exponential stability and solution bounds for systems with bounded nonlinearities estimation of lyapunov exponents of systems with bounded nonlinearities plays an essential part in their robust control known results in this field are based on the gronwall inequality yielding relatively conservative bounds for lyapunov exponents in this note we obtained more accurate upper bounds for the general lyapunov exponent for systems consisting of a known linear time varying part and an unknown nonlinear component with a bounded lipschitz constant at zero consequently a sufficient condition for exponential stability of this system is formulated the systems are indicated for which the obtained bound is precise i e cannot be improved without additional information on the nonlinear term in the presence of a persisting perturbation an upper bound for the solution norm is derived and expressed in the norm of the solution of the corresponding linear system using the obtained results a condition for exponential stability of a linear time varying control system with a nonlinear feedback is derived numerical results are obtained for a second order time varying system and for the lienard equation in the latter case they are favorably compared with stability conditions previously obtained using the lyapunov function method

semi global practical asymptotic stability and averaging abstract we prove a generalized liapunov theorem which guarantees practical asymptotic stability based on this theorem we show that if the averaged system x f av x corresponding to x f x t is globally asymptotically stable then starting from an arbitrarily large set of initial conditions the trajectories of x f x t e converge uniformly to an arbitrarily small residual set around the origin when e 0 is taken sufficiently small in other words the origin is semi globally practically asymptotically stable

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

averaging results and the study of uniform asymptotic stability of homogeneous differential equations that are not fast time varying within the liapunov framework a sufficient condition for uniform asymptotic stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the v function taken along solutions of the system may have positive and negative values it is shown that the proposed condition is useful for the study of uniform asymptotic stability of homogeneous systems with order tau 0 in particular it is established that asymptotic stability of the averaged homogeneous system implies local uniform asymptotic stability of the original time varying homogeneous system this shows that averaging techniques play a prominent role in the study of homogeneous not necessarily fast time varying systems

an averaging theorem for time periodic degree zero homogeneous differential equations abstract this paper considers the stability of the differential equation dot x ex t x e x r n where x t x e is a time periodic degree zero homogeneous vector field and e 0 is a parameter it is shown that asymptotic stability of the time averaged equation implies asymptotic stability of the original system for e sufficiently small

open loop routing of n arrivals to m parallel queues we consider the problem of routing n arrivals to m queues in parallel when no information other than the prior statistics are available for the decision process the work we present here differs from results in the literature in two significant ways 1 we address the nonstationary problem of open loop routing for n spl infin arrivals and 2 we do not decompose the problem into an allocation phase and a routing phase but look instead for an overall optimal policy exhaustive enumeration and dynamic programming turn out to be computationally infeasible approaches for realistic values of the parameters n and m examination of the necessary conditions for optimality as given by pontryagin s maximum principle leads to the formulation of a policy iteration algorithm convergence of the algorithm in a finite number of iterations as well as monotonicity results are established while only convergence to a local minimum is guaranteed extensive computational experimentation points to its near optimality some variants of the basic policy iteration algorithm are also discussed

perturbation theory and singular perturbations for input to state multistable systems on manifolds we consider the notion of input to state multistability which generalizes input to state stability to nonlinear systems evolving on riemannian manifolds and possessing a finite number of compact globally attractive invariant sets and in addition satisfies a specific condition of acyclicity we prove that a parameterized family of dynamical systems whose solutions converge to those of a limiting system inherits such input to state multistability property from the limiting system in a semiglobal practical fashion a similar result is also established for singular perturbation models whose boundary layer subsystem is uniformly asymptotically stable and whose reduced subsystem is input to state multistable known results in the theory of perturbations singular perturbations averaging and highly oscillatory control systems are here generalized to the multistable setting by replacing the classical asymptotic stability requirement of a single invariant set with attractivity and acyclicity of a decomposable invariant one

numerical simulations of incompressible aerodynamic flows using viscous inviscid interaction procedures abstract steady two dimensional laminar incompressible flows over airfoils are simulated using a helmholtz velocity decomposition where the velocity vector is split into a gradient of a potential and a correction representing the rotational components for most aerodynamic flows the rotational components of the velocity vanish outside the boundary layer and the wake region therefore the near and far velocity fields can be represented by a potential function and the pressure can be obtained there from bernoulli s law in the viscous flow region the momentum equations are integrated to calculate the rotational velocity components conservation of mass leads to a poisson s equation for the potential function where the right hand side the forcing function is given in terms of the divergence of the rotational velocity component the latter represents a distribution of sources in the viscous layer and results in a displacement effect on the outside potential field in this formulation the pressure in the momentum equations does not play an essential role since the conservation of mass is imposed through the augmented potential equation after the velocity field is obtained the correct pressure distribution in the viscous flow region is calculated by integrating the normal momentum equation numerical results are presented to confirm the validity and the merits of the present formulation solving a poisson s equation for the potential function rather than the pressure as in standard methods for solving navier stokes equations is the main advantage since the calculations of the rotational velocity components are restricted to the viscous flow region only standard numerical methods are applicable to the present formulation including multigrid acceleration techniques for the augmented potential equation

averaging with disturbances and closeness of solutions abstract we establish that under appropriate conditions the solutions of a time varying system with disturbances converge uniformly on compact time intervals to the solutions of the system s average as the rate of change of time increases to infinity the notions of average used for systems with disturbances are the strong and weak averages introduced in nesic and teel d nesic a r teel input to state stability for time varying nonlinear systems via averaging 1999 submitted for publication see also on averaging and the iss property proceedings of the 38th conference on decision and control phoenix az december 1999 pp 3346 3351

compensating drift vector fields with gradient vector fields for asymptotic submanifold stabilization we derive sufficient conditions on a drift vector field to let an asymptotically stable invariant submanifold of an input affine system without drift remain asymptotically stable for the system with drift in doing so we use the same feedback laws modulo control gain tuning such that no new feedback laws need to be designed for the system with drift our main assumption is that the vector field of the input affine system without drift assumes the form of a gradient vector field for given feedback laws we show how one can assess the performance of the system with drift only via knowledge about the system without drift finally we find that our results are relevant in synchronization problems and backstepping controllers for mechanical systems

a less conservative stability test for second order linear time varying vector differential equations system stability and stability bounds play an essential role in control theory this note is concerned with the exponential stability of a class of second order linear time varying vector differential equations with real piecewise continuous coefficient matrices a less conservative explicit condition for stability of such a system is derived using the matrix measure theory and a more accurate upper bound for the decay exponent of its stable solution is established examples are included for illustration

sufficient conditions for the stability of a class of second order systems this paper provides sufficient conditions to assess the stability and input to state stability of a class of second order systems by only looking at the structure of the dynamic equations these results are proven by using the variable gradient method to build suitable lyapunov functions the paper includes a number of relevant examples that highlight the value of the contribution

on the stability analysis of phasor and classic extremum seeking control abstract in this work we present a semi global practical asymptotic stability analysis for phasor extremum seeking control with a general non linear dynamic system with the same technique applied to the classic band pass filter algorithm we present a more relaxed less constrained semi global practical asymptotic stability condition compared to earlier work the results are based on a non approximated averaging for both control techniques

further results on strict lyapunov functions for rapidly time varying nonlinear systems we explicitly construct global strict lyapunov functions for rapidly time varying nonlinear control systems the lyapunov functions we construct are expressed in terms of oftentimes more readily available lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable this leads to new sufficient conditions for uniform global exponential uniform global asymptotic and input to state stability of fast time varying dynamics we also construct strict lyapunov functions for our systems using a strictification approach we illustrate our results using several examples

on the local input output stability of event triggered control systems this paper studies performance preserving event design in nonlinear event based control systems based on a local mathcal l 2 type performance criterion considering a finite gain local mathcal l 2 stable disturbance driven continuous time system we propose a triggering mechanism so that the resulting sampled data system preserves similar disturbance attenuation local mathcal l 2 gain property the results are applicable to nonlinear systems with exogenous disturbances bounded by some lipschitz continuous function of state it is shown that an exponentially decaying function of time combined with the proposed triggering condition extends the interevent periods compared to the existing works this paper analytically estimates the increase in intersampling periods at least for an arbitrary period of time we also propose a so called discrete triggering condition to quantitatively find the improvement in interevent times at least for an arbitrary number of triggering iterations illustrative examples support the analytically derived results

smoothing point processes as a means to increase throughput unlike the leaky bucket scheme which regulates the input rate the filters we study in this paper reduce the variability of interarrival times subject to a maximum delay constraint for each customer these filters are called smoothing filters for point processes by considering the output processes of various queueing systems we show that an infinite server queue acts as a smoothing filter for a doubly stochastic poisson process and a single server queue with deterministic service times acts as a smoothing filter for a stationary and ergodic point process based on the second point we provide a smoothing algorithm that satisfies a maximum delay constraint the algorithm is shown to be robust and consistent we then consider two examples where these filters can be applied to increase throughput one is the single server loss system with exponential service times the other is the leaky bucket scheme with token buffer size 1 numerical examples and simulations are also given for comparing the tradeoff between delay and throughput our approach is based on the variability ordering and a cut criterion for the majorization ordering the criterion appears to be new and of independent interest

second order global consensus in multiagent networks with random directional link failure in this paper we consider the second order globally nonlinear consensus in a multiagent network with general directed topology and random interconnection failure by characterizing the behavior of stochastic dynamical system with the corresponding time averaged system a criterion for the second order consensus is derived by constructing a lyapunov function for the time averaged network by associating the solution of random switching nonlinear system with the constructed lyapunov function a sufficient condition for second order globally nonlinear consensus in a multiagent network with random directed interconnections is also established it is required that the second order consensus can be achieved in the time averaged network and the lyapunov function decreases along the solution of the random switching nonlinear system at an infinite subsequence of the switching moments a numerical example is presented to justify the correctness of the theoretical results

path following for nonlinear systems with unstable zero dynamics an averaging solution we consider a path following problem in which the goal is to ensure that the error between the system output and the geometric path is asymptotically less than a prespecified constant while guaranteeing a forward motion along the path and boundedness of all states comparing with the results on this problem we exploit averaging techniques to develop an alternative simpler solution for a class of nonlinear systems and for paths satisfying a certain geometric condition

synchronization analysis of coupled lienard type oscillators by averaging sufficient conditions for the synchronization of coupled lienard type oscillators are investigated via averaging technique the coupling considered here is fixed nonsymmetric and nonlinear under the assumption that the interconnection topology defines a connected graph it is shown that the solutions of oscillators converge arbitrarily close to each other starting from initial conditions 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 the nearly synchronized oscillations always take place around some fixed magnitude independent of the initial conditions and the coupling functions

wake classification of heaving airfoils using the spectral hp element method in this paper the two dimensional unsteady flow over a heaving naca0012 airfoil is simulated using a high order numerical method associated with a moving frame of reference technique in order to obtain more accurate and high resolution data this data can be used to characterize oscillating airfoil wakes with very fine temporal and spatial details the mean incidence investigated is 0 and reynolds number r e 10 4 the transition from a drag producing wake to a neutral and a thrust producing wake is observed and analyzed the results obtained are in accordance with previously published experimental and computational investigations furthermore a more detailed wake classification is presented where two new wake configurations are captured the role of the trailing edge and the interaction of the natural shedding frequency of the airfoil and the imposed forcing frequency in the creation of multiple vortices per half cycle shedding mode are investigated the relation between the interaction of the two aforementioned frequencies and the observed shedding modes is established

lyapunov sufficient conditions for uniform semiglobal exponential stability 2017 this manuscript version is made available under the cc by nc nd 4 0 license http creativecommons org licenses by nc nd 4 0

exponential stability and partial averaging the exponential stability of singularly perturbed time varying systems is investigated it turns out that under natural conditions exponential stability of an averaged system is equivalent to exponential stability of the perturbed system for small perturbation parameters explicit estimates for both the approximation of single trajectories and the order of the exponential decay are obtained the method of proof does not require smoothness of the averaged system

a unified framework for input to state stability in systems with two time scales this paper develops a unified framework for studying robustness of the input to state stability iss property and presents new results on robustness of iss to slowly varying parameters to rapidly varying signals and to generalized singular perturbations the common feature in these problems is a time scale separation between slow and fast variables which permits the definition of a boundary layer system like in classical singular perturbation theory to address various robustness problems simultaneously the asymptotic behavior of the boundary layer is allowed to be complex and it generates an average for the derivative of the slow state variables the main results establish that if the boundary layer and averaged systems are iss then the iss bounds also hold for the actual system with an offset that converges to zero with the parameter that characterizes the separation of time scales the generality of the framework is illustrated by making connection to various classical two time scale problems and suggesting extensions

comparison properties of stochastic decision free petri nets stochastic comparison problems arising in the analysis of stochastic decision free petri nets are treated the analysis is based on the evolution equations satisfied by firing times various structural properties are obtained including the association of the firing times and their stochastic and convex monotonicity with respect to the holding time sequences the initial marking and the topology the association and the stochastic monotonicity properties are extended to the counters using an inversion relation it is also proven that the counters and the throughput are stochastically concave in the initial marking provided that the holding times are independent identically distributed and belong to a subclass of the log concave distribution functions that are introduced various bounds for the asymptotic cycle time and the throughput are then derived from these stochastic ordering results comparative results are presented for the marking and response times

a high order immersed interface method for simulating unsteady incompressible flows on irregular domains immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a cartesian grid while good results both qualitative and quantitative have been obtained most of the methods rely on low order corrections to account for the immersed boundary the objective of the present work is to present as an alternative a high order modified immersed interface method for the 2d unsteady incompressible navier stokes equations in stream function vorticity formulation the method employs an explicit fourth order runge kutta time integration scheme fourth order compact finite differences for computation of spatial derivatives and a nine point fourth order compact discretization of the poisson equation for computation of the stream function corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary as confirmed by analytical tests to validate the method in its application to incompressible flows several physically relevant test cases are computed including uniform flow past a circular cylinder and tollmien schlichting waves in a boundary layer

a sufficient condition for the uniform exponential stability of time varying systems with noise abstract the averaging method for nonlinear differential equations with a fast time variable is extended to systems with deterministic bounded noise the averaged system is used to present a sufficient condition for the uniform exponential stability of the original system the method of proof is based on a direct computation of the distance of trajectories of the averaged system to trajectories of the original system and manages without smoothness assumptions on the averaged system

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

optimality gap of constant order policies decays exponentially in the lead time for lost sales models inventory models with lost sales and large lead times have traditionally been considered intractable due to the curse of dimensionality recently goldberg and coauthors laid the foundations for a new approach to solving these models by proving that as the lead time grows large a simple constant order policy is asymptotically optimal however the bounds proven there require the lead time to be very large before the constant order policy becomes effective in contrast to the good numerical performance demonstrated by zipkin even for small lead time values in this work we prove that for the infinite horizon variant of the same lost sales problem the optimality gap of the same constant order policy actually converges exponentially fast to zero with the optimality gap decaying to zero at least as fast as the exponential rate of convergence of the expected waiting time in a related single server queue to its steady state value we also derive simple and explicit bounds for the optimality gap and demons

vibrational control without averaging the standard approach to vibrational control applies first order averaging methods to find an open loop periodic input that stabilizes an unstable equilibrium point while the capability of stabilization without feedback is appealing this formulation has drawbacks from a design perspective an alternative design framework based on stability maps for second order linear periodic systems is not as general but has significant potential advantages the averaging approach only guarantees that a solution exists the designer must then find that solution by other means furthermore the frequencies required may be too high for practical implementation use of stability maps makes a broader class of stabilizing inputs accessible allowing for example the use of lower frequency signals application to nonlinear and higher order systems is demonstrated with two examples the first is stabilization of the classical vertically forced inverted pendulum the second is delay of a pitchfork bifurcation in a fourth order nonlinear system in the second example we show that the averaging based approach necessarily fails to delay the bifurcation while the alternative method achieves significant extension of the stable operating region

on non local stability properties of extremum seeking control in this paper we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted this non local stability result is proved by showing semi global practical stability of the closed loop system with respect to the design parameters we show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking simulation examples illustrate our results

growth conditions for exponential stability of time varying perturbed systems in this paper we derive some sufficient conditions for practical uniform exponential stability of time varying perturbed systems based on lyapunov techniques whose dynamics are in general unbounded in time in the sense that the solutions are uniform stable and converge to a small neighbourhood of the origin under quite general assumptions we first present a new converse stability theorem for a large class of time varying systems which will be used to prove certain stability properties of nonlinear systems with perturbation therefore a new lyapunov function is presented that guarantees practical uniform exponential stability of perturbed systems furthermore some illustrative examples are presented

local asymptotic stability via averaging for time varying systems with unbounded dynamics with respect to time the purpose of this note is to provide sufficient conditions for asymptotic stability for time varying systems whose dynamics are unbounded with respect to time an averaging approach is established that constitutes a generalization of the well known methodology adopted in the literature for systems whose dynamics are bounded with respect to time

uniform semiglobal practical asymptotic stability for non autonomous cascaded systems and applications it is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on adding integrators nevertheless the standing assumptions in most of the present literature on cascaded systems is that when decoupled the subsystems constituting the cascade are uniformly globally asymptotically stable ugas hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable uspas this situation is often encountered in control practice e g in control of physical systems with external perturbations measurement noise unmodelled dynamics etc after giving a rigorous framework for the analysis of such stability properties this paper generalizes previous results for cascades by establishing that under a uniform boundedness condition on its solutions the cascade of two uspas systems remains uspas an analogous result is derived for uniformly semiglobally asymptotically stable usas systems in cascade furthermore we show the utility of our results in the pid control of mechanical systems affected by unknown non dissipative forces and considering the dynamics of the dc motors

input to state stability and averaging of linear fast switching systems we consider the averaging method for stability of rapidly switching linear systems with disturbances we show that the notions of strong and weak averages proposed with partial strong average defined in this note play an important role in the context of switched systems using these notions of average we show that exponential input to state stability iss of the strong and the partial strong average system with linear gain imply exponential iss with linear gain of the actual system similarly exponential iss of the weak average guarantees an appropriate exponential derivative iss diss property for the actual system moreover using the lyapunov method we show that linear iss gains of the actual system and its average converge to each other as the switching rate is increased

practical stability and stabilization presents a practical stability result for dynamical systems depending on a small parameter this result is applied to a practical stability analysis of fast time varying systems studied in averaging theory and of highly oscillatory systems studied by sussmann and liu 1999 furthermore the problem of practically stabilizing control affine systems with drift is discussed

stability of homogeneous nonlinear systems with sampled data inputs abstract the main goal of this article is to use properties of homogeneous systems for addressing the problem of stability for a class of nonlinear systems with sampled data inputs this nonlinear strategy leads to several kinds of stability i e local asymptotic stability global asymptotic stability or global asymptotic set stability depending on the sign of the degree of homogeneity the results are illustrated with the case of the double integrator

extremal splittings of point processes the sequence with nth term defined by n 1 p np is an extremal zero one valued sequence of asymptotic mean p in the following sense for example if a fraction p of customers from a point process with iid interarrival times is sent to an exponential server queue according to a prespecified splitting sequence then the long term average queue size is minimized when the above sequence is used the proof involves consideration of the lower convex envelope j which is a function on rm of a function j on zm an explicit representation is given for j in terms of j for j in a broad class of functions which we call multimodular the expected queue size just before an arrival considered as a function of the zero one splitting sequence is shown to belong to this class

brief on exponential stability of nonlinear time varying differential equations within the liapunov framework a sufficient condition for exponential stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the liapunov function taken along solutions of the system may have positive and negative values verification of the conditions of the main theorem may be harder than in the classical case it is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time varying systems this sets the stability study by means of averaging in a liapunov context in particular it is established that exponential stability of the averaged system implies exponential stability of the original fast time varying system a comparison of our work with results taken from the literature is included

remarks on asymptotic controllability and sampled data feedback stabilization for autonomous systems a weak concept of sampled data feedback stabilization for the case of autonomous systems is presented and its lyapunov characterization is established sufficient conditions are derived for the existence of a time varying sampled data feedback exhibiting global stabilization for certain class of nonlinear systems

averaging criteria for asymptotic stability of time varying systems we establish averaging type sufficient conditions for local asymptotic stability for nonlinear time varying systems our main result is based on an extension of the averaging methodology employed in a recent paper by tsinias and stamati published in the same journal dealing with asymptotic stability for slow time varying systems

minimizing delays in the gi g 1 queue what service time distribution minimizes delays in a gi g 1 queue with given renewal arrival process and given mean service time it is natural to conjecture that the deterministic service time distribution with unit mass on the mean is optimal for all objective functions of the form efw where f is a nondecreasing function of the steady state delay w however we show that this conjecture is false in fact for hyperexponential interarrival time distributions mixtures of two exponential distributions the service time distribution minimizing the average delay maximizes the proportion of customers delayed

averaging techniques without requiring a fast time varying differential equation an averaging result is presented for local uniform asymptotic stability of nonlinear differential equations without requiring a fast time varying vectorfield the nonlinearity plays a crucial role close to the origin the trajectories vary slowly compared to the time dependence of the vectorfield the result generalises averaging results which prove stability properties for systems having a homogeneous vectorfield with positive order the result is illustrated with several examples

persistent excitation in adaptive systems the importance of the concept of persistent excitation pe in adaptive identification and control has been recognized for some time recently it has become evident that it also plays a central role in many questions related to the robustness of adaptive systems there is every reason to believe that arguments involving this concept will continue to feature prominently in the analysis of most of the important problems of adaptive control hence there is a real need for a deeper understanding of the concept the paper is written with three objectives the first which is tutorial in nature is to provide a general framework for the discussion of persistent excitation and to collect results in the area which are scattered throughout the adaptive literature the second objective is to present some new results related to the uniform asymptotic stability u a s and robustness of adaptive systems and the relation of pe to the stability properties of a class of non linear systems the final objective is to di

a perturbation based proportional integral extremum seeking control approach this paper proposes a proportional integral extremum seeking control technique the technique is a generalization of the standard perturbation based techniques which provides fast transient performance of the closed loop system to the optimum equilibrium of a measured cost function under the assumption that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown it is shown that for a class of minimum phase nonlinear system with a cost function of relative degree one the closed loop esc can practically stabilize the unknown equilibrium optimum the stabilization result provides an alternative approach to output feedback control of nonlinear systems the effectiveness of the proposed approach is demonstrated using simulation examples

synchronization and dynamic consensus of heterogeneous networked systems we present an analysis framework for the study of synchronization of heterogeneous nonlinear systems interconnected over networks described by directed graphs heterogeneous systems may have totally different dynamical models albeit of the same dimension or may possess equal models with different lumped parameters we show that their behavior when network interconnected is fully characterized in terms of two properties whose study may be recasted in terms of the stability analysis of two corresponding interconnected dynamical systems that evolve in orthogonal spaces on one hand we have the so called emergent dynamics and on the other the synchronization error dynamics based on this premise we introduce the concept of dynamic consensus and we present results on robust stability which assess the conditions for practical asymptotic synchronization of networked systems and characterize their collective behavior to illustrate our main theoretical findings we broach a brief case study on mutual synchronization of heterogeneous chaotic oscillators

asymptotic optimality of constant order policies for lost sales inventory models with large lead times lost sales inventory models with large lead times which arise in many practical settings are notoriously difficult to optimize due to the curse of dimensionality in this paper we show that when lead times are large a very simple constant order policy first studied by reiman performs nearly optimally the main insight of our work is that when the lead time is very large such a significant amount of randomness is injected into the system between when an order for more inventory is placed and when the order is received that being smart algorithmically provides almost no benefit our main proof technique combines a novel coupling for suprema of random walks with arguments from queueing theory

stabilization of bilinear sparse matrix control systems using periodic inputs abstract in this brief paper using results from the theory of averaging of bilinear systems we provide a graph theoretic characterization for the existence of periodic control inputs that stabilize a sparse matrix system to the origin in particular we introduce a class of extensions to the directed graph corresponding to a given sparse matrix system which when contains a stable sparse matrix system implies that the original system is stabilizable using periodic inputs when this condition holds we provide a systematic procedure for designing such controllers our technical approach combines ideas from the theory of bilinear control systems and averaging theory with graph theoretic results

a numerical technique for the solution of the navier stokes equations of unsteady flow abstract a numerical technique is developed on the solution of the navier stokes equations of unsteady axisymmetric flow of a viscous incompressible fluid in any orthogonal system of coordinates using a finite difference scheme for time and spatial derivatives the discretization of equations of motion leads to a convergent and efficient algorithm for the unkown values of the functions of the flow at the n 1 th time level in terms of the known values at the n th time level for any nodal point accordingly this technique is used for the numerical simulation of taylor vortices stable or time dependent in spherical annular gaps at large aspect ratios 0 4 0 44 0 48 and 0 5 for the first time the method also applies to more composite problems such as mhd flows flows with heat transfer etc our computations are compared with available numerical results and experimental measurements with very good agreement in all cases

robustness of exponential stability to singular perturbations and delays singularly perturbed nonlinear differential equations with small time delays in the slow variables are considered averages of the fast variables are used in order to obtain a sufficient condition under which the exponential stability of the slow subsystem is robust to singular perturbations and delays

an implicit potential method for incompressible flows summary in this paper we consider a novel numerical scheme for solving incompressible flows on collocated grids the implicit potential method utilizes an implicit potential velocity obtained from a helmholtz decomposition for the mass conservation and employs a modified form of bernoulli s law for the coupling of the velocity pressure corrections it requires the solution only of the momentum equations does not involve the solution of additional partial differential equations for the pressure and is applied on a collocated grid the accuracy of the method is tested through comparison with analytical experimental and numerical data from the literature and its efficiency and robustness are evaluated by solving several benchmark problems such as flow around a circular cylinder and in curved square and circular ducts copyright 2013 john wiley sons ltd

nash equilibrium seeking in noncooperative games we introduce a non model based approach for locally stable convergence to nash equilibria in static noncooperative games with n players in classical game theory algorithms each player employs the knowledge of the functional form of his payoff and the knowledge of the other players actions whereas in the proposed algorithm the players need to measure only their own payoff values this strategy is based on the extremum seeking approach which has previously been developed for standard optimization problems and employs sinusoidal perturbations to estimate the gradient we consider static games with quadratic payoff functions before generalizing our results to games with non quadratic payoff functions that are the output of a dynamic system specifically we consider general nonlinear differential equations with n inputs and n outputs where in the steady state the output signals represent the payoff functions of a noncooperative game played by the steady state values of the input signals we employ the standard local averaging theory and obtain local convergence results for both quadratic payoffs where the actual convergence is semi global and non quadratic payoffs where the potential existence of multiple nash equilibria precludes semi global convergence our convergence conditions coincide with conditions that arise in model based nash equilibrium seeking however in our framework the user is not meant to check these conditions because the payoff functions are presumed to be unknown for non quadratic payoffs convergence to a nash equilibrium is not perfect but is biased in proportion to the perturbation amplitudes and the higher derivatives of the payoff functions we quantify the size of these residual biases and confirm their existence numerically in an example noncooperative game in this example we present the first application of extremum seeking with projection to ensure that the players actions remain in a given closed and bounded action set

asymptotic stability of nonautonomous systems by liapunov s direct method abstract this paper discusses the asymptotic stability of nonautonomous systems by means of the direct method of liapunov we assume existence of a positive time invariant liapunov function with negative semi definite derivative we focus on the extra conditions needed in order to guarantee asymptotic stability and present a theorem which offers a new criterion for asymptotic stability the theorem is illustrated first by recovering barbashin s principle for autonomous and periodic systems and second by studying the nonlinear pendulum with time varying damping for which we derive a new asymptotic stability result

maximizing map sensitivity and higher derivatives via extremum seeking we present a generalization to the scalar newton based extremum seeking algorithm which through perturbation induced measurements of an unknown steady state input to output map maximizes the map s higher derivatives as with other extremum seeking es problems the scheme relies on derivative estimators and learning dynamics operating in different time scales we provide analysis for the typical deterministic sinusoidal perturbation of the optimal parameter estimate also we alternatively include a stochastic method where the map is perturbed via the sinusoid of brownian motion about the boundary of a circle by properly demodulating the map output corresponding to the manner in which it is perturbed the es algorithm maximizes the n rm th derivative only through measurements of the map the newton based es approach removes the dependence of the convergence rate on the unknown hessian of the higher derivative an effort to improve performance over standard gradient based es our design stems from the existing multivariable newton based es algorithm where a differential riccati equation estimates the inverse hessian of the function to be maximized algebraically computing a direct estimate of the inverse hessian is susceptible to singularity whereas employing the riccati filter removes that potential we prove local stability of the algorithm for general nonlinear equilibrium profiles of dynamic maps and compare the newton based method against the gradient based method we also extend this abstraction to multiplayer noncooperative games but limit our attention to a two player game for notational simplicity and length considerations

a new asymptotic stability criterion for nonlinear time variant differential equations a new sufficient condition for asymptotic stability of ordinary differential equations is proposed unlike classical lyapunov theory the time derivative along solutions of the lyapunov function may have positive and negative values the classical lyapunov approach may be regarded as an infinitesimal version of the present theorem verification in practical problems is harder than in the classical case an example is included in order to indicate how the present theorem may be applied

brief paper on global extremum seeking in the presence of local extrema we propose a global extremum seeking scheme which can seek the global optimal value in the presence of local extrema it is shown that the proposed global extremum seeking scheme can converge to an arbitrarily small neighborhood of the global extremum from an arbitrarily large set of initial conditions if sufficient conditions are satisfied a simple example illustrates the effectiveness of the proposed scheme

technical communique on the choice of dither in extremum seeking systems a case study we discuss how the choice of dither excitation signal affects the performance of extremum seeking using a benchmark situation a static scalar map and a simple scalar extremum seeking scheme our comparisons are based on the performance of the system with different dithers in terms of three performance indicators the speed of convergence domain of attraction and accuracy i e the ultimate bound on trajectories our analysis explicitly shows how the dither shape affects each of these performance indicators our study suggests that the practitioners using extremum seeking control should consider the dither shape as an important design parameter computer simulations support our theoretical findings

synchronization with partial state coupling on so n this paper studies autonomous synchronization of k agent orientations in so n by using links that each convey a priori different partial state information between two agents the latter compare the action of their states on a common link dependent vector of mathbb r n such setting appears when each pair of agents compares the expression in their respective body frames of a common external direction force field heading of moving object etc to synchronize their states agents must combine this information over time or throughout the network a gradient coupling law for synchronization is proposed extensive convergence analysis of the coupled agents is provided both for fixed and time varying reference vectors the results are compared to a similar setting with states in mathbb r n and agents coupled through scalar product of their state with a reference vector

a sufficient condition for asymptotic stability for a class of time varying parameterized systems abstract we derive sufficient conditions for local asymptotic stability for a class of parameterized time varying systems whose dynamics are in general unbounded in time our main result generalizes a well known limiting dynamics based approach due to peuteman and aeyels 1999 in 9 for fast time varying systems whose dynamics are bounded in time its proof is based on a new result providing a lyapunov characterization for exponential stability