control lyapunov razumikhin functions and robust stabilization of time delay systems motivated by control lyapunov functions and razumikhin theorems on stability of time delay systems we introduce the concept of control lyapunov razumikhin functions clrf the main reason for considering clrfs is construction of robust stabilizing control laws for time delay systems most existing universal formulas that apply to clfs are not applicable to clrfs it turns out that the domination redesign control law applies achieving global practical stability and under an additional assumption global asymptotic stability this additional assumption is satisfied in the practically important case when the quadratic part of a clrf is itself a clrf for the jacobian linearization of the system the clrf based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin while in general construction of clrfs is an open problem we show that for several classes of time delay systems a clrf can be constructed in a systematic way

adaptive fuzzy tracking control of nonlinear time delay systems with dead zone output mechanism based on a novel smooth model this paper presents a novel fuzzy adaptive controller for controlling a class of dead zone output nonlinear systems with time delays a new approximate model is first designed to describe a special dead zone phenomenon encountered by the output mechanism of nonlinear systems and the proposed smooth model can be conveniently fused with available adaptive fuzzy control techniques in addition the coupling effect that the dead zone output and the time delayed states coexist in a common coupling function makes the tracking control design more complicated to further address this difficulty a compensation method using mean value theorem with lyapunov krasovskii function is presented in this paper by using the proposed output dead zone model and based on lyapunov synthesis a new optimized algorithm is developed to guarantee the prescribed convergence of tracking error and the boundedness of all the signals in the closed loop systems simulations have been implemented to verify the performance of the proposed fuzzy adaptive controller

approximation based control of nonlinear mimo time delay systems approximation based control is presented for a class of multi input multi output mimo nonlinear systems in block triangular form with unknown state delays neural networks nns are utilized to approximate and compensate for unknown functions in the system dynamics including the unknown bounds of the functions of delayed states the use of a separation technique removes the need for any assumption on the function of delayed states and allows the handling of multiple delays in each function of delayed states by combining the use of lyapunov krasovskii functionals and adaptive nn backstepping the proposed control guarantees that all closed loop signals remain bounded while the outputs converge to a neighborhood of the desired trajectories simulation results demonstrate the effectiveness of the proposed scheme

an improved razumikhin type theorem and its applications an improved razumikhin type theorem is established and the advantage of the established theorem for reducing conservatism is discussed for a class of time delay systems a simple asymptotic stability condition is deduced as an application of the established theorem two illustrative examples are given to show the superiority of the results to those in the literature

adaptive nn controller design for a class of nonlinear mimo discrete time systems an adaptive neural network tracking control is studied for a class of multiple input multiple output mimo nonlinear systems the studied systems are in discrete time form and the discretized dead zone inputs are considered in addition the studied mimo systems are composed of n subsystems and each subsystem contains unknown functions and external disturbance due to the complicated framework of the discrete time systems the existence of the dead zone and the noncausal problem in discrete time it brings about difficulties for controlling such a class of systems to overcome the noncausal problem by defining the coordinate transformations the studied systems are transformed into a special form which is suitable for the backstepping design the radial basis functions nns are utilized to approximate the unknown functions of the systems the adaptation laws and the controllers are designed based on the transformed systems by using the lyapunov method it is proved that the closed loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set the simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm

time varying input and state delay compensation for uncertain nonlinear systems a robust controller is developed for uncertain second order nonlinear systems subject to simultaneous unknown time varying state delays and known sufficiently small time varying input delays in addition to additive sufficiently smooth disturbances an integral term composed of previous control values facilitates a delay free open loop error system and the development of the feedback control structure a stability analysis based on lyapunov krasovskii lk functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying numerical simulations illustrate robustness of the developed method to various combinations of simultaneous input and state delays

adaptive neural control of mimo nonlinear state time varying delay systems with unknown dead zones and gain signs in this paper adaptive neural control is proposed for a class of uncertain multi input multi output mimo nonlinear state time varying delay systems in a triangular control structure with unknown nonlinear dead zones and gain signs the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions the unknown time varying delays are compensated for using appropriate lyapunov krasovskii functionals in the design the approach removes the assumption of linear functions outside the deadband as an added contribution by utilizing the integral lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead zone disturbance the closed loop control system is proved to be semi globally uniformly ultimately bounded simulation results demonstrate the effectiveness of the approach

adaptive consensus control for a class of nonlinear multiagent time delay systems using neural networks because of the complicity of consensus control of nonlinear multiagent systems in state time delay most of previous works focused only on linear systems with input time delay an adaptive neural network nn consensus control method for a class of nonlinear multiagent systems with state time delay is proposed in this paper the approximation property of radial basis function neural networks rbfnns is used to neutralize the uncertain nonlinear dynamics in agents an appropriate lyapunov krasovskii functional which is obtained from the derivative of an appropriate lyapunov function is used to compensate the uncertainties of unknown time delays it is proved that our proposed approach guarantees the convergence on the basis of lyapunov stability theory the simulation results of a nonlinear multiagent time delay system and a multiple collaborative manipulators system show the effectiveness of the proposed consensus control algorithm

on almost global existence for nonrelativistic wave equations in 3d almost global solutions are constructed to three dimensional quadratically nonlinear wave equations the proof relies on generalized energy estimates and a new decay estimate the method applies to equations that are only classically invariant such as the nonlinear system of hyperelasticity 1996 john wiley sons inc

adaptive variable structure control of a class of nonlinear systems with unknown prandtl ishlinskii hysteresis control of nonlinear systems preceded by unknown hysteresis nonlinearities is a challenging task and has received increasing attention in recent years due to growing industrial demands involving varied applications in the literature many mathematical models have been proposed to describe the hysteresis nonlinearities the challenge addressed here is how to fuse those hysteresis models with available robust control techniques to have the basic requirement of stability of the system the purpose of the note is to show such a possibility by using the prandtl ishlinskii pi hysteresis model an adaptive variable structure control approach serving as an illustration is fused with the pi model without necessarily constructing a hysteresis inverse the global stability of the system and tracking a desired trajectory to a certain precision are achieved simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach

adaptive neural network dynamic surface control for a class of time delay nonlinear systems with hysteresis inputs and dynamic uncertainties in this paper an adaptive neural network nn dynamic surface control is proposed for a class of time delay nonlinear systems with dynamic uncertainties and unknown hysteresis the main advantages of the developed scheme are 1 nns are utilized to approximately describe nonlinearities and unknown dynamics of the nonlinear time delay systems making it possible to deal with unknown nonlinear uncertain systems and pursue the mathcal l infty performance of the tracking error 2 using the finite covering lemma together with the nns approximators the krasovskii function is abandoned which paves the way for obtaining the mathcal l infty performance of the tracking error 3 by introducing an initializing technique the mathcal l infty performance of the tracking error can be achieved 4 using a generalized prandtl ishlinskii pi model the limitation of the traditional pi hysteresis model is overcome and 5 by applying the young s inequalities to deal with the weight vector of the nns the updated laws are needed only at the last controller design step with only two parameters being estimated which reduces the computational burden it is proved that the proposed scheme can guarantee semiglobal stability of the closed loop system and achieves the mathcal l infty performance of the tracking error simulation results for general second order time delay nonlinear systems and the tuning metal cutting system are presented to demonstrate the efficiency of the proposed method

on the global existence and stability of a multi dimensional supersonic conic shock wave we establish the global existence and stability of a three dimensional supersonic conic shock wave for a compactly perturbed steady supersonic flow past an infinitely long circular cone with a sharp angle the flow is described by a 3 d steady potential equation which is multi dimensional quasilinear and hyperbolic with respect to the supersonic direction making use of the geometric properties of the pointed shock surface together with the rankine hugoniot conditions on the conic shock surface and the boundary condition on the surface of the cone we obtain a global uniform weighted energy estimate for the nonlinear problem by finding an appropriate multiplier and establishing a new hardy type inequality on the shock surface based on this we prove that a multi dimensional conic shock attached to the vertex of the cone exists globally when the mach number of the incoming supersonic flow is sufficiently large moreover the asymptotic behavior of the 3 d supersonic conic shock solution which is shown to approach the corresponding background shock solution in the downstream domain for the uniform supersonic constant flow past the sharp cone is also explicitly given

reinforcement learning design based adaptive tracking control with less learning parameters for nonlinear discrete time mimo systems based on the neural network nn approximator an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output mimo nonlinear discrete time systems with unknown functions and disturbances in the design procedure two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function an optimal control signal and adaptation laws can be generated based on two nns in the previous approaches the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design consequently compared with the existing results the main contributions of this paper are 1 only two parameters are needed to be adjusted and thus the number of the adaptation laws is smaller than the previous results and 2 the updating parameters do not depend on the number of the subsystems for mimo systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks it is proven that the tracking errors the adaptation laws and the control inputs are uniformly bounded using lyapunov analysis method the simulation examples are employed to illustrate the effectiveness of the proposed algorithm

robust stability of interval time delay systems with delay dependence abstract this paper proposes a sufficient robust stability condition for interval time delay systems with delay dependence the properties of the comparison theorem and matrix measure are employed to investigate the problem the stability criteria are delay dependent and less conservative than delay independent stability criteria 5 6 12 16 and delay dependent stability criteria 1 14 15 17 when delay is small however the results of this paper indeed give us one more choice for the stability examination of the interval time delay systems simulation examples are given to demonstrate the application of our result

mathematical models for hysteresis the various existing classical models for hysteresis preisach ishlinskii duhem madelung are surveyed as well a more modern treatments by contemporary workers the emphasis is on a clear mathematical description of the formulation and properties of each model in addition the authors try to make the reader aware of the many open questions in the study of hysteresis

adaptive fuzzy control for a class of stochastic pure feedback nonlinear systems with unknown hysteresis this paper addresses the problem of adaptive fuzzy control for a class of stochastic pure feedback nonlinear systems with unknown direction hysteresis compared with the existing researches on hysteresis problem the stochastic disturbances and the unknown hysteresis are simultaneously considered in the pure feedback systems in addition the hysteresis parameters as well as the direction of hysteresis are unknown by introducing an auxiliary virtual controller and employing the new properties of nussbaum function the major technique difficulty arising from the unknown direction hysteresis is overcome based on the fuzzy logic system s online approximation capability a novel adaptive fuzzy control scheme is presented via the backstepping technique it is shown that the proposed control scheme guarantees that all the signals of the closed loop system are semiglobally uniformly bounded in probability and the tracking error converges to a neighborhood of the origin in the sense of mean quantic value finally simulation results further demonstrate the effectiveness of the proposed control scheme

lyapunov exponents periodic orbits and horseshoes for semiflows on hilbert spaces two settings are considered flows on finite dimensional riemann ian manifolds and semiflows on hilbert spaces with conditions consistent with those in systems defined by dissipative parabolic pdes under certain assump tions on lyapunov exponents and entropy we prove the existence of geometric structures called horseshoes this implies in particular the presence of infinitely many periodic solutions for diffeomorphisms of compact manifolds analogous results are due to a katok here we extend katok s results to i continuous time and ii infinite dimensions courant institute of mathematical sciences new york university 251 mercer street new york new york 10012 e mail address lian cims nyu edu courant institute of mathematical sciences new york university 251 mercer street new york new york 10012 e mail address lsy cims nyu edu

adaptive fuzzy quantized control of time delayed nonlinear systems with communication constraint abstract this paper explores the problem of quantized fuzzy adaptive tracking control for a class of time delayed uncertain nonlinear systems with communication constraint the control signal is first quantized in a newly proposed asymmetric hysteresis type quantizer before it is transmitted over the networks with limited bandwidth then one of major difficulties that block the controller design is that the real control signal is hidden in the coupling dynamics between nonaffine system nonlinearity and rate dependent hysteretic quantizer to remove this obstacle a control separation method established mainly on a new nonlinear decomposition of quantizer is proposed unlike previous linear decomposition of quantizer the nonlinear one does not recourse to some conservative assumptions either on control input or system nonlinearities in combination with fuzzy backstepping technique and lyapunov krasovskii functional an adaptive fuzzy controller is developed to guarantee the boundedness of all closed loop signals and the asymptotic convergence of tracking error to an adjustable region of zero finally two simulations associated with practical control systems are conducted to verify the effectiveness and applicability of the proposed control protocol

formation of singularities in three dimensional compressible fluids presented are several results on the formation of singularities in solutions to the three dimensional euler equations for a polytropic ideal fluid under various assumptions on the initial data in particular it is shown that a localized fluid which is initially compressed and outgoing on average will develop singularities regardless of the size of the initial disturbance

a criterion for the triviality of the centralizer for vector fields and applications abstract in this paper we establish a criterion for the triviality of the c 1 centralizer for vector fields and flows in particular we deduce the triviality of the centralizer at homoclinic classes of c r vector fields r 1 furthermore we show that the set of flows whose c 1 centralizer is trivial include i c 1 generic volume preserving flows ii c 2 generic hamiltonian flows on a generic and full lebesgue measure set of energy levels and iii c 1 open set of non hyperbolic vector fields that admit a lorenz attractor we also provide a criterion for the triviality of the c 0 centralizer of continuous flows

robust adaptive control of a class of nonlinear systems with unknown backlash like hysteresis deals with adaptive control of a class of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation by exploiting solution properties of the differential equation and combining those properties with adaptive control techniques a robust adaptive control algorithm is developed without constructing a hysteresis inverse the new control law ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision simulations performed on a nonlinear system illustrate and clarify the approach

almost global existence for quasilinear wave equations in three space dimensions this article studies almost global existence for solutions of quadratically quasi linear systems of wave equations in three space dimensions the approach here uses only the classical invariance of the wave operator under translations spatial rotations and scaling using these techniques we can handle wave equations in minkowski space or dirichlet wave equations in the exterior of a smooth star shaped obstacle we can also apply our methods to systems of quasilinear wave equations having different wave speeds this extends our work 11 for the semilinear case previous almost global ex istence theorems for quasilinear equations in three space dimensions were for the non obstacle case in 9 john and klainerman proved almost global existence on minkowski space for quadratic quasilinear equations using the lorentz invariance of the wave operator in addition to the symmetries listed above subsequently in 14 klainerman and sideris obtained the same result for a class of quadratic divergence form nonlinearities without relying on lorentz invariance this line of thought was refined and applied to prove global in time results for null form equa tions related to the theory of elasticity in sideris 22 23 and for multiple speed systems of null form quasilinear equations in sideris and tu 24 and yokoyama 29 the main difference between our approach and the earlier ones is that we ex ploit the 0 x 1 decay of solutions of wave equations with sufficiently decaying initial data as much as we involve the stronger 0 t l decay here of course x x x2 x is the spatial component and t the time component of a space time vector t x g m x e3 establishing 0 x 1 decay is considerably easier and can be achieved using only the invariance with respect to translations and spatial rotation a weighted l2 space time estimate for inhomogeneous wave equations proposition 3 1 below from 11 is important in making the spatial decay useful for the long time existence argument for semilinear systems one can show almost global existence from small data using only this spatial decay 11 for quasilinear systems however we also have to show that both first and second derivatives of u decay like 1 t fortunately we can do this using a variant of some l1 l estimates of john h rmander

on the stability of uncertain systems with multiple time varying delays in this paper criteria for the global asymptotic stability of a class of uncertain systems with multiple time varying delays are proposed based on the improved razumikhin type theorem delay dependent and delay independent criteria are provided to guarantee the global asymptotic stability of such systems our main results are generalizations of some recent results reported in the literature in the case with multiple time varying delays a numerical example is also given to illustrate our results

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

adaptive control of nonlinearly parameterized systems the smooth feedback case studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization using a parameter separation technique and the tool of adding a power integrator we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation in contrast to the existing results in the literature a key feature of our adaptive regulator is its minimum order property namely no matter how big the number of unknown parameters is the order of the dynamic compensator is identical to one and is therefore minimal as a consequence global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one dimensional adaptive controllers without imposing any extra e g convex concave conditions on the unknown parameters

global shock waves for the supersonic flow past a perturbed cone we prove the global existence of a shock wave for the stationary supersonic gas flow past an infinite curved and symmetric cone the flow is governed by the potential equation as well as the boundary conditions on the shock and the surface of the body it is shown that the solution to this problem exists globally in the whole space with a pointed shock attached at the tip of the cone and tends to a self similar solution under some suitable conditions our analysis is based on a global uniform weighted energy estimate for the linearized problem combining this with the local existence result of chen li 1 we establish the global existence and decay rate of the solution to the nonlinear problem

nonlinear stability of a self similar 3 dimensional gas flow we show that the 3 dimensional supersonic gas flow past an infinite cone is nonlinear staple upon the perturbation of the obstacle the perturbed flow exists globally in space and tends to the self similar flow downstream there is a thin layer of concentration of vorticities and entropy variation our analysis is based on an approximation scheme using local self similar solutions as building blocks this enables us to obtain global estimates of the nonlinear interactions of waves needed for the stability analysis

adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash like hysteresis in this note we consider the same class of systems as in a previous paper i e a class of uncertain dynamic nonlinear systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation in the presence of bounded external disturbances by using backstepping technique robust adaptive backstepping control algorithms are developed unlike some existing control schemes for systems with hysteresis the developed backstepping controllers do not require the uncertain parameters within known intervals also no knowledge is assumed on the bound of the disturbance like term a combination of the external disturbances and a term separated from the hysteresis model it is shown that the proposed controllers not only can guarantee global stability but also transient performance

adaptive neural control for a class of nonlinear systems with uncertain hysteresis inputs and time varying state delays in this paper adaptive variable structure neural control is investigated for a class of nonlinear systems under the effects of time varying state delays and uncertain hysteresis inputs the unknown time varying delay uncertainties are compensated for using appropriate lyapunov krasovskii functionals in the design and the effect of the uncertain hysteresis with the prandtl ishlinskii pi model representation is also mitigated using the proposed control by utilizing the integral type lyapunov function the closed loop control system is proved to be semi globally uniformly ultimately bounded sguub extensive simulation results demonstrate the effectiveness of the proposed approach

global transonic conic shock wave for the symmetrically perturbed supersonic flow past a cone in this paper we are concerned with the global existence and stability of a steady transonic conic shock wave for the symmetrically perturbed supersonic flow past an infinitely long conic body the flow is assumed to be polytropic isentropic and described by a steady potential equation theoretically as indicated in r courant k o friedrichs supersonic flow and shock waves interscience publishers inc new york 1948 it follows from the rankine hugoniot conditions and the entropy condition that there will appear a weak shock or a strong shock attached at the vertex of the sharp cone in terms of the different pressure states at infinity behind the shock surface which correspond to the supersonic shock and the transonic shock respectively in the references shuxing chen zhouping xin huicheng yin global shock wave for the supersonic flow past a perturbed cone comm math phys 228 2002 47 84 dacheng cui huicheng yin global conic shock wave for the steady supersonic flow past a cone polytropic case preprint 2006 dacheng cui huicheng yin global conic shock wave for the steady supersonic flow past a cone isothermal case pacific j math 233 2 2007 257 289 and zhouping xin huicheng yin global multidimensional shock wave for the steady supersonic flow past a three dimensional curved cone anal appl 4 2 2006 101 132 the authors have established the global existence and stability of a supersonic shock for the perturbed hypersonic incoming flow past a sharp cone when the pressure at infinity is appropriately smaller than that of the incoming flow at present for the supersonic symmetric incoming flow we will study the global transonic shock problem when the pressure at infinity is appropriately large

the centralizer of komuro expansive flows and expansive mathbb r d actions in this paper we study the centralizer of flows and mathbb r d actions on compact riemannian manifolds we prove that the centralizer of every c infty komuro expansive flow with non resonant singularities is trivial meaning it is the smallest possible and deduce there exists an open and dense subset of geometric lorenz attractors with trivial centralizer we show that mathbb r d actions obtained as suspension of mathbb z d actions are expansive if and only if the same holds for the mathbb z d actions we also show that homogeneous expansive mathbb r d actions have quasi trivial centralizers meaning that it consists of orbit invariant continuous linear reparameterizations of the mathbb r d action in particular homogeneous anosov mathbb r d actions have quasi trivial centralizer

technical communique a direct adaptive controller for dynamic systems with a class of nonlinear parameterizations in this note the adaptive control problem is considered for a class of nonlinearly parametrized systems by introducing a novel kind of lyapunov functions a direct adaptive controller is developed for achieving asymptotic tracking control the transient performance of the resulting closed loop system can be guaranteed by suitably choosing the lyapunov function to construct the controller the effectiveness of the proposed scheme is illustrated with two examples