necessary and sufficient small gain conditions for integral input to state stable systems a lyapunov perspective this paper is concerned with conditions for the stability of interconnected nonlinear systems consisting of integral input to state stable iiss systems with external inputs the treatment of iiss and input to state stable iss systems is unified both necessary conditions and sufficient conditions are investigated using a lyapunov formulation in the presence of model uncertainty this paper proves that for the stability of the interconnected system at least one subsystem is necessarily iss which is a stronger stability property in the set of iiss the necessity of a small gain type property is also demonstrated this paper proposes a common form of smooth lyapunov functions which can establish the iiss and the iss of the interconnection comprising iiss and iss subsystems whenever the small gain type condition is satisfied the result covers situations more general than the earlier study and removes technical conditions assumed in the previous literature global asymptotic stability is discussed as a special case

further results on output feedback stabilization for a class of stochastic nonlinear systems for a class of stochastic nonlinear systems in which the drift and diffusion vector fields depend on the unmeasurable states besides the measurable output the research purpose of this technical note is to find the maximum value interval of observer gain for the desired control performance for this interval the designed output feedback controller ensures that the equilibrium at the origin is globally asymptotically stable in probability and the inverse optimal stabilization in probability is achieved

identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

a blind approach to hammerstein model identification this paper discusses the hammerstein model identification using a blind approach by fast sampling at the output it is shown that identification of the linear part can be achieved based only on the output measurements that makes the hammerstein model identification possible without knowing the structure of the nonlinearity and the internal variables

a homogeneous domination approach to state feedback of stochastic high order feedforward nonlinear systems this paper investigates stochastic high order feedforward nonlinear systems for the first time by introducing the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

technical communique sliding mode control of singular stochastic hybrid systems this paper is concerned with the sliding mode control smc of nonlinear singular stochastic systems with markovian switching an integral sliding surface function is designed and the resulting sliding mode dynamics is a full order markovian jump singular stochastic system by introducing some specified matrices a new sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic stability of the sliding mode dynamics then a smc law is synthesized for reaching motion moreover when there exists an external disturbance the 2 disturbance attenuation performance is analyzed for the sliding mode dynamics some related sufficient conditions are also established

dual mode predictive control algorithm for constrained hammerstein systems in the process industry there exist many systems which can be approximated by a hammerstein model moreover these systems are usually subjected to input magnitude constraints in this paper a multi channel identification algorithm mcia is proposed in which the coefficient parameters are identified by least squares estimation lse together with a singular value decomposition svd technique compared with traditional single channel identification algorithms the present method can enhance the approximation accuracy remarkably and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation pe condition of the inputs then to facilitate the following controller design this mcia is converted into a two stage single channel identification algorithm ts scia which preserves most of the advantages of mcia with this ts scia as the inner model a dual mode non linear model predictive control nmpc algorithm is developed in detail over a finite horizon an optimal input profile found by solving a open loop optimal control problem drives the non linear system state into the terminal invariant set afterwards a linear output feedback controller steers the state to the origin asymptotically in contrast to the traditional algorithms the present method has a maximal stable region a better steady state performance and a lower computational complexity finally simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms

further results on output feedback regulation of stochastic nonlinear systems with siiss inverse dynamics this article further discusses the problem of output feedback regulation for more general stochastic nonlinear systems with stochastic integral input to state stable inverse dynamics and focuses on solving the important and unsolved problem proposed in yu and xie yu x and xie x j 2010 output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics ieee transactions on automatic control 55 304 320 how to weaken the conditions on nonlinearities in drift and diffusion vector fields under the weaker conditions how to make full use of the known information of stochastic nonlinear systems to design an adaptive output feedback controller such that all the closed loop signals are almost surely bounded and the output is driven to zero almost surely

continuous time hammerstein system identification a continuous time hammerstein system i e a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one is identified the system is driven and disturbed by white random signals the a priori information about both subsystems is nonparametric which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown an algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown the impulse response of the dynamic part is recovered with a correlation method the algorithms are computationally independent results of a simulation example are given

state feedback control of high order stochastic nonlinear systems with siiss inverse dynamics this technical note considers a class of high order stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states a new design and analysis approach to the problem of state feedback global regulation is developed to guarantee that all the signals of the closed loop system are bounded almost surely and the states can be regulated to zero almost surely

nonparametric density estimation prediction and regression for markov sequences abstract let xi be a stationary markov sequence having a transition probability density function f y x giving the pdf of x i 1 xi x in this study nonparametric density and regression techniques are employed to infer f y x and m x e x i 1 xi x it is seen that under certain regularity and markovian assumptions the asymptotic convergence rate of the nonparametric estimator mn x to the predictor m x is the same as it would have been had the xi s been independently and identically distributed and this rate is optimal in a certain sense consistency can be maintained after differentiability and even the markovian assumptions are abandoned computational and modeling ramifications are explored i claim that my methodology offers an interesting alternative to the popular arma approach

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

a fourier error analysis for radial basis functions and the discrete singular convolution on an infinite uniform grid part 1 on an infinite grid with uniform spacing h the cardinal basis cj x h for many spectral methods consists of translates of a master cardinal function cj x h c x h j the cardinal basis satisfies the usual lagrange cardinal condition cj mh jm where jm is the kronecker delta function all such shift invariant subspace master cardinal functions are of localized sinc form in the sense that c x sinc x s x for a localizer function s which is smooth and analytic on the entire real axis and the whittaker cardinal function is sinc x sin x x the localized sinc approximation to a general f x is f localized sinc x h j f j h s x j h h sinc x jh h in contrast to most radial basis function applications matrix factorization is unnecessary we prove a general theorem for the fourier transform of the interpolation error for localized sinc bases for exponentially convergent radial basis functions rbfs gaussians inverse multiquadrics etc and the basis functions of the discrete singular convolution dsc the localizer function is known exactly or approximately this allows us to perform additional error analysis for these bases we show that the error is similar to that for sinc bases except that the localizer acts like a diffusion in fourier space smoothing the sinc error

brief paper inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable after considering the stabilization of a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input in this brief paper we further address the problem of state feedback inverse optimal stabilization in probability i e our redesigned stabilizing backstepping controller is also optimal with respect to meaningful cost functionals

dynamic system identification with order statistics systems consisting of linear dynamic and memory less nonlinear subsystems are identified the paper deals with systems in which the nonlinear element is followed by a linear element as well as systems in which the subsystems are connected in parallel the goal of the identification is to recover the nonlinearity from noisy input output observations of the whole system signals interconnecting the elements are not measured observed values of the input signal are rearranged in increasing order and coefficients for the expansion of the nonlinearity in trigonometric series are estimated from the new sequence of observations obtained in this way two algorithms are presented and their mean integrated square error is examined conditions for pointwise convergence are also established for the nonlinearity satisfying the lipschitz condition the error converges to zero the rate of convergence derived for differentiable nonlinear characteristics is insensitive to the roughness of the probability density of the input signal results of numerical simulation are also presented

the carleman approximation approach to solve a stochastic nonlinear control problem this note investigates the optimal linear quadratic control problem in the discrete time framework for stochastic systems affected by disturbances generated by a nonlinear stochastic exosystem the application of the maximum principle to nonlinear optimal control problems does not admit in general implementable solutions therefore it is worthwhile to look for finite dimensional approximation schemes the approach followed in this note is based on the degree carleman approximation of a stochastic nonlinear system applied to the exosystem and provides a real time algorithm to design an implementable control law simulations support theoretical results and show the improvements when the approximation index is increased

wavelet amendment of polynomial models in hammerstein systems identification a new wavelet algorithm for on line improvement of an existing polynomial model of nonlinearity in a hammerstein system is proposed and its properties are examined the algorithm employs wavelet bases on interval convergence of the resulting assembly comprising the parametric polynomial model and a nonparametric wavelet add on to the system nonlinearity is shown rates of convergence for uniformly smooth and piecewise smooth nonlinearities with discontinuities are both established

nonparametric estimation and adaptive control of functional autoregressive models this paper deals with nonparametric estimation and adaptive control of nonlinear systems of the form x n 1 f x n u n xi n 1 n in bkn where the state x n is observed f is an unknown function and the control un is chosen in order to track a given reference trajectory we estimate the function f using a nonparametric estimator and study two adaptive control laws built from this nonparametric estimator and derived from the self tuning control the first one can be used for open loop stable systems and requires an additional exciting noise the second one needs some a priori knowledge on function f but allows us to control open loop unstable systems we establish some general results on the nonparametric estimator of f like the uniform almost sure convergence over dilating sets and then prove that both adaptive control laws are asymptotically optimal in quadratic mean in addition we give a strongly consistent estimator of the covariance matrix of the unobservable white noise xi n

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

brief paper output feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable this brief paper investigates the problem of output feedback stabilization for a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input based on the ideas of the homogeneous systems theory and the adding a power integrator technique an output feedback controller is constructed to ensure that the equilibrium at the origin of the closed loop system is globally asymptotically stable gas in probability the efficiency of the output feedback controller is demonstrated by a simulation example

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

uniform consistency of kernel estimators of a regression function under generalized conditions abstract in this article we prove uniform consistency of kernel estimators of a multivariate regression function under various assumptions on the distribution of the data in addition to the usual assumptions that the data are iid and that the distribution of the regressors is absolutely continuous we consider the cases that some regressors are discrete and the data are either stationary mixing themselves or generated by a class of functions of one sided infinite stationary mixing sequences moreover we demonstrate the performance of the kernel estimation method under these generalized conditions by a numerical example

adaptive backstepping controller design using stochastic small gain theorem a more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper with the concept of input to state practical stability isps and nonlinear small gain theorem being extended to stochastic case by combining stochastic small gain theorem with backstepping design technique an adaptive output feedback controller is proposed it is shown that the closed loop system is practically stable in probability a simulation example demonstrates the control scheme

output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics this paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics the contributions of this work are characterized by the following novel features 1 motivated by the concept of integral input to state stability iiss in deterministic systems and stochastic input to state stability siss using lyapunov function in stochastic systems a concept of stochastic integral input to state stability siiss using lyapunov function is first introduced two important properties of siiss are obtained i siiss is strictly weaker than siss using lyapunov function ii siiss is stronger than the minimum phase property however only under the minimum phase assumption there is no dynamic output feedback control law for global stabilization in probability 2 almost sure boundedness a reasonable and stronger concept than boundedness in probability is introduced the purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed loop control system 3 some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed loop system are established 4 a unifying framework is proposed to design a dynamic output feedback control law which drives the states to the origin almost surely while maintaining all the closed loop signals bounded almost surely

asymptotic properties of least squares estimates of hammerstein wiener models this paper investigates the asymptotic properties of least squares estimates of hammerstein wiener model structures and in doing so establishes consistency and asymptotic normality under fairly mild conditions on the additive noise process the inputs and the static non linearities in relation to the asymptotic distributional results a consistent procedure for the estimation of the asymptotic variance of the parameter estimates is provided a key theme of this paper is to demonstrate how recent results from the econometrics literature may be employed in an engineering setting in this respect the hammerstein wiener model structure serves as a demonstration example a simulation study complements the theoretical findings

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

a new deterministic identification approach to hammerstein systems the deterministic identification of hammerstein systems is investigated in this paper based on the over sampling technique a new deterministic identification approach is presented which blindly identifies the linear dynamic part followed by the estimation of the nonlinear function the proposed method allows us to identify the hammerstein system using an over sampling rate smaller than the numerator polynomial s length of the linear dynamic part as required by other existing methods in addition it can obtain the true values of the system parameters in the noise free case and an asymptotically consistent estimate in the presence of noise the richness condition of the system input and the selection of the over sampling rate are studied for the identifiability of the hammerstein system simulation examples are given to show the performance of the proposed method

output tracking of high order stochastic nonlinear systems with application to benchmark mechanical system this note considers output tracking of high order stochastic nonlinear systems without imposing any restriction on the high order and the drift and diffusion terms by using the backstepping design technique a smooth state feedback controller is given to guarantee that the solution process is bounded in probability and the error signal between the output and the reference signal can be regulated into a small neighborhood of the origin in probability a practical example of stochastic benchmark mechanical system and simulation are provided to demonstrate the effectiveness of the control scheme

a lyapunov approach to cascade interconnection of integral input to state stable systems this technical note deals with the stability of cascade interconnection of integral input to state iiss time varying systems a new technique to construct smooth lyapunov functions of cascaded systems is proposed from the construction sufficient conditions for internal stability and stability with respect to external signals are derived one of the derived conditions is a trade off between slower convergence of the driving system and steeper input growth of the driven system the trade off is no more necessary if the speed of convergence of the driven system is not radially vanishing the results are related to trajectory based approaches and small gain techniques for feedback interconnection the difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts

on estimation of a class of nonlinear systems by the kernel regression estimate the estimation of a multiple input single output discrete hammerstein system is studied such a system contains a nonlinear memoryless subsystem followed by a dynamic linear subsystem the impulse response of the dynamic linear subsystem is obtained by the correlation method the main results concern the estimation of the nonlinear memoryless subsystem no conditions are imposed on the functional form of the nonlinear subsystem and the nonlinearity is recovered using the kernel regression estimate the distribution free pointwise and global convergence of the estimate is demonstrated that is no conditions are imposed on the input distribution and convergence is proven for virtually all nonlinearities the rates of pointwise as well as global convergence are obtained for all input distributions and for lipschitz type nonlinearities

state dependent scaling problems and stability of interconnected iiss and iss systems this paper addresses the problem of establishing stability of nonlinear interconnected systems this paper introduces a mathematical formulation of the state dependent scaling problems whose solutions directly provide lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner stability criteria are interpreted as sufficient conditions for the existence of solutions to the state dependent scaling problems computing solutions to the problems is straightforward for systems covered by classical stability criteria it however could be too difficult for systems with strong nonlinearity the main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input to state stable iiss systems and input to state stable iss systems this paper derives small gain type theorems for interconnected systems involving iiss systems from the state dependent scaling formulation this paper provides solutions and lyapunov functions explicitly the new framework seamlessly generalizes the iss small gain theorem and classical stability criteria such as the lp small gain theorem the passivity theorems the circle and popov criteria state dependence of the scaling is crucial for effective treatment of essential nonlinearities while constants are sufficient for classical nonlinearities

brief paper a note on control of a class of discrete time stochastic systems with distributed delays and nonlinear disturbances this paper is concerned with the state feedback control problem for a class of discrete time stochastic systems involving sector nonlinearities and mixed time delays the mixed time delays comprise both discrete and distributed delays and the sector nonlinearities appear in the system states and all delayed states the distributed time delays in the discrete time domain are first defined and then a special matrix inequality is developed to handle the distributed time delays within an algebraic framework an effective linear matrix inequality lmi approach is proposed to design the state feedback controllers such that for all admissible nonlinearities and time delays the overall closed loop system is asymptotically stable in the mean square sense sufficient conditions are established for the nonlinear stochastic time delay systems to be asymptotically stable in the mean square sense and then the explicit expression of the desired controller gains is derived a numerical example is provided to show the usefulness and effectiveness of the proposed design method

design adaptive nonparametric regression abstract in this article we study the method of nonparametric regression based on a weighted local linear regression this method has advantages over other popular kernel methods moreover such a regression procedure has the ability of design adaptation it adapts to both random and fixed designs to both highly clustered and nearly uniform designs and even to both interior and boundary points it is shown that the local linear regression smoothers have high asymptotic efficiency i e can be 100 with a suitable choice of kernel and bandwidth among all possible linear smoothers including those produced by kernel orthogonal series and spline methods the finite sample property of the local linear regression smoother is illustrated via simulation studies nonparametric regression is frequently used to explore the association between covariates and responses there are many versions of kernel regression smoothers some estimators are not good for random designs such as in observational studies and

stochastic input to state stability and applications to global feedback stabilization notions of stochastic input to state stability are introduced and their lyapunov characterizations are established these notions constitute extensions of the deterministic iss proposed by e sonta

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

reduced order observer based output feedback regulation for a class of nonlinear systems with iiss inverse dynamics global asymptotic regulation via output feedback based on a reduced order observer is considered for a class of nonlinear systems with integral input to state stable iiss inverse dynamics the contributions are that 1 we further consider the conditions on changing supply rates in iiss systems and discuss the necessity of some conditions by constructing a counter example 2 for a more general class of nonlinear systems with iiss inverse dynamics a reduced order observer is introduced and by the combined approach of backstepping and changing iiss supply rates an output feedback controller is given to drive the output of system to the origin asymptotically and maintain other closed loop signals bounded

output feedback stabilization using small gain method and reduced order observer for stochastic nonlinear systems this technical note further investigates more general stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and focuses on solving the following problems 1 a class of counterexamples which are different from that in are reconstructed to discuss the relationship between two small gain type conditions on siiss and 2 under the weaker conditions on nonlinearities based on a reduced order observer small gain type condition on siiss and stochastic lasalle theorem an output feedback controller is constructed to guarantee the global asymptotical stability in probability of the closed loop stochastic system

global finite time stabilisation for a class of stochastic nonlinear systems by output feedback in this paper the problem of global finite time stabilisation by output feedback is considered for a class of stochastic nonlinear systems first based on homogeneous systems theory and the adding a power integrator technique a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system then the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms it is shown that the proposed output feedback control law can guarantee that the closed loop system is global finite time stable in probability finally simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme

nonparametric estimation of a regression function consider the regression model yi g xi ei i 1 2 n where xi s denote unordered design variables and g is an unknown function defined on the interval 0 1 assume ei are iid random variables with zero mean and finite variance priestley and chao 1972 and clark 1977 proposed estimators g2nand g3n respectively for g in this paper the asymptotic behavior of g2nand g3nis studied utilizing the properties of the new estimator g1n it is shown that g1n g2n g3nare asymptotically equivalent in various senses moreover consistency results are established and rates of uniform convergence obtained for example if e e 3 if g is lipschitz of order 1 and if n is any sequence of constants tending to as n then for all 0 a leqq b 1 n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 mathord left vphantom n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 right kern nulldelimiterspace beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 as n finally when g is monotone a strong consistent isotonic estimator gn is considered

nonparametric estimation of a regression function consider the regression model y i g x i e i i 1 2 n where x i s denote unordered design variables and g is an unknown function defined on the interval 0 1 assume e i are iid random variables with zero mean and finite variance priestley and chao 1972 and clark 1977 proposed estimators g 2n and g 3n respectively for g in this paper the asymptotic behavior of g 2n and g 3n is studied utilizing the properties of the new estimator g 1n it is shown that g 1n g 2n g 3n are asymptotically equivalent in various senses moreover consistency results are established and rates of uniform convergence obtained for example if e e 3 if g is lipschitz of order 1 and if n is any sequence of constants tending to as n then for all 0 a leqq b 1 n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 mathord left vphantom n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 right kern nulldelimiterspace beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 as n finally when g is monotone a strong consistent isotonic estimator g n is considered

state feedback stabilization for stochastic feedforward nonlinear systems with time varying delay this paper investigates a class of stochastic feedforward nonlinear systems with time varying delay by introducing the homogeneous domination approach to stochastic systems a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

analysis and identification of hammerstein model non linear delay systems using block pulse function expansions algorithms for the analysis and identification of non linear delay systems described by a hammerstein model which consists of a single value non linearity followed by a linear time delayed plant are presented by using the finite dimensional block pulse expansion the solution of a hammerstein model non linear dynamic system with time delay is reduced to the solution of a set of linear algebraic equations in addition through the block pulse expansions of the measured input output data parameters of both the linear time delayed plant and the polynomial approximation of the non linear gain are estimated using the least squares method examples are given to illustrate the utility of this method

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

hammerstein system identification with the nearest neighbor algorithm the nonlinear characteristic in a hammerstein system i e a system in which a nonlinear memoryless subsystem and a linear dynamic are connected in a cascade is recovered with the nonparametric nearest neighbor regression estimate the a priori information is nonparametric both the nonlinear characteristic and the impulse response are completely unknown and can be of any form local and global properties of the estimate are examined whatever the probability density of the input signal the estimate converges at every continuity point of the characteristic as well as in the global sense we derive the asymptotic bias and variance of the proposed estimate as a result the optimal rate of convergence is established that additionally is independent of the shape of the input density results of numerical simulations are also presented

bandpass nonlinear systems identification by higher order cross correlation nonlinear systems constituted by a zero memory nonlinearity cascaded with linear filters can be identified by input output cross correlation using a gaussian input signal the method is extended to complex systems through a pair of complex invariance theorems the stated properties allow identifying the linear parts of systems characterized by magnitude phase nonlinearities with the joint use of second and third order input output moments the method can be employed for a wide class of communication bandpass circuits when signals are represented by complex envelopes

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

nonparametric identification of a particular nonlinear time series system a nonlinear time series system is identified the system has a cascade structure that is it consists of a nonlinear memoryless element followed by a dynamic linear system given a gaussian input a hermite series based method for recovering the system nonlinearity is presented the proposed identification procedure is nonparametric since it is able to be consistent for a broad class of nonpolynomial characteristics the consistency and rate of convergence of the procedure are established also some data driven methods for selecting the optimal number of terms in the procedure are proposed the results are illustrated by a numerical example

the concept of exponential input to state stability for stochastic systems and applications to feedback stabilization abstract this paper presents a version of the well known sontag s input to state stability property for stochastic systems this concept is used to derive sufficient conditions for global stabilization for certain class of stochastic nonlinear systems by means of static and dynamic output feedback

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

a unifying framework for global regulation via nonlinear output feedback from iss to iiss this paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input to state stable inverse dynamics subject to possibly unknown control direction the contribution of the paper is two fold firstly we consider the problem of global regulation instead of global asymptotic stabilization gas for systems with generalized dynamic uncertainties it is shown by an elementary example that gas is not solvable using conventional smooth output feedback secondly we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system using our framework most of the known classes of output feedback form systems are broadened in several directions unmeasured states and unknown parameters can appear nonlinearly restrictive matching and growth assumptions are removed the dynamic uncertainty satisfies the weaker condition of sontag s integral input to state stability and the sign of high frequency gain may be unknown a constructive strategy is proposed to design a dynamic output feedback control law that drives the state to the origin while keeping all other closed loop signals bounded

controller design oriented model identification method for hammerstein system abstract the paper proposes a new polynomial identification method for the hammerstein system by combining the results of parameter estimation theory and functions approximation theory the method circumvents many disadvantages of the earlier methods it is suitable for producing the controller design oriented model of hammerstein system consistency and convergency analysis are given for the obtained parameter estimates of the system s linear dynamics and approximating polynomial of its nonlinear memoryless element respectively simulation study verifies the effectiveness of the method