nonmonotonic twist maps abstract we investigate a family of nonmonotonic radial twist maps constructed by unfolding the linear twist function we find several new modes of reconnection and derive conditions for them to occur reconnection and bifurcation of higher order resonances are studied in detail including vortex pairs and triplets the structural instability of some of these exotic figures is mitigated by the presence of chaotic separatrix layers invariant curves of involution pairs are utilized to locate and chart their often very complex metamorphoses

brief paper output regulation for linear distributed parameter systems using finite dimensional dual observers in this article the solution of the output regulation problem is considered for linear infinite dimensional systems where the outputs to be controlled cannot be measured it is shown that this problem can be solved by a finite dimensional dual observer that is directly implementable so that the separation principle can be applied for the stabilization as in finite dimensions a parametric design of these dual observers is proposed for riesz spectral systems that allows to achieve a low controller order and a desired control performance for the closed loop system the presented results are illustrated by determining a finite dimensional regulator for an euler bernoulli beam with kelvin voigt damping that achieves tracking for steplike reference inputs and that asymptotically rejects sinusoidal disturbances

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

control of a tip force destabilized shear beam by observer based boundary feedback we consider a model of the undamped shear beam with a destabilizing boundary condition the motivation for this model comes from atomic force microscopy where the tip of the cantilever beam is destabilized by van der waals forces acting between the tip and the material surface previous research efforts relied on collocated actuation and sensing at the tip exploiting the passivity property between the corresponding input and output in the beam model in this paper we design a stabilizing output feedback controller in a noncollocated setting with measurements at the free end tip of the beam and actuation at the beam base our control design is a novel combination of the classical damping boundary feedback idea with a recently developed backstepping approach a change of variables is constructed which converts the beam model into a wave equation for a very short string with boundary damping this approach is physically intuitive and allows both an elegant stability analysis and an easy selection of design parameters for achieving desired performance our observer design is a dual of the similar ideas combining the damping feedback with backstepping adapted to the observer error system both stability and well posedness of the closed loop system are proved the simulation results are presented

analysis and output tracking design for the direct contact membrane distillation parabolic system abstract this paper considers the performance output tracking for a boundary controlled direct contact membrane distillation dcmd system first the mathematical properties of a recently developed mathematical model of the dcmd system are discussed this model consists of parabolic equations coupled at the boundary then the existence and uniqueness of the solutions are analyzed using the theory of operators some regularity results of the solution are also established a particular case showing the diagonal property of the principal operator is studied then based on one side feedback law the control problem which consists of tracking both the feed and permeate outlet temperatures of the membrane distillation system is formulated a servomechanism and an output feedback controller are proposed to solve the control problem in addition an extended state observer aimed at estimating both the system state and disturbance based on the temperature measurements of the inlet is proposed thus by some regularity for the reference signal and when the disturbance vanishes we prove the exponential decay of the output tracking error moreover we show the performance of the control strategy in presence of the flux noise

the spatio temporal structure of spiral defect chaos abstract we present a study of the recently discovered spatially extended chaotic state known as spiral defect chaos which occurs in low prandtl number large aspect ratio rayleigh benard convection we employ the modulus squared of the space time fourier transform of time series of two dimensional shadowgraph images to construct the structure factor s k this analysis is used to characterize the average spatial and temporal scales of the chaotic state we find that the correlation length and time can be described by power law dependences on the reduced rayleigh number these power laws have as yet no theoretical explanation

an adaptive servomechanism for a class of infinite dimensional systems a universal adaptive controller is constructed that achieves asymptotic tracking of a given class of reference signals and asymptotic rejection of a prescribed set of disturbance signals for a class of multivariable infinite dimensional systems that are stabilizable by high gain output feedback the controller does not require an explicit identification of the system parameters or the injection of a probing signal in contrast to most of the work in universal adaptive control this paper is based on an input output approach and the results do not require a state space representation of the plant the abstract input output results are applied to retarded systems and integrodifferential systems

disturbance estimator and servomechanism based performance output tracking for a 1 d euler bernoulli beam equation in this paper we consider performance output tracking for a one dimensional euler bernoulli beam equation with boundary moment control and unmatched internal uncertainty and external disturbance for such system the reference feng and guo 2017 firstly studied the active disturbance rejection control adrc problem we design an infinite dimensional disturbance estimator to estimate the total disturbance internal uncertainty and external disturbance and the system state simultaneously a servomechanism generated by the reference signal is designed based on the estimated total disturbance we design an output feedback control law such that the performance output signal tracks the reference signal and all the signals of closed loop system are bounded some illustrative simulations are presented

a sampled data servomechanism for stable well posed systems in this technical note an approximate tracking and disturbance rejection problem is solved for the class of exponentially stable well posed infinite dimensional systems by invoking a simple sampled data low gain controller suggested by the internal model principle the reference signals are finite sums of sinusoids and the disturbance signals are asymptotic to finite sums of sinusoids

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

tracking control of the uncertain heat and wave equation via power fractional and sliding mode techniques in the present paper preliminary results towards the generalization to the infinite dimensional setting of some well known robust finite dimensional control algorithms are illustrated more specifically we deal with the tracking problem for some classes of linear uncertain infinite dimensional systems evolving in hilbert spaces we design distributed variable structure stabilizers that are shown to be effective in the presence of external disturbances the main focus of the present paper is on the rejection of nonvanishing external disturbances the generalization to the infinite dimensional setting of the well known finite dimensional controllers namely the power fractional controller s p bhat and d s bernstein siam j control optim 38 2000 pp 751 766 and two second order sliding mode control algorithms the twisting and supertwisting algorithms l fridman and a levant higher order sliding modes as a natural phenomenon in control theory in robust control via variable structure and lyapunov techniques springer verlag berlin 1996 pp 107 133 a levant internat j control 58 1993 pp 1247 1263 is the main contribution of the present investigation first the distributed twisting control algorithm is developed to address the asymptotic state tracking of the perturbed wave equation next the finite time state tracking of the unperturbed heat equation is provided by means of a distributed power fractional controller finally the distributed supertwisting controller is suggested to address the asymptotic state tracking of the heat equation in spite of the presence of persistent disturbances constructive proofs of stability are developed via the lyapunov functional technique which leads to simple tuning rules for the controller parameters simulation results are discussed to verify the effectiveness of the proposed schemes

performance output tracking for multidimensional heat equation subject to unmatched disturbance and noncollocated control this paper investigates performance output tracking for a boundary controlled multidimensional heat equation it is assumed that the so called total disturbance which is composed of internal possibly nonlinear uncertainty and external disturbance the equation is subject to is on one part of the boundary and that the control is applied on the rest of the boundary using only partial boundary measurement we first propose an extended state observer to estimate both system state and the total disturbance this allows us to design a servomechanism and then an output feedback controller under the condition that both the reference signal and the disturbance vanish or belong to spaces h 1 0 infty l 1 gamma 1 and l 2 0 infty l 2 gamma 0 respectively we show that the over all control strategy achieves three objectives on the system performance first exponentially output tracking for arbitrary given reference signal second uniformly boundedness of all internal signals and third the internal asymptotic stability of the closed loop system in addition the control strategy turns out to be robust to the measurement noise we provide numerical experiments to illustrate the effectiveness of the proposed control strategy

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

performance output tracking for a wave equation subject to unmatched general boundary harmonic disturbance in this paper we consider performance output reference tracking for a wave equation with general harmonic disturbance at one end and the control at the other end we first design a state reference system determined completely by the measured output and the reference signal where the parameter update law is presented an adaptive servomechanism output feedback control is then designed it is shown that the closed loop system is well posed three control objectives are achieved a the performance output is tracking the reference signal b all the internal loops are bounded c when the disturbance and reference are disconnected the closed loop is exponentially stable finally the state of system is shown to be tracking the reference state and the updated parameters are convergent to their true values

performance output exponential tracking for a wave equation with a general boundary disturbance abstract in this paper we consider performance output tracking for a wave equation with a general boundary disturbance the control and the disturbance are unmatched different from the existing results the hidden regularity instead of the high gain or variable structure is utilized in the adaptive servomechanism design as a result we are able to cope with more complicated and general disturbances moreover the performance output can track the reference signal exponentially and at the same time all the states of the subsystems involved are uniformly bounded more specially the overall closed loop system is exponentially stable when the disturbance and reference are disconnected to the system the numerical simulations are presented to illustrate the effect of the proposed scheme

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

manifold reconnection in chaotic regimes in this paper we extend the concept of separatrix reconnection into chaotic regimes we show that even under chaotic conditions one can still understand abrupt jumps of diffusive like processes in the relevant phase space in terms of relatively smooth realignments of stable and unstable manifolds of unstable fixed points

a dynamic compensator for in domain control of burgers equation this paper addresses the problem of output regulation control of a burgers equation under pointwise in domain actuation a dynamic compensator that generates the in domain control is developed for

performance output tracking and disturbance rejection for an euler bernoulli beam equation with unmatched boundary disturbance abstract this paper considers performance output tracking and disturbance rejection for a boundary controlled one dimensional euler bernoulli beam equation suffered unknown external bounded disturbance by first proposing a disturbance estimator and then based on this disturbance estimator we construct a servomechanism to track the reference signal and reject the external disturbance four control objectives are achieved a the output is exponentially tracking the reference signal b the disturbance is rejected c all the states of internal loops are bounded d when the disturbance and reference are disconnected the closed loop is exponentially stable finally the state of the system is shown to be exponentially tracking the reference state

finite dimensional regulators for a class of infinite dimensional systems abstract we show that the direct approach developed by the author for stabilization of certain classes of distributed parameter systems can be extended to cover regulation problems as well an iterative design algorithm is presented together with proof that the algorithm will converge after a finite number of steps the procedure is illustrated with an example of a constant disturbance acting on a delay system

global structure of periodicity hubs in lyapunov phase diagrams of dissipative flows infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow namely a r ossler s oscillator we show that spirals associated with periodicity hubs emerge and accumulate at the folding of certain fractal like sheaves of shilnikov homoclinic bifurcations of a common saddle focus equilibrium the specific organization of hub networks is found to depend strongly on the interaction between the homoclinic orbits and the global structure of the underlying attractor

internal model based tracking and disturbance rejection for stable well posed systems in this paper we solve the tracking and disturbance rejection problem for infinite dimensional linear systems with reference and disturbance signals that are finite superpositions of sinusoids we explore two approaches both based on the internal model principle in the first approach we use a low gain controller and here our results are a partial extension of results by hamalainen and pohjolainen in their papers the plant is required to have an exponentially stable transfer function in the callier desoer algebra while in this paper we only require the plant to be well posed and exponentially stable these conditions are sufficiently unrestrictive to be verifiable for many partial differential equations in more than one space variable our second approach concerns the case when the second component of the plant transfer function from control input to tracking error is positive in this case we identify a very simple stabilizing controller which is again an internal model but which does not require low gain we apply our results to two problems involving systems modeled by partial differential equations the problem of rejecting external noise in a model for structure acoustics interactions and a similar problem for two coupled beams

robust attractor of non twist systems abstract we present a new kind of one dimensional attractor which has not yet been predicted in the non linear dynamics theory we consider a non linear map which presents typical non twist manifestations as isochronous resonances and shearless torus it is known that this torus corresponds to a very sturdy barrier in the phase space of some area preserving systems we show that when dissipation is present in the system the shearless curve carries its robustness to the dissipative scenario it becomes a powerful attractor which we call shearless attractor which is persistent under the variation of the parameters and it exchanges its stability from chaotic to quasi periodic or vice versa depending on the set of parameters

labyrinthic standard non twist map we introduce the labyrinthic standard non twist map which is a modified non twist standard map with an additional perturbation which is a period multiple of the original perturbation period in phase space this map can present several sets of invariant meandering curves due to the reconnection process of isochrones resonances inside each meander set we can find a non twist invariant curve called the shearless curve with an extreme rotation number which generates a wide stickiness effect in phase space when it is broken the birth break of these shearless curves as well as their effects on the dynamical transport are studied showing the formation of many transport barriers in the system

a wavelet based algorithm for pattern analysis abstract patterns with a local roll structure arise in many diverse physical systems which have little in common at the microscopic level in this paper we construct an algorithm based on the wavelet transform that can be used as a diagnostic tool to extract from such patterns macroscopic information like the local director field the local amplitude away from defects and slowly varying fields such as mean drift which may be soft modes of pattern it allows a precise detection of phase grain boundaries and point defects several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm finally the algorithm is applied to actual experimental convection patterns allowing us to draw several conclusions about the nature of the wave director field in such patterns