adaptive predefined performance control for mimo systems with unknown direction via generalized fuzzy hyperbolic model an adaptive predefined performance control problem is investigated for a class of multiple input multiple output systems with unknown control direction and unknown backlash like hysteresis nonlinearities by using generalized fuzzy hyperbolic model gfhm compared with the existing methods the main features are as follows the prediction error is introduced to construct the adaptive laws which means that the approximate accuracy of the gfhm is solved the nussbaum type gain is utilized to deal with the unknown control direction which avoids the requirement of direction a priori and by transforming the tracking errors into new error variables the prescribed steady state and transient performance can be ensured it is shown that the proposed control approach can guarantee that all the signals of the resulting closed loop systems are bounded and the output tracks a desired trajectory while the tracking errors are confined all times within the prescribed bounds finally two simulation results and some comparisons are provided to verify the effectiveness of the proposed approach since the proposed control strategy is only implemented in a healthy case how to extend the strategy to a faulty case will be a further topic

mathematical analysis and numerical solution of models with dynamic preisach hysteresis abstract hysteresis is a phenomenon that is observed in a great variety of physical systems which leads to a nonlinear and multivalued behavior making their modeling and control difficult even though the analysis and mathematical properties of several rate independent and rate dependent hysteresis models are known this is not the case for the bertotti s rate dependent extension of the classical preisach model the so called dynamic preisach model for which current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics both being crucial in practice this paper deals with the description and mathematical analysis of the dynamic preisach hysteresis model toward that end we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field h and the magnetic induction b in which the values of b not only depends on the present values of h but also on the past history and its velocity we first analyze mathematically some important properties of the model and compare them with known results for the static preisach model then we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations under suitable assumptions we prove the existence of a solution of a weak formulation of the problem and solve it numerically finally we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic preisach model

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

systems of controlled functional differential equations and adaptive tracking an adaptive servomechanism is developed in the context of the problem of approximate or practical tracking with prescribed asymptotic accuracy by the system output of any admissible reference signal absolutely continuous and bounded with essentially bounded derivative for every member of a class of controlled dynamical systems modelled by functional differential equations

piecewise linear identification for the rate independent and rate dependent duhem hysteresis models we consider the semilinear duhem model and develop an identification method for rate independent and rate dependent hysteresis for rate independent hysteresis we reparameterize the system in terms of the input signal so that the system has the form of a switching linear time invariant system with ramp plus step forcing for rate dependent hysteresis the system can be viewed as a switching linear time invariant system for triangle wave inputs least squares based methods are developed to identify the rate independent and rate dependent semilinear duhem models

stability analysis and stabilization of systems with input backlash this technical note deals with the stability analysis and stabilization of linear systems with backlash in the input uniform ultimate boundedness stability and stabilization problems are tackled allowing to characterize suitable regions of the state space in which the closed loop trajectories can be captured in the state feedback control design computational oriented solutions are derived to solve suboptimal convex optimization problems able to give a constructive solution

practical adaptive fuzzy tracking control for a class of perturbed nonlinear systems with backlash nonlinearity abstract this paper addresses the adaptive fuzzy tracking control problem for a class of perturbed nonlinear systems with backlash nonlinearity in the proposed control scheme fuzzy logic systems are used to approximate the unknown nonlinearity in each backstepping design and the classic adaptive technique is employed to deal with some unknown parameters the proposed fuzzy controller is developed by introducing some non negative switching functions and novel parameter adaptation learning laws are designed using the modification method it is emphasized that with the help of novel parameter adaptation laws the high gain phenomenon in the previous work can be avoided in addition by borrowing the property of the introduced non negative functions and the inequality technique an adaptive technique is employed to estimate the norm of the ideal weight vector such that the number of adaptation learning parameters online is reduced by employing barbalat s lemma it can be proved that all the signals in the closed loop system remain semi globally uniformly ultimately bounded and especially that the tracking error converges to an accuracy predefined a priori two simulation examples are provided to verify the effectiveness of the proposed control scheme

adaptive control for uncertain continuous time systems using implicit inversion of prandtl ishlinskii hysteresis representation in this note an implicit inversion approach is introduced to avoid difficulties associated with stability analysis in the direct application of inversion for operator based hysteresis models based on this implicit inversion an adaptive control algorithm is formulated for continuous time linear dynamical systems preceded with hysteresis nonlinearities described by the prandtl ishlinskii model a stability analysis of the controlled system is performed to show that zero output tracking error can be achieved simulation results show the effectiveness of the proposed algorithm

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

the number of subgroups of a finite group let a be a finite group and let p be a prime suppose that ps is the highest power of p dividing a a where a is the commutator subgroup of a and that the type 1 2 with 1 2 of a

using interior point methods for fast parallel algorithms for bipartite matching and related problems in this paper interior point methods for linear programming developed in the context of sequential computation are used to obtain a parallel algorithm for the bipartite matching problem this algorithm finds a maximum cardinality matching in a bipartite graph with n nodes and m edges in o sqrt m log 3 n time on a crcw pram the results here extend to the weighted bipartite matching problem and to the zero one minimum cost flow problem yielding o sqrt m log 2 n log nc algorithms where c 1 is an upper bound on the absolute value of the integral weights or costs in the two problems respectively the results here improve previous bounds on these problems and introduce interior point methods to the context of parallel algorithm design

existence of fractional integral equation with hysteresis the existence of solutions to an integral equation of fractional order with hysteresis has been established a fixed point theorem due to schauder is the main tool in carrying out our proof

adaptive control based barrier lyapunov functions for a class of stochastic nonlinear systems with full state constraints abstract an adaptive control scheme is developed in the paper for nonlinear stochastic systems with unknown parameters all the states in the systems are required to be constrained in a bounded compact set i e the full state constraints are considered in the systems it is for the first time to control nonlinear stochastic systems with the full state constraints in contrast to deterministic systems the stochastic systems with the full state constraints are more difficult to be stabilized and the design procedures are more complicated by constructing barrier lyapunov functions blf in symmetric and asymmetric forms it can be ensured that all the states of the stochastic systems are not to transgress their constraint bounds thus the proposed scheme not only solves the stability problem of stochastic systems but also overcomes the effect of the full state constraints on the control performance finally it is proved that all the signals in the closed loop system are semi global uniformly ultimately bounded sguub in probability the system output is driven to follow the reference signals and all the states are ensured to remain in the predefined compact sets the validity of the proposed scheme is verified by a simulation example

a system of odes with a hysteresis effect abstract the paper deals with a class of ordinary differential systems which contains a differential inclusion describing input output relations of hysteresis type existence and uniqueness of local and global solutions of the systems under consideration are proved

adaptive neural tracking control for a class of nonstrict feedback stochastic nonlinear systems with unknown backlash like hysteresis this paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict feedback form with unknown backlash like hysteresis nonlinearities to overcome the design difficulty of nonstrict feedback structure variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic by combining radial basis function neural networks universal approximation capability with an adaptive backstepping technique an adaptive neural control algorithm is proposed it is shown that the proposed controller guarantees that all the signals in the closed loop system are four moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results further show the effectiveness of the presented control scheme

local matching dynamics in social networks we study stable marriage and roommates problems under locality constraints each player is a vertex in a social network and strives to be matched to other players the value of a match is specified by an edge weight players explore possible matches only based on their current neighborhood we study convergence of natural better response dynamics that converge to locally stable matchings matchings that allow no incentive to deviate with respect to their imposed information structure in the social network if we have global information and control to steer the convergence process then quick convergence is possible and for every starting state we can construct in polynomial time a sequence of polynomially many better response moves to a locally stable matching in contrast for a large class of oblivious dynamics including random and concurrent better response the convergence time turns out to be exponential in such distributed settings a small amount of random memory can ensure polynomial convergence time even for many to many matchings and more general notions of neighborhood here the type of memory is crucial as for several variants of cache memory we provide exponential lower bounds on convergence times

hom a g abstract in this paper we prove that for any finite group g and any finite abelian group a the number of homomorphism from a to g is divisible by the greatest common divisor of a and g this result is a generalization of an old theorem of frobenius on the number of solutions of the equation x n 1 on a finite group

stability of systems with the duhem hysteresis operator in this paper we discuss the dissipativity property of the counterclockwise duhem operator sufficient conditions on the functions which define the duhem operator are given such that the duhem operator has counterclockwise input output dynamics in particular an explicit construction of the storage functions satisfying the counterclockwise dissipation inequality is given the constructed storage function is also related to the underlying anhysteresis function which is commonly used to describe hysteresis in magnetic materials the results can thus facilitate analysis of systems with the counterclockwise duhem operator via the dissipativity approach

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

nonlinear resonance in systems with hysteresis a general approach is suggested for the analysis of nonlinear resonance in control systems including an integral linear term and a nonlinear term with hysteresis this approach uses a special property of nonlinear terms which is valid for many important classes of hysteresis operators for systems with such hysteresis nonlinearities we introduce a method to derive conditions for the existence of forced oscillations and for systems with a parameter of nonlinear resonance at infinity

properties of solutions to a class of differential models incorporating preisach hysteresis operator abstract we consider a class of equations which have been recently proposed as a mathematical tool for modelling dynamics of hydrological economic and biological systems exhibiting hysteresis and related memory effects the detail of the modelling approach is illustrated by an example from the hydrological context where a balance equation is coupled with a hysteretic constitutive relationship between the water content in the soil and the matric potential m of the soil matrix and where the preisach hysteresis operator is used as a model of this constitutive relationship in particular we present assumptions which eliminate spatial variation and lead to balance equations in the form of odes two examples of such hydrological models are considered followed by a less detailed discussion of applications of similar modelling approach and equations in economics and biology in the proposed formalism the closed system is described by an operator differential equation where the rate of change of the output of the preisach operator is a function of its input and time in the main part of the paper for such operator differential equations we study the initial value problem uniqueness existence extendability of solutions their dependence on initial data and the structure of the projection of the phase portrait onto the t m plane solutions are characterised by jumps of the derivative induced by either of the two reasons one is the memory of past extremum values of the solution the other is a singularity at the lines of zero flow we analyse the singularity and calculate the value of the jumps thus providing an important input to numerical solution of the equation furthermore we identify possible non uniqueness points and points of sensitivity to small perturbations of initial data as well as conditions that ensure uniqueness and stability to such perturbations regularisation of the equation and natural monotonicity conditions ensuring global stability of a periodic solution for the equation with periodic input are discussed rigorous analysis of the well posedness of the models is presented for the first time

continuous time adaptive control of systems with unknown backlash this paper addresses one of the nondifferentiable nonlinearities which appear very often in industrial control applications backlash the authors first present a right inverse of backlash and then give one of its possible implementations characteristics like backlash are seldom known so an adaptive version of the authors backlash inverse is more suitable for applications the authors develop an adaptive backlash inverse scheme and apply it to feedback control of a known linear plant with an unknown backlash at its input the authors use simulation results to illustrate achieved performance improvements

asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented we consider two possible input nonlinearities that is backlash like hysteresis and symmetric dead zone which can be simultaneously dealt with by using the proposed compensation controllers the knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required only the boundedness of the reference signal is assumed the nussbaum gain approach is employed to remove the assumption on the control gain sign the first scheme is based on the backstepping technique the final step of the recursive design is crucial for the closed loop stability in the second scheme a direct adaptive control law is designed the controller has a simple structure and only one adaptation parameter is updated in both controllers it is shown that asymptotic tracking is ensured two numerical examples are provided to show the effectiveness of the theor

a class of differential delay systems with hysteresis asymptotic behaviour of solutions abstract a class of differential delay systems with hysteresis is considered conditions ensuring boundedness of solutions and related asymptotic and integrability properties are expressed in terms of data associated with the linear component of the overall system and a lipschitz constant associated with the hysteretic component

stochastic averaging of duhem hysteretic systems abstract the response of duhem hysteretic system to externally and or parametrically non white random excitations is investigated by using the stochastic averaging method a class of integrable duhem hysteresis models covering many existing hysteresis models is identified and the potential energy and dissipated energy of duhem hysteretic component are determined the duhem hysteretic system under random excitations is replaced equivalently by a non hysteretic non linear random system the averaged ito s stochastic differential equation for the total energy is derived and the fokker planck kolmogorov equation associated with the averaged ito s equation is solved to yield stationary probability density of total energy from which the statistics of system response can be evaluated it is observed that the numerical results by using the stochastic averaging method is in good agreement with that from digital simulation

extending hysteresis operators to spaces of piecewise continuous functions we consider continuous time hysteresis operators defined to be causal and rate independent operators mapping input signals u r r to output signals v r r we show how a hysteresis operator defined on the set of continuous piecewise monotone functions can be naturally extended to piecewise continuous piecewise monotone functions we prove that the extension is also a hysteresis operator and that a number of important properties of the original operator are inherited by the extension moreover we define the concept of a discrete time hysteresis operator and we show that discretizing continuous time hysteresis operators using standard sampling and hold operations leads to discrete time hysteresis operators we apply the concepts and results described above in the context of sampled data feedback control of linear systems with input hysteresis 2003 elsevier science usa all rights reserved

wave propagation in nonlinear and hysteretic media a numerical study abstract this paper considers the problem of one dimensional wave propagation in nonlinear hysteretic media the constitutive law in the media is prescribed by an integral relationship based on the duhem model of hysteresis it is found that the well known nonlinear elastic stress strain relationship is a special case of this integral relationship it is also shown that the stress strain relationship from the mccall and guyer model of hyesteretic materials can also be derived from this integral stress strain relationship the first part of this paper focuses on a material with a quadratic stress strain relationship where the initial value problem is formulated into a system of conservation laws analytical solutions to the riemann problem are obtained by solving the corresponding eigenvalue problem and serve as reference for the verification and illustration of the accuracy obtained using the applied numerical scheme proposed by kurganov and tadmor the second part of this research is devoted to wave propagation in hysteretic media several types of initial excitations are presented in order to determine special characteristics of the wave propagation due to material nonlinearity and hysteresis the results of this paper demonstrate the accuracy and the robustness of this numerical scheme to analyze wave propagation in nonlinear materials

a new approach to stable matching problems it is shown that stable matching problems are the same as problems about stable configurations of x networks consequences include easy proofs of old theorems a new simple algorithm for finding a stable matching an understanding of the difference between stable marriage and stable roommates np completeness of three party stable marriage cc completeness of several stable matching problems and a fast parallel reduction from the stable marriage problem to the assignment problem

random response of preisach hysteretic systems an approximate method for analyzing the response of preisach hysteretic systems with non local memory under stationary gaussian excitation is proposed the covariance matrix equation of system response is derived the cross correlation function of preisach hysteretic force and response in the covariance equation is evaluated based on the switching probability analysis and the gaussian approximation of response process and an explicit expression for the cross correlation function is given for the case of symmetric preisach weighting function it is shown that the numerical result obtained by using the proposed method is in good agreement with that from digital simulation

technical communique stability analysis for linear systems with input backlash through sufficient lmi conditions this paper addresses the problem of stability analysis for a given class of nonlinear systems resulting from the connection of a linear system with an isolated backlash operator constructive conditions based on lmis to ensure closed loop stability are proposed by using some suitable lyapunov functionals with quadratic terms and lure type terms and generalized sector conditions additionally the boundary of the associated set of all the admissible equilibrium points is precisely defined

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

decentralized adaptive stabilization in the presence of unknown backlash like hysteresis due to the difficulty of handling both hysteresis and interactions between subsystems there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis even though the problem is practical and important in this paper we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach for each subsystem a general transfer function with arbitrary relative degree is considered the interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions in the first scheme no knowledge is assumed on the bounds of unknown system parameters in case that the uncertain parameters are inside known compact sets we propose an alternative scheme where a projection operation is employed in the adaptive laws in both schemes the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws it is shown that the designed local adaptive controllers can ensure all the signals in the closed loop system bounded a root mean square type of bound is obtained for the system states as a function of design parameters this implies that the transient system performance can be adjusted by choosing suitable design parameters with scheme ii the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available in the absence of hysteresis perfect stabilization is ensured and the l 2 norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied

adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash like hysteresis in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of uncertain nonlinear systems with unknown backlash like hysteresis and unmeasured states the fuzzy logic systems are used to approximate the nonlinear system functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are semi globally uniformly ultimately bounded suub and both observer error and tracking error can converge to a small neighborhood of the origin two simulations are included to illustrate the effectiveness of the proposed approach

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

tracking control of a biaxial piezo actuated positioning stage using generalized duhem model nonlinear hysteresis modeling is studied using a novel pzt actuated flexure based mechanism to compare the performance of variant hysteresis models with respect to the tracking reference we reformulate the bouc wen model the dahl model and the duhem model as a generalized duhem model system parameters for these three hysteresis models are formulated into nonlinear optimization problems with constraints these optimization problems are solved by the particle swarm optimization method since the duhem model includes both electrical and mechanical domains it has a smaller modeling error compared to the other two hysteresis models the simulation results are confirmed by modeling the proposed biaxial piezo actuated positioning stage of these hysteresis models cross coupling effects between the x and y axis actuation are also alleviated by a novel feedforward compensation mechanism based on the duhem model with crossover terms finally a real time experiment is performed to confirm the feasibility of the proposed method the experimental results validate the capability of the proposed controller to achieve precision tracking tasks with submicron precision

a sublinear parallel algorithm for stable matching abstract a parallel algorithm for the stable matching problem is presented the algorithm is based on the primal dual interior path following method for linear programming the main result is that a stable matching can be found in o m time by a polynomial number of processors where m is the total length of preference lists of individuals

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

properties of the preisach model for hysteresis as shown by krasnosel skii the classical preisach model allows to construct a hysteresis operator wbetween spaces of real functions of time this construction via the definition of a measure mu in the so called preisach plane is recalled characterizations in terms of mu are given for several mapping and continuity properties of w in various function spaces for the invertibility of w and for the corresponding mapping and continuity properties of the inverse

stable adaptive fuzzy control of nonlinear systems preceded by unknown backlash like hysteresis this paper deals with adaptive control of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is described by a dynamic equation by utilizing this dynamic model and by combining a fuzzy universal function approximator with adaptive control techniques a stable adaptive fuzzy control algorithm is developed without constructing a hysteresis inverse the stability of the closed loop system is shown using lyapunov arguments the effectiveness of the proposed method is demonstrated through simulations

adaptive neural output feedback control of output constrained nonlinear systems with unknown output nonlinearity this paper addresses the problem of adaptive neural output feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states a modified bouc wen model is first employed to capture the output hysteresis phenomenon in the design procedure for its fusion with the neural networks and the nussbaum type function two key lemmas are established using some extended properties of this model to avoid the bad system performance caused by the output nonlinearity a barrier lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error in addition a robust filtering method is designed to cancel the restriction that all the system states require to be measured based on the lyapunov synthesis a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed loop system simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper

dynamics of relay relaxation oscillators relaxation oscillators can usually be represented as a feedback system with hysteresis the relay relaxation oscillator consists of relay hysteresis and a linear system in feedback the objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators in particular we give a complete analysis for the case of unimodal periodic orbits and illustrate the presence of degenerate and asymmetric orbits we also discuss how complex orbits can arise from bifurcation of unimodal orbits finally we focus on oscillators with an integrator as the linear component and study the entrainment under external forcing and phase locking when such oscillators are coupled in a ring

discrete time and sampled data low gain control of infinite dimensional linear systems in the presence of input hysteresis we introduce a general class of causal dynamic discrete time nonlinearities which have certain monotonicity and lipschitz continuity properties in particular the discretizations of a large class of continuous time hysteresis operators obtained by applying the standard sampling and hold operations belong to this class it is shown that closing the loop around a power stable linear infinite dimensional discrete time single input single output system subject to an input nonlinearity from the class under consideration and compensated by a discrete time integral controller guarantees asymptotic tracking of constant reference signals provided that a the positive integrator gain is sufficiently small and b the reference value is feasible in a very natural sense we apply this result in the development of sampled data low gain integral control for exponentially stable regular linear infinite dimensional continuous time systems subject to input hysteresis

an adi method for hysteretic reaction diffusion systems in this paper we consider a mathematical model motivated by patterned growth of bacterial cells the model is a system of differential equations that consists of two subsystems one is a system of ordinary differential equations and the other is a reaction diffusion system an alternating direction implicit adi method is derived for numerically solving the system the adi method given here is different from the usual adi schemes for parabolic equations due to the special treatment of nonlinear reaction terms in the system stability and convergence of the adi method are proved we apply these results to the numerical solution of a problem in microbiology

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

proportional derivative control of hysteretic systems we discuss a tracking controller strategy for hysteretic systems including magnetic and smart actuators by using two output feedbacks we show that a dual loop proportional derivative controller derived from two feedback signals is sufficient to achieve tracking control we further discuss regularity well posedness and stability and obtain sufficient conditions on controller gains for ultimate bounded tracking control of hysteretic systems

on the characterization of the duhem hysteresis operator with clockwise input output dynamics abstract in this paper we investigate the dissipativity property of a certain class of duhem hysteresis operator which has clockwise cw input output i o behavior in particular we provide sufficient conditions on the duhem operator such that it is cw and propose an explicit construction of the corresponding function satisfying dissipation inequality of cw systems the result is used to analyze the stability of a second order system with hysteretic friction which is described by a dahl model

semilinear duhem model for rate independent and rate dependent hysteresis the classical duhem model provides a finite dimensional differential model of hysteresis in this paper we consider rate independent and rate dependent semilinear duhem models with provable properties the vector field is given by the product of a function of the input rate and linear dynamics if the input rate function is positively homogeneous then the resulting input output map of the model is rate independent yielding persistent nontrivial input output closed curve that is hysteresis at arbitrarily low input frequency if the input rate function is not positively homogeneous the input output map is rate dependent and can be approximated by a rate independent model for low frequency inputs sufficient conditions for convergence to a limiting input output map are developed for rate independent and rate dependent models finally the reversal behavior and orientation of the rate independent model are discussed

parabolic problems with the preisach hysteresis operator in boundary conditions parabolic initial boundary value problems coupled via the boundary condition with ordinary differential equations whose right hand side contains the preisach hysteresis operator are considered in particular these problems model thermocontrol processes in chemical reactors climate control systems biological cells etc for the preisach operator with and without time delay solvability periodicity of solutions and global b attractors are studied

periodic solutions to a heat equation with hysteresis in the source term this paper is concerned with a parabolic problem with hysteresis effects in the heat source which models the feedback control the existence of periodic solutions is proved by the viscosity approach when the heat force changes periodically in time more precisely with the help of the subdifferential operator theory and the poincare map the existence of solutions to the approximation problem is shown and the solution of the periodic problem is obtained under consideration by using a passage to limit procedure