems. Based on the method, a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given.

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arXiv2010

Synchronization analysis of coupled planar oscillators by averaging

Sufficient conditions for synchronization of coupled Lienard-type oscillators are investigated via averaging technique. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the relative distance (between the states of the pair being coupled) vector. Under the assumption that the interconnection topology defines a connected graph, it is shown that the solutions of oscillators can be made converge arbitrarily close to each other, while let initially be arbitrarily far apart, provided that the frequency of oscillations is large enough and the initial phases of oscillators all lie in an open semicircle. It is also shown that (almost) synchronized oscillations always take place at some fixed magnitude independent of the initial conditions. Similar results are generated for nonlinearly-coupled harmonic oscillators.

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arXiv2009

Nonlinearly coupled harmonic oscillators: high frequency oscillations yield synchronization

Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the relative distance (between the states of the pair being coupled) vector. Under the assumption that the interconnection topology defines a connected graph, it is shown that the synchronization manifold is semiglobally practically asymptotically stable in the frequency of oscillations.

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arXiv2008

Sufficient conditions on observability grammian for synchronization in arrays of coupled time-varying linear systems

Synchronizability of stable, output-coupled, identical, time-varying linear systems is studied. It is shown that if the observability grammian satisfies a persistence of excitation condition, then there exists a bounded, time-varying linear feedback law that yields exponential synchronization for all fixed, asymmetrical interconnections with connected graphs. Also, a weaker condition on the grammian is given for asymptotic synchronization. No assumption is made on the strength of coupling. Moreover, related to the main problem, a particular array of output-coupled systems that is pertinent to much-studied consensus problems is investigated. In this array, the individual systems are integrators with identical, time-varying, symmetric positive semi-definite output matrices. Trajectories of this array are shown to stay bounded using a time-invariant, quadratic Lyapunov function. Also, sufficient conditions on output matrix for synchronization are provided. All of the results in the paper are generated for both continuous time and discrete time.

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