variable delay feedback control of unstable steady states in retarded time delayed systems we study the stability of unstable steady states in scalar retarded time delayed systems subjected to a variable delay feedback control the important aspect of such a control problem is that time delayed systems are already infinite dimensional before the delayed feedback control is turned on when the frequency of the modulation is large compared to the system s dynamics the analytic approach consists of relating the stability properties of the resulting variable delay system with those of an analogous distributed delay system otherwise the stability domains are obtained by a numerical integration of the linearized variable delay system the analysis shows that the control domains are significantly larger than those in the usual time delayed feedback control and that the complexity of the domain structure depends on the form and the frequency of the delay modulation

consensus in networks of agents with unknown high frequency gain signs and switching topology the agreement control problem of single and double integrator agents with unknown and nonidentical control directions is addressed in this note under switching network topology distributed nonlinear pi control laws are proposed which ensure asymptotic consensus among the agents based on a new boundedness lemma and a generalized version of barbalat s lemma for uniformly piecewise right continuous functions theoretical results are verified by simulation studies

output tracking control for generalised high order nonlinear system with serious uncertainties abstractthis paper focuses on the problem of output tracking control for a class of generalised high order uncertain nonlinear systems serious uncertainties are composed of unknown high order terms unknown nonlinear functions and the signal to be tracked the new feedback scheme guarantees that the tracking error belongs to a prescribed small neighbourhood of the origin in finite time design procedures are presented by combining improved adding a power integrator method with the recursive construction as an application the control methodology is used in the tracking control of the mass spring mechanical system

meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature abstract we give a detailed description of the schwartz kernel of the resolvent of the laplacian on a certain class of complete riemannian manifolds with negative sectional curvature near infinity these manifolds have compactifications as c manifolds with boundary on which the metric is conformai to a c metric up to the boundary with conformal factor 2 where is a defining function for the boundary the modified resolvent r s 2 n 1 defined and analytic in r n is shown to extend to be meromorphic in the whole complex plane when s 2 is equal to the sectional curvature at infinity for hyperbolic spaces obtained as quotients hn 1 where is a discrete group of fractional linear transformations having a geometrically finite fundamental domain without cusps at infinity s is constant we then deduce from the existence of this meromorphic extension of the resolvent the existence of a similar extension for the eisenstein series the basic method used to produce a parametrix for the laplacian is part of a more general construction by g mendoza and the second author but since this is not yet available the present paper has been made essentially self contained

global stabilisation of high order nonlinear systems with multiple time delays this paper focuses on the stabilisation for a class of high order nonlinear systems with multiple time delays growth restriction on system nonlinearities is further relaxed design procedures of a continuous controller are provided by the method of adding a power integrator and the stability of the resulting closed loop system is rigorously proven with the help of the elegant choice of a lyapunov krasovskii functional finally a simulation example is provided to demonstrate the validness of the proposed approach

analytical investigation of modulated time delayed feedback control the influence of time dependent control parameters on time delayed feedback schemes for control of chaos is investigated by analytical means for the logistic map the linear stability of the period two orbit subjected to a modulated time delayed feedback loop is calculated we find enhanced control performance due to phase lags between the periodic orbit and the controller

pbc based pulse stabilization of periodic orbits abstract we investigate prediction based schemes to stabilize periodic solutions to potentially chaotic systems of periodic difference equations using pulses at times being a multiple of the period by introducing the concept of a stability domain we obtain precise information on the possibility to stabilize given solutions to avoid destabilizing bifurcations as well as on the magnitude of the required control

on the eigenvalue spectrum for time delayed floquet problems abstract a linear homogeneous scalar differential difference equation with harmonic time dependence is investigated the associated eigenvalue problem is solved in terms of a continued fraction expansion for the characteristic equation the dependence of the largest eigenvalue on the system parameters being relevant for stability of periodic states in delay systems is discussed in detail the competition between the two timescales the delay and the external period cause intricate structures the result suggests features to improve control of chaos by time delayed feedback schemes with time dependent control amplitudes

global regulation for a class of stochastic high order nonlinear systems with multiple unknown control directions this paper concerns the global regulation for a class of stochastic high order nonlinear systems which admit more general system form than the existing works for details except for the serious sy

the hausdorff dimension of the limit set of a geometrically finite kleinian group we consider in this paper groups of mobius transformations of l r tj zc such a group is called kleinian if it acts discontinuously somewhere in 1 the action of g extends to the n d dimensional hyperbolic space h i r zc and g is geometrically finite if there is a hyperbolic fundamental polyhedron with a finite number of faces for the action of g in h t for a more precise definition see 15 1 b we prove in this paper that the hausdor f dimension dim l g of the limit set l g of a geometrically finite kleinian group g of 1 is less than n theorem d our proof of this theorem is based on the following obser ation assume that g is of compact t3 pe i e if izi i h iui then i l g g is compact then there is an integer q such that if we divide any n cube q of r into q equal subcubes then at least one of these subcubes does not touch l g let l4 q be the family of these subcubes which touch l g then the n measures of q e le q do not add up to the n measure of q and we get

a unified time varying feedback approach and its applications in adaptive stabilization of high order uncertain nonlinear systems we are concerned with two key problems of adaptive control design one is to find the feasible conditions and the valid boundary of the time varying feedback scheme another one lies in the improved generalization of the homogeneous idea in the global adaptive stabilization of high order uncertain nonlinear systems the distinguished feature of the system to be investigated is the serious coexistence between unknown time varying parameters and unknown time varying control coefficients design procedures of the continuous controller are provided based on the sign function technique and the delicate search of the time varying function and a lyapunov function finally the control of uncertain single link robotic manipulator demonstrates the application of design scheme

continuous global stabilisation of high order time delay nonlinear systems this paper studies the global stabilisation problem for a class of high order nonlinear systems with multiple time delays a distinct property of the systems to be investigated is that powers on the upper bound restrictions of nonlinearities are allowed to take values on a continuous interval by introducing the sign functions and using the generalised method of adding a power integrator this paper successfully designs a continuous global state feedback controller independent of time delays moreover a novel lyapunov krasovskii functional is constructed to prove the globally asymptotic stability of the resulting closed loop system

pyragas stabilizability via delayed feedback with periodic control gain abstract in this paper for the unstable periodic solution of nonlinear differential equation pyragas stabilizability problem is studied an algorithm of stabilization via periodical delayed feedback is obtained the consideration is based on the theory of nonstationary stabilization

adaptive approximation based regulation control for a class of uncertain nonlinear systems without feedback linearizability in this paper for a general class of uncertain nonlinear cascade systems including unknown dynamics which are not feedback linearizable and cannot be solved by existing approaches an innovative adaptive approximation based regulation control aarc scheme is developed within the framework of adding a power integrator api by deriving adaptive laws for output weights and prediction error compensation pertaining to single hidden layer feedforward network slfn from the lyapunov synthesis a series of slfn based approximators are explicitly constructed to exactly dominate completely unknown dynamics by the virtue of significant advancements on the api technique an adaptive api methodology is eventually established in combination with slfn based adaptive approximators and it contributes to a recursive mechanism for the aarc scheme as a consequence the output regulation error can asymptotically converge to the origin and all other signals of the closed loop system are uniformly ultimately bounded simulation studies and comprehensive comparisons with backstepping and api based approaches demonstrate that the proposed aarc scheme achieves remarkable performance and superiority in dealing with unknown dynamics

control of chaos by oscillating feedback parametric feedback control of chaos relies on detailed knowledge of the locations of unstable periodic orbits we show that unstable periodic orbits of dynamical systems with unknown locations but known periodicity ensuremath tau can be stabilized by an oscillating feedback term proportional to ensuremath varepsilon t x ensuremath rightarrow t ensuremath x ensuremath rightarrow t ensuremath ensuremath tau where x ensuremath rightarrow t is the location of the trajectory at time t and ensuremath varepsilon t is periodic in time periodic feedback overcomes the limitations of giona s theorem nonlinearity 4 911 1991 which states that constant feedback i e a time independent ensuremath varepsilon can stabilize an unstable periodic orbit only if the stability matrix has no positive eigenvalues greater than unity as an application of oscillating feedback we use it to stabilize the memory patterns in an associative memory hopfield proc natl acad sci usa 79 2554 1982 81 3088 1984 network thereby enhancing the total capacity of the memory device we extend our method to high dimensional systems described by differential equations in this framework it is possible to stabilize the spatiotemporal chaos generated by the kuramoto sivashinsky equation g j sivashinsky and d m michelson prog theor phys 63 2122 1980

the laplace operator on a hyperbolic manifold ii eisenstein series and the scattering matrix on considere des varietes m isometriques au quotient de l espace hyperbolique a n dimensions h n par un groupe discret geometriquement fini t sans elements paraboliques et sans elements d ordre fini on demontre que la serie de eisenstein associee admet un prolongement mesomorphe au plan complexe et on etudie l operateur diffusion associe

a geometric characterization of strong duality in nonconvex quadratic programming with linear and nonconvex quadratic constraints we first establish a relaxed version of dines theorem associated to quadratic minimization problems with finitely many linear equality and a single nonconvex quadratic inequality constraints the case of unbounded optimal valued is also discussed then we characterize geometrically the strong duality and some relationships with the conditions employed in finsler theorem are established furthermore necessary and sufficient optimality conditions with or without the slater assumption are derived our results can be used to situations where none of the results appearing elsewhere are applicable in addition a revisited theorem due to frank and wolfe along with that due to eaves is established for asymptotically linear sets

global practical tracking for high order uncertain nonlinear systems with unknown control directions this paper addresses the global practical tracking problem for a class of high order uncertain nonlinear systems with unknown control directions under fairly weak conditions although the stabilization problem has been studied for the systems the tracking problem remains unsolved up to now mainly because of the essential differences between stabilization and tracking problems when control directions are unknown in this paper by introducing a novel coordinate transformation and new updating laws an approach is presented for the first time to design a continuous adaptive controller to make the tracking error prescribed arbitrarily small after a finite time and simultaneously to keep all the closed loop states bounded it is worth emphasizing that the proposed adaptive tracking control design scheme is motivated by the recent tracking works inspired by the ideas of universal control and dead zone and obtained by the approaches of nussbaum gain and adding a power integrator most importantly this paper removes the basic assumption that the control directions are precisely known in the related tracking works without additional conditions imposed on the systems and the reference signal