nonlinear finite dimensional control of a class of nonlinear distributed parameter systems using residual mode filters a proof of local exponential stability abstract in any attempt to control an infinite dimensional distributed parameter system dps with a finite dimensional controller some compensation for deleterious controller interaction with unmodeled modes is needed we introduce the concepts of both a finite dimensional nonlinear controller based on any reasonable nonlinear reduced order model of the dps and stability compensation by a finite dimensional nonlinear residual mode filter under appropriate lipschitz continuity conditions on the nonlinearities this new pair of interconnected finite dimensional systems will produce closed loop exponentially stable control of the nonlinear dps

transient measures in the standard map abstract for an area preserving map each chaotic orbit appears numerically to densely cover a region an irregular component of nonzero area surprisingly the measure approximated by a long segment of such an orbit deviates significantly from a constant on the irregular component most prominently there are spikes in the density near the boundaries of the irregular component resulting from the stickiness of its bounding invariant circles we show that this phenomena is transient and therefore numerical ergodicity on the irregular component eventually obtains though the times involved are extremely long 1010 iterates a markov model of the transport shows that the density spikes cannot be explained by the stickiness of a bounding circle of a single class for example a rotational circle however the density spikes do occur in a markov tree model that includes the effects of islands around islands

boundary circles for area preserving maps abstract we report on numerical observations of various properties of boundary circles for area preserving maps we find that the continued fraction expansion of their rotation number generally has a special form we describe how their rotation number changes as parameters are varied we observe a statistically self similar structure in the neighbourhood of boundary circles which is probably relevant to the long time tails of the decay of correlations in the irregular components

practical output regulation for bounded linear infinite dimensional state space systems we develop the mathematical foundations of practical state space output regulation for bounded infinite dimensional linear systems by practical output regulation we mean asymptotic tracking of references and rejection of disturbances with a given accuracy our main results are general upper bounds for the norms perturbations to the parameters of the exosystem the plant and a controller which achieves exact output regulation these bounds depend explicitly on the desired tracking accuracy e 0 in this paper all perturbations are assumed to be bounded additive and linear our results apply for both feedforward and error feedback controllers and for arbitrary bounded uniformly continuous reference disturbance signals

critical behavior of a kam surface i empirical results kolmogorov arnol d moser kam surfaces are studied in the context of a perturbed two dimensional twist map in particular we ask how a kam surface can disappear as the perturbation parameter is increased following greene we use cycles to numerically construct the kam curve and discover that at the critical coupling it shows structure at all length scales aspects of this structure are fitted by a scaling analysis critical indices and scaling functions are determined numerically some evidence is presented which suggests that the results are universal

fuzzy impulsive control for uncertain nonlinear systems with guaranteed cost in this paper a guaranteed cost fuzzy impulsive control gcfic problem is addressed for uncertain continuous time nonlinear systems which can be represented by the takagi sugeno t s fuzzy model with parametric uncertainties based on the t s fuzzy model a novel time varying lyapunov function is initially constructed to derive the existence condition of guaranteed cost fuzzy impulsive controllers which cannot only exponentially stabilize the uncertain fuzzy system but also provide an upper bound on the quadratic cost function then two procedures for designing suboptimal guaranteed cost fuzzy impulsive controllers are given in the sense of minimizing an upper bound of the cost function one casts the controller design into a parameter dependent linear matrix inequality lmi optimization problem and the other casts the controller design into a sequential minimization problem subject to lmi constraints by using the cone complementary linearization ccl algorithm finally an example is presented to illustrate the effectiveness of the proposed method

fuzzy output tracking control of semi linear first order hyperbolic pde systems with matched perturbations abstract this paper considers the design problem of a fuzzy output tracking controller via a finite number of actuators for a class of nonlinear distributed parameter systems with unknown matched perturbations described by semi linear first order hyperbolic partial differential equations pdes firstly a t s fuzzy hyperbolic pde model is assumed to be used to accurately represent the semi linear first order hyperbolic pde system subsequently based on the t s fuzzy pde model the classic variable structure control technique is adopted to develop a fuzzy output tracking controller such that the output of the semi linear pde system exponentially tracks a desired reference and the state of the system is uniformly bounded in the filippov sense by constructing a strict lyapunov function the sufficient condition on the existence of the fuzzy output tracking controller is derived and presented in terms of algebraic linear matrix inequalities lmis in space with an equality constraint it has been shown that when these algebraic lmis with an equality constraint are feasible fuzzy tracking control design can be obtained via the existing convex optimization techniques finally the developed design methodology is successfully applied to the control of a semi linear lotka volterra pde system and the achieved results illustrate its effectiveness

design of distributed h fuzzy controllers with constraint for nonlinear hyperbolic pde systems this paper investigates the problem of designing a distributed h fuzzy controller with constraint for a class of nonlinear spatially distributed processes modeled by first order hyperbolic partial differential equations pdes the purpose of this paper is to design a distributed fuzzy state feedback controller such that the closed loop pde system is exponentially stable with a prescribed h performance of disturbance attenuation while the control constraint is respected initially a takagi sugeno t s hyperbolic pde model is proposed to accurately represent the nonlinear pde system then based on the t s fuzzy pde model a distributed h fuzzy controller design with constraint is developed in terms of a set of coupled differential algebraic linear matrix inequalities d almis in space furthermore a suboptimal distributed h fuzzy controller with constraint is proposed to minimize the level of attenuation the finite difference method in space and the existing linear matrix inequality lmi optimization techniques are employed to approximately solve the suboptimal fuzzy control design problem finally the proposed design method is applied to the distributed control of a nonlinear system described by two coupled first order hyperbolic pdes to illustrate its effectiveness

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

hybrid robust boundary and fuzzy control for disturbance attenuation of nonlinear coupled ode beam systems with application to a flexible spacecraft this paper introduces a hybrid robust boundary and fuzzy control design for disturbance attenuation of a class of coupled systems described by nonlinear ordinary differential equations odes and two nonlinear beam equations initially a takagi sugeno t s model is employed to exactly represent the nonlinear ode subsystem then a fuzzy controller is designed for the ode subsystem based on the t s fuzzy model and a robust boundary controller via beam boundary measurements is proposed for the nonlinear beam subsystem such a hybrid robust boundary and fuzzy controller is developed in terms of a set of space dependent bilinear matrix inequalities bmis by lyapunov s direct method which can exponentially stabilize the coupled system in the absence of disturbances and achieve an prescribed h infty performance of disturbance attenuation in the presence of disturbances furthermore in order to make the level of disturbance attenuation as small as possible a suboptimal h infty control problem is formulated as a bmi optimization problem a two step procedure is subsequently presented to solve this bmi optimization problem by the existing linear matrix inequality optimization techniques finally the proposed control method is applied to the control of a flexible spacecraft to illustrate its effectiveness

h _ infty fuzzy observer based control for a class of nonlinear distributed parameter systems with control constraints an hinfin fuzzy observer based control design is proposed for a class of nonlinear parabolic partial differential equation pde systems with control constraints for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement in the proposed control scheme galerkin s method is initially applied to the pde system to derive a nonlinear ordinary differential equation ode system that accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a fuzzy observer based controller is developed to stabilize the nonlinear pde system and achieve an optimized hinfin disturbance attenuation performance for the finite dimensional slow system while control constraints are respected the outcome of the hinfin fuzzy observer based control problem is formulated as a bilinear matrix inequality bmi optimization problem a local optimization algorithm that treats the bmi as a double linear matrix inequality is presented to solve this bmi optimization problem finally the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness

formulation of a galerkin spectral element fourier method for three dimensional incompressible flows in cylindrical geometries a primitive variable formulation for simulation of time dependent incompressible flows in cylindrical coordinates is developed spectral elements are used to discretise the meridional semi plane coupled with fourier expansions in azimuth unlike previous formulations where special distributions of nodal points have been used in the radial direction the current work adopts standard gauss lobatto legendre nodal based expansions in both the radial and axial directions using a galerkin projection of the symmetrised cylindrical navier stokes equations all geometric singularities are removed as a consequence of either the fourier mode dependence of axial boundary conditions or the shape of the weight function applied in the galerkin projection this observation implies that in a numerical implementation geometrically singular terms can be naively treated by explicitly zeroing their contributions on the axis in integral expressions without recourse to special treatments such as l hopital s rule exponential convergence of the method both in the meridional semi plane and in azimuth is demonstrated through application to a three dimensional analytical solution of the navier stokes equations in which flow crosses the axis

the discrete frenkel kontorova model and its extensions i exact results for the ground states abstract we present a rigorous study of the classical ground states under boundary conditions of a class of one dimensional models generalizing the discrete frenkel kontorova model the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic quasi periodic and chaotic orbits for all boundary conditions we select among all the extremum solutions of the energy of the model those which correspond to the ground states of the infinite system we prove that these ground states are either periodic commensurate or quasi periodic incommensurate but are never chaotic we also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions the topological structure of the whole set of ground states is described in details in addition to physical applications consequences for twist map homeomorphisms are mentioned part ii s aubry p y ledaeron and g andre will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map

harmonic finite element analysis for anisotropic viscoelasticity a numerical methodology for predicting the linear anisotropic viscoelastic behavior of bodies that can be uniquely described in cylindrical coordinates is devised the methodology is an extension of the fourier finite element method and is based on a combination of finite element discretization in the radial and longitudinal directions and fourier decomposition in the angular direction the proposed method is capable of handling inhomogeneous polar orthotropic viscoelastic material properties in general the method provides dimensional reduction in the finite element formulation which leads to a reduction in the complexity of the numerical model including the meshing process overall the method is shown to be competent mainly because of the efficient exploitation of the angular description of the geometry and the properties distribution a numerical example is given for the analysis of an orthotropic viscoelastic ring under asymmetric shear loading

technical communique reducing conservativeness in recent stability conditions of ts fuzzy systems in this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous time takagi sugeno fuzzy systems based on fuzzy lyapunov functions is proposed this new strategy generalizes previous results

disturbance rejection fuzzy control for nonlinear parabolic pde systems via multiple observers a design method of low dimensional disturbance rejection fuzzy control drfc via multiple observers is proposed for a class of nonlinear parabolic partial differential equation pde systems where the disturbance is modeled by an exosystem of ordinary differential equations odes and enters into the pde system through the control channel in the proposed scheme the modal decomposition technique is initially applied to the pde system to derive a slow subsystem of low dimensional nonlinear odes which accurately captures the dominant dynamics of the pde system the resulting nonlinear slow subsystem is subsequently represented by a takagi sugeno t s fuzzy model from the t s fuzzy model and the exosystem a fuzzy slow mode observer and a fuzzy disturbance observer are constructed to estimate the slow mode and the disturbance respectively furthermore a nonlinear observation spillover observer is proposed to compensate the effect of observation spillover then based on these observers a low dimensional drfc design is developed in terms of linear matrix inequalities to guarantee the exponential stability of the closed loop pde system in the presence of the disturbance finally the effectiveness of the proposed design method is demonstrated on the control of one dimensional burgers kpp fisher diffusion reaction system and the temperature profile of a catalytic rod

distributed control of a class of flexible mechanical systems with global constraint in this paper the constrained problem is investigated for both flexible string model and euler bernoulli beam model with the tip payload based on an infinite dimensional generalisation of a distributed control method the control objectives are to develop the control law so that the motion of flexible mechanical systems can track a desired reference signal and ensure that the string or beam remain in a constrained space we prove that with the proposed control the tracking error is exponentially stable without violation of the constraint the proof of convergence is based on an integral barrier lyapunov function iblf and extensive simulations are provided to illustrate the performance of the control system

observer based h_ infty sampled data fuzzy control for a class of nonlinear parabolic pde systems in this paper an observer based h infty sampled data fuzzy control problem is addressed for a class of nonlinear parabolic partial differential equation pde systems with the aid of the modal decomposition technique a nonlinear ordinary differential equation ode model is initially derived to describe the dominant slow dynamics of the pde system subsequently the resulting nonlinear ode model is accurately represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a finite dimensional observer based sampled data fuzzy control design with h infty performance is developed for the pde system via employing a novel time dependent functional the outcome of the observer based h infty sampled data fuzzy control problem can be formulated as a bilinear matrix inequality optimization problem moreover an iterative optimization algorithm based on the linear matrix inequalities is given to obtain a suboptimal h infty sampled data fuzzy controller finally simulation results on the fisher equation and a temperature cooling fin of high speed aerospace vehicle illustrate that the proposed design method is effective

a degenerate bifurcation to chaotic scattering in a multicentre potential many scattering systems can be described as scattering of a point particle off a multicentre potential in this paper we present a two centre system which shows either regular or chaotic scattering depending on the kinetic energy i e the velocity of the incoming particle the transition points to chaotic scattering can be derived analytically by linearization of the poincare map at one of these transition velocities there is a degenerate bifurcation where the invariant set contains a parabolic surface and where the time delay statistics is algebraic with power sigma 2

control of transport in a chaotic lattice abstract we examine a mechanism for the elimination of vertical transport in a square isotropic chaotic lattice we find that applying a shear jet along a line of symmetry in the lattice can completely impede chaotic transport across a specified barrier this is accomplished through a change in allegiance of heteroclinic connections within the lattice this mechanism is relatively insensitive to details such as amplitude or shape of the applied shear it depends quite sensitively however on the precise location of the shear this suggests that the placement of flow control devices in physical situations may be much more critical to transport behavior than are other control parameters in addition we develop a necessary condition for the existence of boundary circles in non twist maps using this condition we find that transport across a barrier can be eliminated for all practical purposes without evidence for an invariant boundary circle

exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant ori abstract an approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in hamiltonian systems of one and a half degrees of freedom similar to that of escande and doveil it is a free semi group with two generators this scheme is solved exactly for its orbits stable manifolds unstable manifolds and critical set various results are found including a cantor set of universal fractal diagrams the robustness of noble tori and a scaling law for areas near critical circles

speed selection for traveling wave solutions to the diffusion reaction equation with cubic reaction term and burgers nonlinear convection the problem of traveling wave tw speed selection for solutions to a generalized murray burgers kpp fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results depending on the magnitude of a parameter inherent in the reaction term i the term is either a concave function or a function with the inflection point and ii transition from pulled to pushed tw solution occurs due to interplay of two nonlinear terms the reaction term and the burgers convection term explicit pushed tw solutions are derived it is shown that physically observable tw solutions i e solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition can be determined by seeking the tw solution characterized by the maximum decay rate at its leading edge in the appendix the developed approach is applied to a non linear diffusion reaction equation that is widely used to model premixed turbulent combustion

robust regulation of distributed parameter systems with infinite dimensional exosystems in this paper a robust regulation problem for infinite dimensional systems with infinite dimensional exosystems is discussed the input and output spaces are also allowed to be infinite dimensional a new definition of internal model in terms of the controller parameters is given it is shown that there exists a feedback controller containing an internal model of the exosystem which robustly regulates the class of signals generated by the exosystem and strongly or weakly stabilizes the closed loop system as far as the authors know the results are new even for finite dimensional systems with infinite dimensional exosystems

brief paper an ilmi approach to robust h2 static output feedback fuzzy control for uncertain discrete time nonlinear systems this paper studies the problem of robust h 2 static output feedback sof fuzzy control for discrete time nonlinear systems with parametric uncertainties the takagi and sugeno fuzzy model is employed to represent an uncertain discrete time nonlinear system a sufficient condition for the existence of robust h 2 sof fuzzy controllers is presented in terms of a set of matrix inequalities which not only guarantees the stability of the closed loop fuzzy system but also provides an upper bound on the quadratic cost function a suboptimal robust h 2 sof fuzzy control problem is addressed in the sense of minimizing the bound an iterative linear matrix inequality ilmi algorithm is proposed to compute the feedback gain matrices of the suboptimal fuzzy controller finally two numerical examples are also provided to demonstrate the effectiveness of the proposed method

fault tolerant control for a class of switched linear hyperbolic systems this paper considers the fault tolerant control ftc problem for switched systems described by linear hyperbolic partial differential equations with the process and boundary faults the effect of

escape exponent for transient chaos and chaotic scattering in non hyperbolic hamiltonian systems it is shown that in non hyperbolic hamiltonian systems where correlations decay as a power law transient chaos and chaotic scattering demonstrate different power laws numerical evidence of this effect for the stadium billiard is presented

robust stabilization design of nonlinear stochastic partial differential systems fuzzy approach abstract in this paper we address the robust stabilization design problem for nonlinear stochastic partial differential systems nspdss in the presence of random external disturbances and measurement noise in the spatio temporal domain we propose a fuzzy stochastic partial differential system to approximate the nspdss based on fuzzy interpolation approach next we develop a fuzzy stochastic spatial state space model to represent the fuzzy stochastic partial differential system by employing a semi discretization finite difference scheme based on this model we propose a robust fuzzy estimator based stabilization controller to stabilize the nspdss furthermore robust stochastic h stabilization design is suggested to attenuate the effects of random external disturbances and measurement noise in the spatio temporal domain from the area energy point of view the lmi technique is applied to solve the issue of control gains and estimator gains of the controller by using a systematic control design procedure finally a simulation is presented as an example to illustrate the design procedure and to confirm the performance of the proposed robust fuzzy estimator based stabilization design for the nspdss

rotational chaos in dissipative systems abstract an investigation is made into chaotic attractors arising from a quasiperiodic transition to chaos using a quantity called the rotation interval the rotation interval describes the short term rotation rates available to the attractor we present algorithms to calculate it given an appropriate map differential equation or time series we find that the rotation interval has a very robust parameter dependence its endpoints are almost always phase locked our numerical ideas are based on the theory of dissipative twist maps which is reviewed this theory is also used to prove a theorem about the non existence of certain strange attractors in nearly conservative systems finally an investigation is made into the relationship between the rotation interval and topological entropy and the breakup of invariant circles

critical function for the standard map abstract the long time behavior of hamiltonian systems is determined by the broken kam tori which lie near the border of chaos the critical function tells us when these tori disintegrate and indirectly the extent to which they interfere with the motion of orbits across them i use lie transforms to find an expression for the critical function from this expression i recover the critical scaling found by renormalization techniques more importantly i find the deviations from scaling and show that they are crucial for understanding long time behavior in hamiltonian systems this resolves a long standing problem raised by the numerical experiments of karney and others in addition i find a relation between the values of the critical function at different frequencies this derivation clarifies the numerical results found by buric percival and vivaldi

brief paper approaches to extended non quadratic stability and stabilization conditions for discrete time takagi sugeno fuzzy systems this paper provides simple and effective linear matrix inequality lmi characterizations for the stability and stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this more general classes of non parallel distributed compensation non pdc control laws and non quadratic lyapunov functions are presented unlike the conventional non quadratic approaches using only current time normalized fuzzy weighting functions we consider not only the current time fuzzy weighting functions but also the l step past l 0 and one step ahead ones when constructing the control laws and lyapunov functions consequently by introducing additional decision variables it can be shown that the proposed conditions include the existing ones found in the literature as particular cases examples are given to demonstrate the effectiveness of the approaches

spectral element fourier method for transitional flows in complex geometries an efficient spectral element fourier method is presented for the direct numerical simulation of transitional internal flows in complex geometries this method is applied for the spatial discretization of the unsteady incompressible three dimensional navier stokes equations in the velocity pressure formulation the resulting discrete equations are solved by a semi implicit method in time where the nonlinear convective term is treated explicitly direct numerical simulations are performed to investigate the spatial structure and temporal evolution of two and three dimensional transitional flows in grooved channels

fuzzy observer based control for nonlinear coupled hyperbolic pde ode systems in this work the fuzzy observer based control problem is investigated for a class of nonlinear coupled systems which consists of a hyperbolic partial differential equation pde containing nonlinearities and a nonlinear ordinary differential equation ode the nonlinear coupled system is represented as a takagi sugeno t s fuzzy coupled hyperbolic pde ode model based on the t s fuzzy model a novel lyapunov functional approach is proposed to design a fuzzy observer based control strategy more specifically a fuzzy observer is presented to estimate the state variables of the fuzzy coupled pde ode system with the measurements of the pde and the exponential convergence of the observer error is proved then a fuzzy controller is given utilizing the estimated states as feedback variables and it is proved that the evolution profiles of the pde and the trajectory of the ode in the closed loop fuzzy system converge exponentially to the desired values respectively the sufficient existence conditions of the fuzzy observer based controller are formulated in terms of a set of space differential linear matrix inequalities sdlmis a recursive algorithm based on the finite difference approximation and the linear matrix inequality techniques are provided to solve the sdlmis finally the results are applied to case study of a predator prey system and the simulations are performed to illustrate the effectiveness of the proposed observer based control law

optimal lq feedback regulation of a nonisothermal plug flow reactor model by spectral factorization the linear quadratic lq optimal temperature and reactant concentration regulation problem is studied for a partial differential equation model of a nonisothermal plug flow tubular reactor by using a nonlinear infinite dimensional hilbert state space description first the dynamical properties of the linearized model around a constant temperature equilibrium profile along the reactor are studied it is shown that it is exponentially stable and approximately reachable next the general concept of lq feedback is introduced it turns out that any lq feedback is optimal from the input output viewpoint and stabilizing for the plug flow reactor linearized model a state lq feedback operator is computed via the solution of a matrix riccati differential equation mrde in the space variable thanks to the reachability property the computed lq feedback is actually the optimal one then the latter is applied to the nonlinear model and the resulting closed loop system dynamical performances are analyzed a criterion is given which guarantees that the constant temperature equilibrium profile is an asymptotically stable equilibrium of the closed loop system moreover under the same criterion it is shown that the control law designed previously is optimal along the nonlinear closed loop model with respect to some cost criterion the results are illustrated by some numerical simulations

output regulation for linear distributed parameter systems this work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system in particular it is shown that the full state feedback and error feedback regulator problems are solvable under the standard assumptions of stabilizability and detectability if and only if a pair of regulator equations is solvable for linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in francis 1997 and isidori and byrnes 1990 we also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function examples are given of periodic tracking set point control and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system

effective dynamics in hamiltonian systems with mixed phase space an adequate characterization of the dynamics of hamiltonian systems at physically relevant scales has been largely lacking here we investigate this fundamental problem and we show that the finite scale hamiltonian dynamics is governed by effective dynamical invariants which are significantly different from the dynamical invariants that describe the asymptotic hamiltonian dynamics the effective invariants depend both on the scale of resolution and the region of the phase space under consideration and they are naturally interpreted within a framework in which the nonhyperbolic dynamics of the hamiltonian system is modeled as a chain of hyperbolic systems

calculation of cantori for hamiltonian flows cantori are the invariant sets remaining after the destruction of kam surfaces and create partial barriers to transport in chaotic regions cantori may be approximated by high order periodic orbits however field line tracing methods for locating periodic orbits perform poorly in chaotic regions to approximate cantori for continuous flow dynamics high order periodic orbits are determined by lagrangian variational methods the method is robust to chaos converges quadratically and the computational cost scales linearly with the periodicity length of the orbit minimizing periodic orbits with periodicities in the tens of thousands that closely approximate cantori have been constructed

static collocated piecewise fuzzy control design of quasi linear parabolic pde systems subject to periodic boundary conditions this paper presents a lyapunov and partial differential equation pde based methodology to solve static collocated piecewise fuzzy control design of quasi linear parabolic pde systems subject to periodic boundary conditions two types of piecewise control i e globally piecewise control and locally piecewise control are considered respectively a takagi sugeno t s fuzzy pde model that is constructed via local sector nonlinearity method is first employed to accurately describe spatiotemporal dynamics of quasi linear pdes based on the t s fuzzy pde model a static collocated piecewise fuzzy feedback controller is constructed to guarantee the locally exponential stability of the resulting closed loop system sufficient conditions for the existence of such fuzzy controller are developed by applying vector valued poincare wirtinger inequality and its variants and a linear matrix inequality lmi relaxation technique these sufficient conditions are presented in terms of standard lmis finally the performance of the suggested fuzzy controller is illustrated by numerical simulation results of a nonlinear pde system described by quasi linear fitzhugh nagumo equation with periodic boundary conditions

exponential stabilization for a class of nonlinear parabolic pde systems via fuzzy control approach this paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations pdes for which a finite number of actuators are used a fuzzy control design methodology is developed for these systems by combining the pde theory and the takagi sugeno t s fuzzy model based control technique initially a t s fuzzy parabolic pde model is proposed to accurately represent a semilinear parabolic pde system then based on the t s fuzzy model a lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed loop pde system is exponentially stable with a given decay rate the stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities sdlmis furthermore a recursive algorithm is presented to solve the sdlmis via the existing linear matrix inequality optimization techniques finally numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method

what makes chaos border sticky a microscopic investigation of long time correlations near the chaos border of a particular model system has been carried out apparent stickiness of chaos border seems to be due to the influence of nearby hyperbolic orbits which are convergent to the invariant curve which constitutes the chaos border the diffusion near the chaos border can be described by a one dimensional biased random walk problem with pausing time which is inversely proportional to the distance from the border monte carlo simulation yields that the first passage time distribution has an algebraic decay tail of the form t with its exponent 2 80 0 05

finite dimensional compensator design for parabolic distributed systems with point sensors and boundary input a compensator design is proposed for a large class of parabolic distributed systems basically it is a modal approach utilizing known finite dimensional algorithms for observer and stabilizer design the observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a distributed or boundary implementation explicit sufficient conditions are given for the convergence of this scheme

pressure based semi analytical solution of radial stokes flows abstract a semi analytical methodology is proposed and implemented to approximate the solution of the partial differential equations that model the radial stokes flow between two parallel disks two traditional approaches for solving partial differential equations of mathematical physics namely eigenfunction expansions and green s function representations are used to obtain directly the pressure distribution for a variety of inflow boundary conditions we combine these standard techniques with a functional analytic framework to propose a proper representation for the pressure this methodology has been implemented first in a symbolic software mathematica and then numerically we provide both validation of the methodology when an exact solution exists and comparison with a spectral element solver for a test case where inflow boundary conditions render the existence of a recirculation zone close to the entrance of the domain we briefly discuss how to extend the methodology to handle the navier stokes equation in radial flow a subject that will be presented in detail in a following paper

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

unstable manifolds for the mackay approximate renormalisation abstract for a renormalisation of a critical phenomenon in some class of dynamical systems it is the unstable manifolds of the critical set which give the universal families which describe the critical transition in this paper we study such manifolds for the mackay 1988 approximate renormalisation scheme which models the breakup of invariant circles of arbitrary rotation number in area preserving twist maps we derive a number of properties of the unstable manifolds and then discuss the implications of these to the full renormalisation in particular a we suggest the importance of continuity in the definition of unstable manifolds and b show that their structure is similar to that observed numerically by mackay and percival 1987 in a related renormalisation finally we show that the residues of approximating periodic orbits are bounded above on the critical set

boundary control of a timoshenko beam system with input dead zone in this paper boundary control is designed for a timoshenko beam system with the input dead zone by the hamilton s principle the dynamics of the timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations the bounded part is separated from the input dead zone and then forms the disturbance like term together with the boundary disturbance which finally acts on the timoshenko beam system boundary control based on the lyapunov s direct method is proposed to ensure the timoshenko beam converge into a small neighbourhood of zero where stability of the system is also analysed besides the existence and uniqueness of the solution of the timoshenko beam system are proved simulations are provided to reveal the applicability and effectiveness of the proposed control scheme

distributed fuzzy control design of nonlinear hyperbolic pde systems with application to nonisothermal plug flow reactor this paper considers the problem of fuzzy control design for a class of nonlinear distributed parameter systems that is described by first order hyperbolic partial differential equations pdes where the control actuators are continuously distributed in space the goal of this paper is to develop a fuzzy state feedback control design methodology for these systems by employing a combination of pde theory and concepts from takagi sugeno t s fuzzy control first the t s fuzzy hyperbolic pde model is proposed to accurately represent the nonlinear first order hyperbolic pde system subsequently based on the t s fuzzy pde model a lyapunov technique is used to analyze the closed loop exponential stability with a given decay rate then a fuzzy state feedback control design procedure is developed in terms of a set of spatial differential linear matrix inequalities sdlmis from the resulting stability conditions furthermore utilizing the finite difference approximation method with a backward difference for the spatial derivative a recursive algorithm is presented to solve the sdlmis via the existing lmi optimization techniques finally the developed design methodology is successfully applied to the control of a nonisothermal plug flow reactor

a renormalization approach to invariant circles in area preserving maps abstract kadanoff and shenker introduced a renormalisation approach to invariant circles in area preserving maps this paper makes more precise the connection between invariant circles and the renormalisation operator restricting attention to noble rotation numbers the stability of a simple fixed point of the renormalisation is analysed corresponding to a linear twist map it is found to be essentially attracting so that noble circles persist under perturbation giving a new view on kam theory shenker and kadanoff found evidence for another fixed point corresponding to a map with a non smooth noble circle further evidence is given in this paper it has essentially only one unstable direction and its stable manifold is believed to give the boundary of the set of twist maps with a noble circle finally noble circles are shown to be locally most robust in an important sense

converse kam theory and practice we unify extend reinterpret and apply criteria of birkhoff 1 herman 9 mather 2 3 aubry et al 4 5 and newman and percival 6 for the nonexistence of invariant circles for area preserving twist maps the criteria enable one to establish regions of phase space through which no rotational invariant circles pass for families of maps the same can be done for regions of the combined space of phase points and parameters the criteria can be implemented rigorously on a computer and give a practical method of proving quite strong results as an example we present a computer program which proved that the standard map has no rotational invariant circles for any parameter value k 63 64

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

fuzzy state space modeling and robust observer based control design for nonlinear partial differential systems in this paper a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems npdss based on galerkin s method a takagi sugeno t s fuzzy pds is first proposed to model an npds then the t s fuzzy pds can be represented by a finite dimensional t s fuzzy subsystem in controlled mode and a coupled infinite dimensional t s fuzzy subsystem in residual mode therefore the npds can be partitioned into a finite dimensional t s fuzzy slow state space subsystem to be controlled and a coupled infinite dimensional fast residual subsystem to be tolerated based on the small gain theorem a robust fuzzy observer based controller is developed to tolerate the coupled residual subsystem to asymptotically stabilize the npds furthermore based on the dissipative theory an hinfin control design is proposed to attenuate the effects of external disturbances and measurement noises on the robust stabilization of npdss the matlab linear matrix inequality toolbox can be employed to efficiently solve the optimal hinfin fuzzy observer based control design problem of npdss finally a simulation example is given to illustrate the design procedure and confirm the performance of the proposed robust fuzzy observer based control method for the perturbative npdss

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

markov tree model of transport in area preserving maps abstract transport in an area preserving map with a mixture of regular and chaotic regions is described in terms of the flux through invariant cantor sets called cantori a model retaining a discrete set of cantori approaching a boundary circle gives the markov chain description of hanson cary and meiss the inclusion of cantori surrounding island chains and islands about islands etc gives a markov tree model with a slower decay rate the survival probability distribution is shown to decay asymptotically as a power law the decay exponent agrees reasonably well with the computations of karney and of chirikov and shepelyanski

resonances and transport in the sawtooth map we study transport in a completely chaotic hamiltonian system the hyperbolic sawtooth map analytical expressions are obtained for its cantori and resonances we show that resonances give a complete partition of phase space the flux leaking out of a resonance is given by its turnstiles whose form and areas are obtained analytically when the total flux out of a resonance becomes one third the area of an island the topology of the turnstiles changes at the same parameter value a horseshoe is formed corresponding to the orbits trapped within the resonance based on this a coding scheme for the trapped orbits is introduced and expressions for trapped ordered orbits are obtained the partial flux transferred from one resonance to another is determined by the degree of overlap of their turnstiles we calculate the survival probability within a resonance using the markov model the results are compared with results obtained numerically and from periodic orbit theory

fractal bifurcation sets renormalization strange sets and their universal invariants the transition structure of the most common routes to chaos are organized by fractal bifurcation sets examples include the quasiperiodic transitions to chaos and the period doubling structure found in arnol d tongues in this paper i discuss the universality of such fractal bifurcation sets and their relation to strange invariant sets of renormalization transformations an important result is that fractal bifurcation sets from within the same universality chaos are lipeomorphic this implies that they have the same fractal structure and in particular the same hausdorff dimension and scaling spectra some other invariants are introduced

algebraic decay in self similar markov chains a continuous time markov chain is used to model motion in the neighborhood of a critical invariant circle for a hamiltonian map states in the infinite chain represent successive rational approximants to the frequency of the invariant circle for the case of a noble frequency the chain is self similar and the nonlinear integral equation for the first passage time distribution is solved exactly the asymptotic distribution is a power law times a function periodic in the logarithm of the time for parameters relevant to the critical noble circle the decay proceeds ast 4 05

extended chaos and disappearance of kam trajectories abstract in two dimensional area preserving maps kam trajectories serve as natural boundaries between stochastic regions as they disappear points may leak out from one region to the next this escape rate is defined and related to the action generating function analytic and numerical results are presented to describe the behavior of the escape rate near the disappearance of a kam trajectory

dynamics in chaotic zones of area preserving maps close to separatrix and global instability zones abstract the purpose of this paper is to study phenomena in chaotic zones of area preserving maps using simpler models which are easier to analyse theoretically and numerically first of all the study of the dynamics in a neighbourhood of the separatrices of a resonant zone is carried out the well known separatrix map defined on a figure eight when needed is used to determine the location of rotational invariant curves r i c inside and outside the resonance the interest in this part is on a quantitative description of the dynamics in a neighbourhood of the separatrices to produce theoretical estimates of the width of the stochastic zone distance to the r i c existence of tiny islands close to the separatrices in every one of the studied items one has tried to complement the limit analytic study with realistic numerical simulations describing the analogy when possible after this study we focus on the formation of larger domains without r i c e g birkhoff domains to this end we introduce the biseparatrix map model although this is a qualitative model the mechanism of destruction of the last r i c and hence the process of creation of zones without r i c is clarified by means of this simple model several numerical examples illustrate the results obtained and are used as a test of the theoretical quantitative predictions

subdiffusive transport in stochastic webs we study a one parameter family of piecewise linear continuous area preserving maps of the plane at an infinite discrete set of parameter values the phase space is globally connected the transport proceeds in stochastic webs which are structurally similar to those described recently by zaslavsky and coworkers however the transport is subdiffusive i e the energy grows with time as t where 1 this behaviour is explained in terms of a markov model derived from a detailed analysis of the phase space structure and it is shown that 23 asymptotically for a special case we identify sublattices in phase space which show nongeneric transport with 1

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

stability analysis of t s fuzzy control systems by using set theory this paper is concerned with the stability analysis for takagi sugeno t s fuzzy control systems by exploiting the property of the structure of a fuzzy inference engine an equivalence relation on the index set of the product of fuzzy rule weights is defined furthermore a new stability criterion is proposed by using the equivalence relation and formulated into progressively less conservative sets of linear matrix inequalities by using an extension of polya s theorem the new criterion is proved to be with no conservatism for quadratic stability analysis of t s fuzzy control systems with a product inference engine and any possible fuzzy membership functions a numerical example is given to illustrate the effectiveness of the proposed method

exponentially stabilizing fuzzy controller design for a nonlinear ode beam cascaded system and its application to flexible air breathing hypersonic vehicle abstract this paper addresses fuzzy control design for a class of nonlinear systems which are described by nonlinear ordinary differential equations odes cascaded with an euler bernoulli beam ebb equation two design difficulties are involved in the control design addressed in this paper the first one is caused by the ebb equation whose spatiotemporal dynamics is affected by the output of the nonlinear ode subsystem through its differential equation rather than boundary conditions a state differential transformation is introduced for the ebb equation to bring the output of the ode subsystem in the differential equation to its boundary conditions the second one comes from the nonlinear ode subsystem to overcome this difficulty it is assumed that an exact takagi sugeno t s fuzzy ode model is utilized by the sector nonlinearity approach to describe the dynamics of nonlinear ode subsystem based on the t s fuzzy model a composite lyapunov function is constructed to develop a fuzzy controller via the ode state feedback and boundary feedback of transformed ebb equation to exponentially stabilize the nonlinear ode ebb cascaded system the design procedure is presented in terms of bilinear matrix inequalities bmis moreover a simple design method is also provided in terms of linear matrix inequalities lmis from the obtained design procedure finally numerical simulations on flight control with vibration suppression of a flexible air breathing hypersonic vehicle are given to illustrate the effectiveness of the proposed design method

universal small scale structure near the boundary of siegel disks of arbitrary rotation number abstract we present numerical evidence that for analytic maps of the complex plane with a siegel disk of any irrational rotation number and a quadratic critical point on its boundary the small scale structure near the critical point can be described asymptotically by a universal two parameter family we propose an explanation in terms of an ergodic attractor for a renormalisation operator