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

output feedback nn control for two classes of discrete time systems with unknown control directions in a unified approach in this paper output feedback adaptive neural network nn controls are investigated for two classes of nonlinear discrete time systems with unknown control directions 1 nonlinear pure feedback systems and 2 nonlinear autoregressive moving average with exogenous inputs narmax systems to overcome the noncausal problem which has been known to be a major obstacle in the discrete time control design both systems are transformed to a predictor for output feedback control design implicit function theorem is used to overcome the difficulty of the nonaffine appearance of the control input the problem of lacking a priori knowledge on the control directions is solved by using discrete nussbaum gain the high order neural network honn is employed to approximate the unknown control the closed loop system achieves semiglobal uniformly ultimately bounded sguub stability and the output tracking error is made within a neighborhood around zero simulation results are presented to demonstrate the effectiveness of the proposed control

on the uniqueness and ordering of steady states of predator prey systems this paper discusses the relationship between the uniqueness and the ordering of strictly positive solutions of elliptic predator prey interacting systems if v and u v are two such solutions with u or v v then u v v when the positive solutions are numerically close to the extreme case the solution is unique

modeling identification and control of a class of nonlinear systems in this paper we propose a new fuzzy hyperbolic model for a class of complex systems which is difficult to model the fuzzy hyperbolic model is a nonlinear model in nature and can be easily derived from a set of fuzzy rules it can also be seen as a feedforward neural network model and so we can identify the model parameters by bp algorithm we prove that the stable controller can be designed based on linear system theory two methods of designing the controller for the fuzzy hyperbolic model are proposed the results of simulation support the effectiveness of the model and the control scheme

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

some uniqueness and exact multiplicity results for a predator prey model in this paper we consider positive solutions of a predator prey model with diffusion and under homogeneous dirichlet boundary conditions it turns out that a certain parameter m in this model plays a very important role a good understanding of the existence stability and number of positive solutions is gained when m is large in particular we obtain various results on the exact number of positive solutions our results for large m reveal interesting contrast with that for the well studied casem 0 i e the classical lotka volterra predator prey model

observer based adaptive double layer fuzzy control for nonlinear systems with prescribed performance and unknown control direction abstract this paper investigates an observer based adaptive double layer fuzzy control design problem for strict feedback nonlinear systems with prescribed performance and unknown control direction to this end a class of t s fuzzy systems with unknown fuzzy rules are considered and an adaptive interval type 2 it2 fuzzy controller is proposed for these systems by using the presented control scheme the unknown functions of the system can be ultimately approximated by the double layer fuzzy logic systems flss which contain the first layer type 1 flss and the second layer it2 flss a state observer is applied to handle the unmeasurable states and the nussbaum gain method is employed to cope with the unknown control direction in order to guarantee the prescribed performance of the output tracking error a tracking error transformation method is utilized and an improved robust adaptive control scheme is proposed based on the backstepping technique then the stability of the closed loop system and the achievability of the prescribed tracking performance are proved finally simulation results illustrate the efficacy of the proposed control method

global stability and hopf bifurcations of a beddington deangelis type predator prey system with diffusion and delays the dynamics of a diffusive predator prey system with the beddington deangelis functional response and two delays are considered by choosing the sum of two delays as a bifurcation parameter the stability of the constant equilibria and the existence of hopf bifurcations are investigated by analyzing the characteristic equations and the formulas determining the direction and the stability of the bifurcating periodic solutions are derived by using the center manifold and the normal form theory of partial functional differential equations particularly the sufficient conditions of the global stability of the positive equilibrium are given by the upper lower solutions method

adaptive fuzzy control for a class of nonlinear discrete time systems with backlash an adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper the considered systems are of the discrete time form in a triangular structure and include the backlash and the external disturbance by using the prediction function of future states the systems are transformed into an n step ahead predictor the fuzzy logic systems flss are used to approximate the unknown functions unknown backlash and backlash inversion respectively a discrete time tuning algorithm is developed to estimate the optimal fuzzy parameters compared with the previous works for the discrete time systems with backlash the main contributions of the paper are that 1 the rigorous restriction for the functional estimation error is removed and 2 the external disturbance is bounded but the bound is not required to be known a novel controller and the adaptation laws are constructed by using the discrete taylor series expansion and the difference lyapunov analysis and thus those limitations in the previous works are overcome it is proven that all the signals in the closed loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set a simulation example is provided to illustrate the effectiveness of the proposed approach

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

globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

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

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

on positive solutions of some pairs of differential equations this paper is a sequel to the author s paper 6 which studied positive solutions of a pair of differential equations introduced by conway gardner and smoller 4 their equations were equations for population problems in biology their significance is discussed further in 141 the purpose of the present paper is to obtain further results for the conwat gardner smoller equations and to show how the methods in 6 can be modified to decide exactly when the classical predator prey system as in blat and brown 2 has a strictly positive solution we also show how the methods can be applied to a number of other problems in particular our results answer some questions in conway s secondly we show how the asymptotic methods developed in 6 can be used to study the existence and uniqueness of strictly positive solutions of competing species problems our results suggest that this is a much more complicated problem than the predator prey problem we do obtain a condition which is except for a few special cases necessary and sufficient for the existence of a strictly positive solution however the condition is complicated and rather implicit thirdly we prove the uniqueness of the strictly positive solution in the conway smoller system if d is small and n 1 that is the case of ordinary differential equations this partially answers a question in 4 our proof is a local result and can be used in other situations for example it can be used to show that in certain cases of asocial nonlinearities where our notation follows 4 sect 4 there are exactly two strictly positive solutions for small d we also show how our method applies to more general predator prey problems in section 1 we find necessary and sufficient conditions for the existence of strictly positive solutions of predator prey systems in section 2 we study competing species models by iteration and asymptotic methods finally in section 3 we prove our uniqueness results in an appendix we briefly discuss how the methods of section 3 apply to more general models

bifurcation of steady state solutions in predator prey and competition systems we discuss steady state solutions of systems of semilinear reaction diffusion equations which model situations in which two interacting species u and v inhabit the same bounded region it is easy to find solutions to the systems such that either u or v is identically zero such solutions correspond to the case where one of the species is extinct by using decoupling and global bifurcation theory techniques we prove the existence of solutions which are positive in both u and v corresponding to the case where the populations can co exist

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

multiplicity and uniqueness of positive solutions for a predator prey model with b d functional response abstract in this paper we consider positive solutions of a predator prey model with beddington deangelis functional response first we establish the existence of positive solutions and present some sufficient and necessary conditions mainly using the standard fixed point index theory in cone second the multiplicity uniqueness and stability of positive solutions are obtained by means of bifurcation theory perturbation theory of eigenvalues and the fixed point index theory the parameters k and m play very important roles in deciding the number of positive solutions which are showed explicitly in this paper

design and analysis of fuzzy identifiers of nonlinear dynamic systems uses fuzzy systems as identifiers for nonlinear dynamic systems the author provides a theoretical justification for the fuzzy identifiers by proving that they are capable of following the output of a general nonlinear dynamic system to arbitrary accuracy in any finite time interval the fuzzy identifiers are constructed from a set of adaptable fuzzy if then rules and can combine both numerical information in the form of input output pairs obtained by exciting the system with an input signal and measuring the corresponding outputs and linguistic information in the form of if then rules about the behavior of the system in terms of vague and fuzzy words into their designs in a uniform fashion the author develops two fuzzy identifiers the first one is designed through the following four steps 1 define some fuzzy sets in the state space u spl sub r sup n of the system these fuzzy sets do not change 2 construct fuzzy rule bases of the fuzzy identifier which comprise rules whose if parts constitute all the possible combinations of the fuzzy sets defined in 1 3 design the fuzzy systems in the fuzzy identifier based on the fuzzy rule bases of 2 and 4 develop an adaptive law for the free parameters in the fuzzy identifier the second fuzzy identifier is designed in a similar way as the first one except that a the parameters characterizing the fuzzy sets in the state space change during the adaptation procedure and b the fuzzy systems and the adaptive law are different the author proves that 1 both fuzzy identifiers are globally stable in the sense that all variables in the fuzzy identifiers are uniformly bounded and 2 under some conditions the identification errors of both fuzzy identifiers converge to zero asymptotically finally the author simulates the fuzzy identifiers for identifying the chaotic glycolytic oscillator and the results show that 1 the fuzzy identifiers can approximate the chaotic system at a reasonable speed and accuracy without using any linguistic information and 2 by incorporating some fuzzy linguistic if then rules about the behavior of the system into the fuzzy identifiers the speed and accuracy of the fuzzy identifiers are greatly improved

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

fuzzy adaptive output feedback control of mimo nonlinear systems with partial tracking errors constrained in this paper a partial tracking error constrained fuzzy output feedback dynamic surface control dsc scheme is proposed for a class of uncertain multi input and multi output mimo nonlinear systems the considered mimo nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design with the help of fuzzy logic systems identifying the mimo unknown nonlinear systems a fuzzy adaptive observer is established to estimate the unmeasured states by transforming the tracking errors into new virtual error variables and based on the dsc backstepping recursive design technique a new adaptive fuzzy output feedback control method is developed it is proved that the proposed control approach can guarantee that all the signals of the resulting closed loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds the simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme

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

s shaped global bifurcation curve and hopf bifurcation of positive solutions to a predator prey model where d is a bounded domain in r n 1 with smooth boundary d and a b c d m are positive constants problem 1 0 is known as the predator prey model with holling tanner type interactions where u and v represent the densities of the prey and predator respectively hence we are only interested in positive solutions by which we mean that both u and v are positive in d it is easy to see that a 1 is necessary for the existence of positive solutions to 1 0 and we shall also assume that d 1 the case d 1 is rather different and will not be discussed here we are mainly interested in studying the number of positive solutions of 1 0 and the stability of these solutions in particular we shall show that when b d c and m fall into certain range the solution set u v a of 1 0 forms a s shaped smooth curve and that hopf bifurcation occurs along this curve this not only confirms rigorously similar numerical observations on 1 0 made in 4 but also shows that the corresponding parabolic system

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

tracking with prescribed transient performance for hysteretic systems tracking of reference signals assumed bounded with essentially bounded derivative is considered for a class of single input single output nonlinear systems described by a functional differential equation with a hysteresis nonlinearity in the input channel the first control objective is tracking by the output with prescribed accuracy determine a feedback strategy which ensures that for every reference signal and every system of the underlying class the tracking error ultimately satisfies the prescribed accuracy requirements the second objective is guaranteed output transient performance the graph of the tracking error should be contained in a prescribed set performance funnel under a weak sector boundedness assumption on the hysteresis operator both objectives are achieved by a memoryless feedback which is universal for the underlying class of systems

rich dynamics of a stochastic michaelis menten type ratio dependent predator prey system abstract stochastic predator prey systems with different functional responses have been studied but the dynamics of a michaelis menten type ratio dependent predator prey system with stochastic perturbation is not investigated systematically in this paper we give the asymptotic behavior of this system sufficient criteria for the existence of a stationary distribution and ergodicity are obtained which means the species are permanent besides we show the situations in which the species are non persistence finally examples and simulations are carried on to verify these results

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

distances in the highly supercritical percolation cluster on the supercritical percolation cluster with parameter p the distances between two distant points of the axis are asymptotically increased by a factor 1 1 p2 o 1 p with respect to the usual distance the proof is based on an apparently new connection with the tasep totally asymmetric simple exclusion process

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

adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements this paper investigates the adaptive fuzzy backstepping control and h infty performance analysis for a class of nonlinear systems with sampled and delayed measurements in the control scheme a fuzzy estimator fe model is used to estimate the states of the controlled plant while the fuzzy logic systems are used to approximate the unknown nonlinear functions in the nonlinear system the controller is obtained based on the fe model by combining the backstepping technique with the classic adaptive fuzzy control method in the stability analysis all the signals in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded suub and the outputs of the system are proven to converge to a small neighborhood of origin furthermore the h infty performance is investigated and the outputs of the closed loop system are bounded in the h infty sense two examples are given to illustrate the effectiveness of the proposed control scheme

a new approach to fuzzy modeling and control of discrete time systems we present a new approach to fuzzy modeling and control of discrete time systems which is based on the formulation of a novel state space representation using the hyperbolic tangent function the new representation designated the hyperbolic model combines the advantages of fuzzy system theory and classical control theory on the one hand the hyperbolic model is easily derived from a set of mamdani type fuzzy rules on the other hand classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of mamdani type fuzzy rules thus this new approach combines the best of two worlds it enables linguistic interpretability of both the model and the controller and guarantees closed loop stability and robustness

on the indices of fixed points of mappings in cones and applications abstract assume that k is a cone in a banach space and a k k is completely continuous we obtain a formula for the index in k of a fixed point of a under the assumption that a linearization exists and satisfies an invertibility condition we then use this formula to generalize some results of amann on the number of fixed points of a to the case where k has empty interior

stability analysis of systems with impulse effects the authors establish conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulse effects described by systems of nonlinear time varying ordinary differential equations under mild additional assumptions these sufficient conditions turn out to be necessary as well for the case of time invariant systems with impulse effects described by nonlinear ordinary differential equations the above results are used to establish conditions under which the uniform asymptotic stability of equilibria can be deduced from the linearizations of such systems

fuzzy approximation based adaptive control of nonlinear delayed systems with unknown dead zone this paper focuses on the problem of adaptive fuzzy control for a class of nonlinear systems without a strict feedback form a new adaptive fuzzy control scheme is proposed for nonlinear delayed systems with unknown dead zone nonlinearity control design is achieved by introducing a variable separation approach and employing the unique structural property of fuzzy logic systems the proposed adaptive fuzzy controller guarantees that all the closed loop signals are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples illustrate the effectiveness of the proposed approach

uniqueness and stability of a predator prey model with c m functional response in this paper we are concerned with positive solutions of a predator prey model with crowley martin functional response under dirichlet boundary conditions first we establish the existence of positive solutions when a c is close to 1 1 next the stability properties of nonnegative solutions are discussed by spectral analysis in addition we obtain a complete understanding of the uniqueness and non uniqueness of positive solutions by the lyapunov schmidt procedure and the perturbation technique at last some numerical simulations are presented to supplement the analytic results in one dimension

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

coexistence theorems of steady states for predator prey interacting systems on donne des conditions necessaires et suffisantes pour l existence des solutions positives des etats stationnaires pour des systemes predateur proie sous des conditions aux limites de dirichlet sur r n

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

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

parabolic problems for the anderson model i intermittency and related topics the objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics in particular in hydrodynamics on a qualitative level intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments the paper deals with the cauchy problem t u t x hu t x u 0 x t 0 x 0 t x d for the anderson hamiltonianh x x d where is a generally unbounded spatially homogeneous random potential this first part is devoted to some basic problems using percolation arguments a complete answer to the question of existence and uniqueness for the cauchy problem in the class of all nonnegative solutions is given in the case of i i d random variables necessary and sufficient conditions for intermittency of the fieldsu t ast are found in spectral terms ofh rough asymptotic formulas for the statistical moments and the almost sure behavior ofu t x ast are also derived

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

on nonlinear reaction diffusion systems abstract this paper presents a qualitative analysis for a coupled system of two reaction diffusion equations under various boundary conditions which arises from a number of physical problems the nonlinear reaction functions are classified into three basic types according to their relative quasi monotone property for each type of reaction functions an existence comparison theorem in terms of upper and lower solutions is established for the time dependent system as well as some boundary value problems three concrete physical systems arising from epidemics biochemistry and engineering are taken as representatives of the basic types of reacting problems through suitable construction of upper and lower solutions various qualitative properties of the solution for each system are obtained these include the existence and bounds of time dependent solutions asymptotic behavior of the solution stability and instability of nontrivial steady state solutions estimates of stability regions and finally the blowing up property of the solution special attention is given to the homogeneous neumann boundary condition

dynamics of a diffusive predator prey system with a nonlinear growth rate for the predator abstract in this paper we investigate a diffusive predator prey system with holling type ii functional response and a nonlinear growth rate for the predator our results include the global attractivity of constant equilibria and non existence of non constant positive steady states these results give some ranges for the model parameters within which spatiotemporal pattern formation is impossible

fuzzy approximation based adaptive backstepping optimal control for a class of nonlinear discrete time systems with dead zone in this paper an adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete time systems the controlled systems are in a strict feedback frame and contain unknown functions and nonsymmetric dead zone for this class of systems the control objective is to design a controller which not only guarantees the stability of the systems but achieves the optimal control performance as well this immediately brings about the difficulties in the controller design to this end the fuzzy logic systems are employed to approximate the unknown functions in the systems based on the utility functions and the critic designs and by applying the backsteppping design technique a reinforcement learning algorithm is used to develop an optimal control signal the adaptation auxiliary signal for unknown dead zone parameters is established to compensate for the effect of nonsymmetric dead zone on the control performance and the updating laws are obtained based on the gradient descent rule the stability of the control systems can be proved based on the difference lyapunov function method the feasibility of the proposed control approach is further demonstrated via two simulation examples

model approximation for fuzzy switched systems with stochastic perturbation in this paper the model approximation problem is investigated for a takagi sugeno fuzzy switched system with stochastic disturbance for a high order considered system our attention is focused on the construction of a reduced order model which not only approximates the original system well with a hankel norm performance but translates it into a lower dimensional fuzzy switched system as well by using the average dwell time approach and the piecewise lyapunov function technique a sufficient condition is first proposed to guarantee the mean square exponential stability with a hankel norm error performance for the error system the model approximation is then converted into a convex optimization problem by using a linearization procedure finally simulations are provided to illustrate the effectiveness of the proposed theory

robust adaptive fuzzy control for a class of nonlinear coupled ode beam systems with boundary uncertainty abstract this paper investigates a robust adaptive fuzzy control problem for a class of nonlinear ordinary differential equations odes coupled with a beam equation subject to boundary uncertainty a fuzzy control scheme based on the takagi sugeno t s fuzzy model is employed for the nonlinear ode subsystem with ode state feedback for the beam with boundary uncertainty a robust adaptive fuzzy boundary control scheme is adopted where a linear controller via boundary measurements is used to stabilize the beam and a robust adaptive fuzzy compensator is utilized to counteract the boundary uncertainty the asymptotic stabilization condition is derived for the nonlinear coupled ode beam system by means of the lyapunov s direct method which is provided in terms of a set of bilinear matrix inequalities bmis furthermore a two step procedure is presented to solve the bmi feasibility problem by the existing linear matrix inequality lmi optimization techniques finally a simulation study is conducted on a flexible spacecraft to demonstrate the effectiveness of the proposed method

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

adaptive dynamic surface control for mimo nonlinear time varying systems with prescribed tracking performance in this paper an adaptive dynamic surface control scheme is proposed for a class of multi input multi output mimo nonlinear time varying systems by fusing a bound estimation approach a smooth function and a time varying matrix factorisation the obstacle caused by unknown time varying parameters is circumvented the proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step moreover all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance simulation results are presented to illustrate the effectiveness of the proposed scheme

approximate inversion of the preisach hysteresis operator with application to control of smart actuators hysteresis poses a challenge for control of smart actuators a fundamental approach to hysteresis control is inverse compensation for practical implementation it is desirable for the input function generated via inversion to have regularity properties stronger than continuity in this paper we consider the problem of constructing right inverses for the preisach model for hysteresis under mild conditions on the density function we show the existence and weak star continuity of the right inverse when the preisach operator is considered to act on holder continuous functions next we introduce the concept of regularization to study the properties of approximate inverse schemes for the preisach operator then we present the fixed point and closest match algorithms for approximately inverting the preisach operator the convergence and continuity properties of these two numerical schemes are studied finally we present the results of an open loop trajectory tracking experiment for a magnetostrictive actuator

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

hybrid adaptive fuzzy identification and control of nonlinear systems we present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller and adaptive fuzzy identification model parameters first using adaptive fuzzy building blocks with a common set of parameters we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of uncertain structure nonlinear dynamic systems we then propose a hybrid adaptive ha law for adjusting the parameters the ha law utilizes two types of errors in the adaptive system the tracking error and the modeling error performance analysis using a lyapunov synthesis approach proves the superiority of the ha law over the direct adaptive da method in terms of faster and improved tracking and parameter convergence furthermore this is achieved at negligible increased implementation cost or computational complexity we prove a theorem that shows the properties of this hybrid adaptive fuzzy control system i e bounds for the integral of the squared errors and the conditions under which these errors converge asymptotically to zero are obtained finally we apply the hybrid adaptive fuzzy controller to control a chaotic system and the inverted pendulum system

qualitative analysis on a diffusive predator prey model with toxins abstract this paper is concerned with the diffusive predator prey model with toxins subject to dirichlet boundary conditions the uniform persistence of positive solution is given under certain conditions in addition by the liapunov schmidt method the existence and stability of the bifurcation solution from a double eigenvalues are investigated moreover by the fixed point index theory and perturbation theory of eigenvalues the uniqueness stability and multiplicity of coexistence states are analyzed when some key parameter changes finally some numerical simulations are presented to verify the theoretical conclusions and further to reflect the importance of parameters to the number of coexistence states

complete mathematical analysis of predator prey models with linear prey growth and beddington deangelis functional response the dynamics of a predator prey model with a beddington deangelis functional response and linear intrinsic growth rate of the prey population is fully analyzed conditions on local and global stability of the interior equilibrium are established the equilibria type are determined all possible global asymptotic behaviors of the system are considered including the determination of the extinction conditions and existence of periodic orbits it is shown that mutual interference between predators can alone stabilize predator prey interactions even when only a linear intrinsic growth rate of the prey population is considered in the mathematical model additional biological implications and a set of numerical simulations supporting the analysis are also presented

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

adaptive fuzzy control for a class of unknown nonlinear dynamical systems in this study we investigate an adaptive fuzzy controller design for a class of nonlinear multi input multi output mimo systems in interconnected form the systems considered comprise n subsystems and an unknown interconnection term is included in every equation for each subsystem the interconnection term is a function of all the states from the first to the n 1 th subsystems moreover the effects of dead zone models are considered in each subsystem of the systems these properties of the systems cause the difficulties and add further complexity to the design in order to overcome these difficulties we use the following methods 1 the fuzzy logic systems are employed to approximate the appropriate unknown functions of the systems 2 a novel backstepping design procedure is constructively designed and 3 compensative adaptation laws are provided to compensate for the effects of the dead zone inputs we show that all the signals in the closed loop system are bounded and that the outputs converge to a compact set by using the lyapunov analysis theorem simulated examples are presented that validate the effectiveness of the approach

brief paper adaptive tracking of nonlinear systems with non symmetric dead zone input quite successfully adaptive control strategies have been applied to uncertain dynamical systems subject to dead zone nonlinearities however adaptive tracking of systems with non symmetric dead zone characteristics has not been fully discussed with minimal knowledge of the dead zone parameters it is shown that the controlled system preceded by a non symmetric dead zone input can be represented as an uncertain nonlinear system subject to a linear input with time varying input coefficient to cope with this problem a new adaptive compensation algorithm is employed without constructing the dead zone inverse the proposed adaptive scheme requires only the information of bounds of the dead zone slopes and treats the time varying input coefficient as a system uncertainty the new control scheme ensures bounded error trajectory tracking and assures the boundedness of all the signals in the adaptive closed loop by appropriate selections of the controller parameters we show that the smoothness of the controller does not affect the accuracy of trajectory tracking control a numerical example is included to show the effectiveness of the theoretical results

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

the effect of mutual interference between predators on a predator prey model with diffusion abstract we consider a diffusive predator prey model with beddington deangelis functional response under homogeneous dirichlet boundary conditions the effect of large k which represents the extent of mutual interference between predators is extensively studied by making use of the fixed point index theory we obtain a complete understanding of the existence uniqueness and stability of positive steady states when k is sufficiently large moreover we present some numerical simulations that supplement the analytic results in one dimension

nontrivial solutions of predator prey systems with small diffusion on considere le systeme elliptique non lineaire u x au bu 2 cuv pour xed d v x ev fv 2 guv d region bornee de r n on etudie comment la famille des solutions non negatives de ce systeme change quand les parametres du systeme changent

robust adaptive control of a class of nonlinear systems with unknown dead zone this paper deals with the adaptive control of a class of continuous time nonlinear dynamic systems preceded by an unknown dead zone by using a new description of a dead zone and by exploring the properties of this dead zone model intuitively and mathematically a robust adaptive control scheme is developed without constructing the dead zone inverse the new control scheme ensures global stability of the adaptive system and achieves desired tracking precision simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach

global and local consistencies in distributed fault diagnosis for discrete event systems in this paper we present a unified framework for distributed diagnosis we first introduce the concepts of global and local consistency in terms of supremal global and local supports then present two distributed diagnosis problems based on them after that we provide algorithms to achieve supremal global and local supports respectively and discuss in detail the advantages and disadvantages of each finally we present an industrial example to demonstrate our distributed diagnosis approach