unknown time varying input delay compensation for uncertain nonlinear systems abstract a tracking controller is developed for a class of uncertain nonlinear systems subject to unknown time varying input delay and additive disturbances a novel filtered error signal is designed using the past states in a finite integral over a constant estimated delay interval the maximum tolerable error between unknown time varying delay and a constant estimate of the delay is determined to establish uniformly ultimately bounded convergence of the tracking error to the origin the controller development is based on an approach which uses lyapunov krasovskii functionals to analyze the effects of unknown sufficiently slowly time varying input delays a stability analysis is provided to prove ultimate boundedness of the tracking error signals numerical simulation results illustrate the performance of the developed robust controller

equivalence of linear time delay systems the question of characterizing those time delay systems which are equivalent up to bicausal transformations to a delay free system is a natural and fundamental problem which has been raised since the early 1980s surprisingly this problem remains largely open despite that some partial answers have been provided this technical note tackles this problem for linear systems with constant time delays and gives necessary and sufficient conditions to eliminate whenever is possible or to reduce the number of time delays and a constructive way to get the corresponding bicausal change of coordinates

competition for synchronization in a phase oscillator system abstract a system of phase oscillators with a central oscillator co and a set of n peripheral oscillators pos is considered feed forward and feedback connections between the co and pos are determined by two interaction functions which are assumed to be smooth odd and periodic to describe the competition of pos for synchronization with the co we study the asymptotic stability of fixed points corresponding to in phase synchronization of a group of k pos while other pos are in anti phase with the co it is shown that stability conditions can be formulated in terms of four parameters that describe the slopes of the interaction functions at zero and half period points analytical description of stability in terms of the regions in 4 dimensional parameter space is given combining stability analysis with the detailed study of geometry of invariant manifolds the bifurcations of fixed points are investigated we show that various dynamical regimes such as multistability heteroclinic orbits and chaos are possible analytical stability conditions for global synchronization of pos with the co are formulated for the systems with local connections between pos it is shown that synchronization in a large system with local connections becomes unstable even under weak desynchronizing influence from the co the application of the results to modeling in neuroscience and in particular for modeling visual attention is discussed

emergent behaviors of a holonomic particle system on a sphere we study sufficient conditions for the asymptotic emergence of synchronous behaviors in a holonomic particle system on a sphere which was recently introduced by lohe non abelian kuramoto model and synchronization j phys a math theor 42 395101 395126 2009 these conditions depend only on the coupling strength and initial position diameter for identical particles we show that the position diameter approaches zero asymptotically under these sufficient conditions i e all particles approach to the same position for non identical particles the particle positions do not shrink to one point but can be squeezed into some small region whose diameter is inversely proportional to the coupling strength when the coupling strength is large we also provide several numerical results to confirm our analytical findings

technical communique h optimal terminal control for linear systems with delayed states and controls in this paper we consider a linear time varying system with state and control delay terms both lumped and distributed subject to unknown square integrable disturbances using a differential games approach we provide a necessary and sufficient condition for the existence of an optimal control law minimizing the h norm of the operator mapping the disturbance to the weighted control and terminal state

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

the versal deformation space of a reflexive module on a rational cone abstract by an approach based on results of a ishii we describe the versal deformation space of any reflexive module on the cone over the rational normal curve of degree m for each component a resolution is given as the total space of a vector bundle on a grassmannian the vector bundle is a sum of copies of the cotangent bundle the canonical sub bundle the dual of the canonical quotient bundle and the trivial line bundle via an embedding in a trivial bundle we obtain the components by projection in particular we give equations for the minimal stratum in the chern class filtration of the versal deformation space we obtain a combinatorial description of the local deformation relation and a classification of the components in particular we give a formula for the number of components

prediction based stabilization of linear systems subject to input dependent input delay of integral type in this paper it is proved that a predictor based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input dependent input delay this class is characterized by the delay being implicitly related to past values of the input via an integral model this situation is representative of systems where transport phenomena take place as is frequent in the process industry the sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale arguments of proof for this novel result include general halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems

exponential input to state stabilization of a class of diagonal boundary control systems with delay boundary control abstract this paper deals with the exponential input to state stabilization with respect to boundary disturbances of a class of diagonal infinite dimensional systems via delay boundary control the considered input delays are uncertain and time varying the proposed control strategy consists of a constant delay predictor feedback controller designed on a truncated finite dimensional model capturing the unstable modes of the original infinite dimensional system we show that the resulting closed loop system is exponentially input to state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback

collective synchronization in the presence of reactive coupling and shear diversity we analyze the synchronization dynamics of a model obtained from the phase reduction of the mean field complex ginzburg landau equation with heterogeneity we present exact results that uncover the role of dissipative and reactive couplings on the synchronization transition when shears and natural frequencies are independently distributed as it occurs in the purely dissipative case an excess of shear diversity prevents the onset of synchronization but this does not hold true if coupling is purely reactive in this case the synchronization threshold turns out to depend on the mean of the shear distribution but not on all the other distribution s moments

new formulation of predictors for finite dimensional linear control systems with input delay we consider a one dimensional controlled reaction diffusion equation where the control acts on the boundary and is subject to a constant delay such a model is a paradigm for more general parabolic systems coupled with a transport equation we prove that this is possible to stabilize in h 1 norm this process by means of an explicit predictor based feedback control that is designed from a finite dimensional subsystem the implementation is very simple and efficient and is based on standard tools of pole shifting our feedback acts on the system as a finite dimensional predictor we compare our approach with the backstepping method

exact results for the kuramoto model with a bimodal frequency distribution we analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed the dynamics of this system has been the subject of long standing interest in 1984 kuramoto proposed several conjectures about its behavior ten years later crawford obtained the first analytical results by means of a local center manifold calculation nevertheless many questions have remained open especially about the possibility of global bifurcations here we derive the system s stability diagram for the special case where the bimodal distribution consists of two equally weighted lorentzians using an ansatz recently discovered by ott and antonsen we show that in this case the infinite dimensional problem reduces exactly to a flow in four dimensions depending on the parameters and initial conditions the long term dynamics evolves to one of three states incoherence where all the oscillators are desynchronized partial synchrony where a macroscopic group of phase locked oscillators coexists with a sea of desynchronized ones and a standing wave state where two counter rotating groups of phase locked oscillators emerge analytical results are presented for the bifurcation boundaries between these states similar results are also obtained for the case in which the bimodal distribution is given by the sum of two gaussians

onset of synchronization in complex networks of noisy oscillators we study networks of noisy phase oscillators whose nodes are characterized by a random degree counting the number of its connections both these degrees and the natural frequencies of the oscillators are distributed according to a given probability density replacing the randomly connected network by an all to all coupled network with weighted edges allows us to formulate the dynamics of a single oscillator coupled to the mean field and to derive the corresponding fokker planck equation from the latter we calculate the critical coupling strength for the onset of synchronization as a function of the noise intensity the frequency distribution and the first two moments of the degree distribution our approach is applied to a dense small world network model for which we calculate the degree distribution numerical simulations prove the validity of the made replacement we also test the applicability to more sparsely connected networks and formulate homogeneity and absence of correlations in the degree distribution as limiting factors of our approach

receding horizon controls for input delayed systems this paper presents a receding horizon control rhc for an unconstrained input delayed system to begin with we derive a finite horizon optimal control for a quadratic cost function including two final weighting terms the rhc is easily obtained by changing the initial and final times of the finite horizon optimal control a linear matrix inequality lmi condition on two final weighting matrices is proposed to meet the cost monotonicity under which the optimal cost on the horizon is monotonically nonincreasing with time and hence the asymptotical stability is guaranteed only if an observability condition is met it is shown through simulation that the proposed rhc stabilizes the input delayed system effectively and its performance can be tuned by adjusting weighting matrices with respect to the state and the input

the dynamics of chimera states in heterogeneous kuramoto networks abstract we study a variety of mixed synchronous incoherent chimera states in several heterogeneous networks of coupled phase oscillators for each network the recently discovered ott antonsen ansatz is used to reduce the number of variables in the partial differential equation pde governing the evolution of the probability density function by one resulting in a time evolution pde for a variable with as many spatial dimensions as the network bifurcation analysis is performed on the steady states of these pdes the results emphasise the commonality of the dynamics of the different networks and provide stability information that was previously inferred

phase locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies abstract we study phase locking in a network of coupled nonlinear oscillators with local interactions and random intrinsic frequencies the oscillators are located at the vertices of a graph and interact along the edges they are coupled by sinusoidal functions of the phase differences across the edges and their intrinsic frequencies are independent and identically distributed with finite mean and variance we derive an exact expression for the probability of phase locking in a linear chain of such oscillators and prove that this probability tends to zero as the number of oscillators grows without bound however if the coupling strength increases as the square root of the number of oscillators the probability of phase locking tends to a limiting distribution the kolmogorov smirnov distribution this latter result is obtained by showing that the phase locking problem is equivalent to a discretization of pinned brownian motion the results on chains of oscillators are extended to more general graphs in particular for a hypercubic lattice of any dimension the probability of phase locking tends to zero exponentially fast as the number of oscillators grows without bound we also consider a less stringent type of synchronization characterized by large clusters of oscillators mutually entrained at the same average frequency it is shown that if such clusters exist they necessarily have a sponge like geometry

synchronization of coupled rotators josephson junction ladders and the locally coupled kuramoto model we show that the resistively shunted junction rsj equations describing a ladder array of overdamped critical current disordered josephson junctions that are current biased along the rungs of the ladder can be mapped onto a kuramoto model with nearest neighbor sinusoidal couplings this result is obtained by an averaging method in which the fast dynamics of the rsj equations are integrated out leaving the dynamics which describe the time scale over which neighboring junctions along the rungs of the ladder phase and frequency synchronize we quantify the degree of frequency synchronization of the rung junctions by calculating the standard deviation of their time averaged voltages ensuremath sigma ensuremath omega and the phase synchronization is quantified by calculating the time average of the modulus of the kuramoto order parameter r we test the results of our averaging process by comparing the values of ensuremath sigma ensuremath omega and r for the original rsj equations and our averaged equations we find excellent agreement for dc bias currents of i b i c ensuremath gtrsim 3 where i c is the average critical current of the rung junctions and critical current disorders of up to 10 we also study the effects of thermal noise on the synchronization properties of the overdamped ladder finally we find that including the effects of junction capacitance can lead to a discontinuous synchronization transition as the strength of the coupling between neighboring junctions is smoothly varied

consensusability of multi agent systems with time varying communication delay abstract this paper studies the consensusability problem of continuous time multi agent systems with time varying communication delay in undirected network we design a consensus protocol based on the low gain solution of a parametric algebraic riccati equation are and not use the precise information of the amount of time varying delay by studying the joint effect of agent dynamic and network topology sufficient conditions are given for consensus when all poles of the system matrix are on the closed left half plane in case of non zero poles on the imaginary axis maximal admissible upper bound of the time varying delay is given in terms of both the agent dynamic and network topology otherwise consensus can be achieved for the time varying delay with arbitrarily large upper bound finally simulation results are presented to demonstrate the effectiveness of the theoretical results

a positivity based approach to delay dependent stability of systems with large time varying delays abstract in this paper we propose new explicit tests for positivity and exponential stability of systems with large time varying delays our approach is based on nonoscillation of solutions of the corresponding diagonal scalar delay differential equations numerical examples illustrate the efficiency of the results

rapid stabilisation of an euler bernoulli beam with the internal delay control in this paper we are concerned with rapid stabilisation of an euler bernoulli beam with internal delayed control herein we introduce a new approach of the feedback control design from the system

predictor based sampled data exponential stabilization through continuous discrete observers the problem of stabilizing a linear continuous time system with discrete time measurements and a sampled input with a pointwise constant delay is considered in a first part we design a continuous discrete observer which converges when the maximum time interval between two consecutive measurements is sufficiently small in a second part we construct a dynamic output feedback by using a technique which is strongly reminiscent of the reduction model approach it stabilizes the system when the maximal time between two consecutive sampling instants is sufficiently small no limitation on the size of the delay is imposed and an iss property with respect to additive disturbances is established

the infinite time quadratic control problem for linear systems with state and control delays an evolution equation approach we show how a linear differential delay equation with delays in the control can be reformulated as an evolution equation with bounded input operator as a simple application we solve an infinite time quadratic cost control problem for the delay differential equation we also point out how our results even when specialized to the case where delays in the control disappear extend results previously published in the literature

control of linear systems with fixed noncommensurate point delays the first solution is given to the fundamental open problem of stabilizability and detectability necessary sufficient conditions for internal stabilization by feedback of retarded and a large class of neutral delay differential systems with several fixed noncommensurate point delays using causal compensators observers and state feedback or dynamic output feedback which are also the same type of neutral or retarded delay differential systems with fixed point delays only our results are rank conditions on the system matrices zi f g and zif t h t evaluated at points in the complex plane and are the weakest possible generally applicable sufficient such rank conditions for stabilization of neutral systems in the light of what is known on the stability of such systems these conditions are necessary for most practical purposes the class of systems we consider includes all retarded delay differential systems with noncommensurate fixed point delays in the case of retarded systems these rank conditions are necessary and sufficient conditions for stabilization via compensators which are causal retarded delay differential systems with fixed point delays only these constitute the first full solution of these previously unsolved problems of stabilizability and detectability which together are necessary and sufficient conditions for internal stabilization by feedback for delay differential systems even in the retarded single fixed point delay case an application of our results to a problem of practical importance in control of linear systems with no delays provides a stabilization criterion interesting in itself

structure and stability of the equilibrium set in potential driven flow networks abstract in this paper we address local bifurcation properties of a family of networked dynamical systems specifically those defined by a potential driven flow on a directed graph these network flows include linear consensus dynamics or kuramoto models of coupled nonlinear oscillators as particular cases as it is well known for consensus systems these networks exhibit a somehow unconventional dynamical feature namely the existence of a line of equilibria following from a well known property of the graph laplacian matrix in connected networks with positive weights negative weights which arise in different contexts e g in consensus models in signed graphs or in kuramoto models with antagonistic actors may on the one hand lead to higher dimensional manifolds of equilibria and on the other be responsible for bifurcation phenomena in this direction we prove a saddle node bifurcation theorem for a broad family of potential driven flows in networks with one or more negative weights the goal is to state the conditions in structural terms that is in terms of the expressions defining the flowrates and the graph theoretic properties of the network not only the eigenvalue requirements but also the nonlinear transversality assumptions supporting the bifurcation motivate an analysis of independent interest concerning the rank degeneracies of nodal matrices arising in the linearized dynamics this analysis is performed in terms of the contraction deletion structure of spanning trees and uses several results from matrix analysis different examples illustrate the results some linear problems including signed graphs are aimed at illustrating the analysis of nodal matrices whereas in a nonlinear framework we apply the characterization of saddle node bifurcations to networks with a sinusoidal kuramoto like flow

the noisy voter model under the influence of contrarians abstract the influence of contrarians on the noisy voter model is studied at the mean field level the noisy voter model is a variant of the voter model where agents can adopt two opinions optimistic or pessimistic and can change them by means of an imitation herding and an intrinsic noise mechanisms an ensemble of noisy voters undergoes a finite size phase transition upon increasing the relative importance of the noise to the herding form a bimodal phase where most of the agents share the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states by the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents anti herding we first consider the case of only contrarians and show that the only possible steady state is the unimodal one more generally when voters and contrarians are present we show that the bimodal unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four and their characteristic rates are small enough for the number of contrarians bigger or equal to four the voters and the contrarians can be seen only in the unimodal phase moreover if the number of voters and contrarians as well as the noise and herding rates are of the same order then the probability functions of the steady state are very well approximated by the gaussian distribution

conformists and contrarians in a kuramoto model with identical natural frequencies we consider a variant of the kuramoto model in which all the oscillators are now assumed to have the same natural frequency but some of them are negatively coupled to the mean field these contrarian oscillators tend to align in antiphase with the mean field whereas the positively coupled conformist oscillators favor an in phase relationship the interplay between these effects can lead to rich dynamics in addition to a splitting of the population into two diametrically opposed factions the system can also display traveling waves complete incoherence and a blurred version of the two faction state exact solutions for these states and their bifurcations are obtained by means of the watanabe strogatz transformation and the ott antonsen ansatz curiously this system of oscillators with identical frequencies turns out to exhibit more complicated dynamics than its counterpart with heterogeneous natural frequencies

output stabilization of time varying input delay systems using interval observation technique the output stabilization problem for a linear system with an unknown bounded time varying input delay is considered the interval observation technique is applied in order to obtain guaranteed interval estimate of the system state the procedure of the interval observer synthesis uses lower and upper estimates of the unknown delay and requires to solve a special silvester s equation the interval predictor is introduced in order to design a linear stabilizing feedback the control design procedure is based on linear matrix inequalities lmi the theoretical results are supported by numerical simulations and compared with a control design scheme based on a luenberger like observer

change of rings in deformation theory of modules given a b module m and any presentation b a j the obstruction theory of m as a b module is determined by the usual obstruction class o a for deforming m as an a module and a new obstruction class o j these two classes give the tool for constructing two obstruction maps which depend on each other and which characterise the hull of the deformation functor we obtain relations between the obstruction classes by studying a change of rings spectral sequence and by representing certain classes as elements in the yoneda complex calculation of the deformation functor of m as a b module including the generalised massey products is thus possible within any a free 2 presentation of m

linear quadratic regulation and stabilization of discrete time systems with delay and multiplicative noise this paper is concerned with the long standing problems of linear quadratic regulation lqr control and stabilization for a class of discrete time stochastic systems involving multiplicative noises and input delay these fundamental problems have attracted resurgent interests due to development of networked control systems an explicit analytical expression is given for the optimal lqr controller more specifically the optimal lqr controller is shown to be a linear function of the conditional expectation of the state with the feedback gain based on a riccati zxl difference equation it is also shown that the system is stabilizable in the mean square sense if and only if an algebraic riccati zxl equation has a particular solution these results are based on a new technical tool which establishes a non homogeneous relationship between the state and the costate of this class of systems and the introduction of a new lyapunov function for the finite horizon optimal control design

an internal state decomposition approach to a discrete time h2 control problem with irrational input non minimum phase property abstract an internal state decomposition approach to a class of discrete time h 2 control problems with irrational non minimum phase property at the control input is proposed this is a generalization of the state variable transformation to derive the discrete time smith predictor for a single input delay system the h 2 optimal controller is derived using the orthogonality principle in h 2 space as a direct consequence of the state decomposition the characterization of the optimal cost by the previous and alternative truncation operators is also discussed

dynamics of a semiconductor laser array with delayed global coupling we study the dynamics of an array of single mode semiconductor lasers globally but weakly coupled by a common external feedback mirror and by nearest neighbor interactions we seek to determine the conditions under which all lasers of the array are in phase whether in a steady periodic quasiperiodic or chaotic regime in order to maximize the output far field intensity we show that the delay may be a useful control parameter to achieve in phase synchronization for the in phase steady state there is a competition between a delay induced hopf bifurcation leading to an in phase periodic regime and a delay independent hopf bifurcation leading to an antiphased periodic regime both regimes are described analytically and secondary hopf bifurcations to quasiperiodic solutions are found close to the stable steady state the array is described by a set of kuramoto equations for the phases of the fields above the first hopf bifurcation these equations are generalized by the addition of second and third order time derivatives of the phases

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

output feedback adaptive control of a wave pde with boundary anti damping abstract we develop an adaptive output feedback controller for a wave pde in one dimension with actuation on one boundary and with an unknown anti damping term on the opposite boundary this model is representative of a torsional stick slip instability in drillstrings in deep oil drilling as well as of various acoustic instabilities the key feature of the proposed controller is that it requires only the measurements of boundary values and not of the entire distributed state of the system our approach is based on employing riemann variables to convert the wave pde into a cascade of two delay elements with the first of the two delay elements being fed by control and the same element in turn feeding into a scalar ode this enables us to employ a prediction based design for systems with input delays suitably converted to the adaptive output feedback setting the result s relevance is illustrated with simulation example

adaptive sinusoidal disturbance cancellation for unknown lti systems despite input delay solutions exist for the problems of canceling sinusoidal disturbances and compensating input delays in this paper two problems are considered simultaneously and an adaptive controller is designed to cancel unknown sinusoidal disturbances forcing an unknown linear time invariant system in controllable canonical form despite input delay the design is based on three steps 1 parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters 2 representation of the delay as a transport pde 3 design of the adaptive controller by using the backstepping boundary control technique for pdes it is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t with perfect disturbance estimation the effectiveness of the controller is illustrated with a simulation example of a second order system

algebraic relaxation of an order parameter in randomly coupled limit cycle oscillators in their recent paper phys rev e 58 1789 1998 stiller and radons sr study following our earlier work phys rev lett 68 1073 1992 the behavior of globally and randomly coupled phase oscillators with distributed intrinsic frequencies they claim that their simulation results do not confirm the power law behavior of an order parameter found numerically by the author attributing its cause to the poor precision of the author s integration scheme here demonstrated is that the power law survives even for a scheme better than sr s provided that finite size effects are properly taken into account as was done in our previous work

local stabilization of nonlinear systems through the reduction model approach we study a general class of nonlinear systems with input delays of arbitrary size we adapt the reduction model approach to prove local asymptotic stability of the closed loop input delayed systems using feedbacks that may be nonlinear our lyapunov krasovskii functionals make it possible to determine estimates of the basins of attraction for the closed loop systems

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

dynamics of majority rule in two state interacting spin systems we introduce a two state opinion dynamics model where agents evolve by majority rule in each update a group of agents is specified whose members then all adopt the local majority state in the mean field limit where a group consists of randomly selected agents consensus is reached in a time that scales ln n where n is the number of agents on finite dimensional lattices where a group is a contiguous cluster the consensus time fluctuates strongly between realizations and grows as a dimension dependent power of n the upper critical dimension appears to be larger than 4 the final opinion always equals that of the initial majority except in one dimension

robustness of adaptive control under time delays for three dimensional curve tracking we analyze the robustness of a class of controllers that enable three dimensional curve tracking by a free moving particle the free particle tracks the closest point on the curve by building a strict lyapunov function and robustly forward invariant sets we show input to state stability under predictable tolerance and safety bounds that guarantee robustness under control uncertainty input delays and a class of polygonal state constraints including adaptive tracking and parameter identification under unknown control gains such an understanding may provide certified performance when the control laws are applied to real life systems

glassy synchronization in a population of coupled oscillators a phase model for a population of oscillators with random excitatory and inhibitory mean field coupling and subject to external white noise random forces is proposed and studied in the thermodynamic limit different stable phases for the oscillator population may be found i an incoherent state where all possible values of an oscillator phase are equally probable ii a synchronized state where the population has a nonzero collective phase iii a glassy phase where the global synchronization is zero but the oscillators are in phase with the random disorder and iv a mixed phase where the oscillators are partially synchronized and partially in phase with the disorder these predictions are based upon bifurcation analysis of the reduced equation valid at the thermodynamic limit and confirmed by brownian simulation

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

averaging of globally coupled oscillators abstract we study a specific system of symmetrically coupled oscillators using the method of averaging the equations describe a series array of josephson junctions we concentrate on the dynamics near the splay phase state also known as the antiphase state ponies on a merry go round or rotating wave we calculate the floquet exponents of the splay phase periodic orbit in the weak coupling limit and find that all of the floquet exponents are purely imaginary in fact all the floquet exponents are zero except for a single complex conjugate pair thus nested two tori of doubly periodic solutions surround the splay phase state in the linearized averaged equations we numerically integrate the original system and find startling agreement with the averaging results on two counts the observed ratio of frequencies is very close to the prediction and the solutions of the full equations appear to be either periodic or doubly periodic as they are in the averaged equations such behavior is quite surprising from the point of view of generic dynamical systems theory one expects higher dimensional tori and chaotic solutions we show that the functional form of the equations and not just their symmetry is responsible for this nongeneric behavior

collective synchronisation in lattices of nonlinear oscillators with randomness the authors study mutual synchronisation in a model of interacting limit cycle oscillators with random intrinsic frequencies it is shown rigorously that the model exhibits no long range order in one dimension and that in higher dimensional lattices large clusters of synchronised oscillators necessarily have a sponge like structure surprisingly the phase locking behaviour of the mean field model is completely different from that of any finite dimensional lattice indicating that d infinity is the upper critical dimension for phase locking

stabilization of discrete time linear systems with an unknown time varying delay by switched low gain feedback in this note we investigate the stabilization of discrete time linear systems with an unknown time varying delay existing literature on the stabilization of time delay systems require some knowledge such as an upper bound of the delay in this paper by proposing a switched low gain feedback control law we are able to achieve asymptotic stabilization of the system without any knowledge of the delay in addition the proposed switched low gain feedback law also significantly improves the closed loop system performance in terms of overshoot and convergence speed in comparison with the traditional fixed gain design simulation study illustrates the effectiveness of our theoretical results

constants of motion for superconducting josephson arrays abstract we show that series arrays of n identical overdamped josephson junctions have extremely degenerate dynamics in particular we prove that such arrays have n 3 constants of motion for all n 3 the analysis is based on a coordinate transformation that reduces the governing equations to an n 3 parameter family of low dimensional systems in the weak coupling limit the reduced equations can be analyzed completely either all solutions approach the synchronous state or they converge to a continuous family of incoherent oscillations depending on a certain parameter value at the transitional value of this parameter the system becomes completely integrable then the phase space is foliated by invariant two dimensional tori for any n 3 the infinite n limit of the system is an integro partial differential equation with rigorously low dimensional dynamics it supports solitons in the integrable case and chaotic waves in the non integrable case

prediction based control for systems with state and several input delays in this contribution an extension of the prediction based design scheme proposed in tsubakino etal 2015 for compensation of input delays to the case of systems with input and state delays is presented to derive safely implementable control laws we propose to apply additional input filters and obtain a closed loop system in the form of a set of retarded type differential equations an example illustrating the design scheme is given