persistency of excitation for nonminimal models of systems having purely deterministic disturbances all results to date on the question of persistency of excitation depend on the model being minimal thus the results do not apply to systems having purely deterministic disturbances since these automatically give rise to uncontrollable modes on the unil circle this note presents new results on persistency of excitation applicable to nonminimal models of systems having purely deterministic disturbances

adaptive identification of linear systems subject to gross errors in this note we investigate the convergence of a robust recursive identifier for linear models subject to impulsive disturbances under the assumption that the disturbance is unknown and can be of arbitrarily large magnitude the analyzed algorithm attempts to minimize online the sum of absolute errors so as to achieve a sparse prediction error sequence it is proved that the identifier converges exponentially fast into an euclidean ball whose size is determined by the richness properties of the estimation data the frequency of occurrence of impulsive errors and the parameters of the algorithm

improved least squares identification an improved recursive least squares algorithm for parameter estimation is presented which includes on off criteria to prevent parameter drift during periods of low excitation a variable forgetting factor which maintains the trace of the covariance matrix at a user specified value data preprocessing and normalization to improve numerical accuracy scaling of the regressor vector to minimize the condition number of the covariance matrix plus independent estimation of the mean values of the input output data which can be used to eliminate errors due to d c bias or slowly drifting elements in the regressor vector the algorithm can also include parameter projection to constrain the estimates to a priori specified regions and retains the formal properties such as convergence of a true weighted least squares algorithm the proposed algorithm is compared with other modifications suggested in the literature and its advantages are demonstrated by a simulated example

nontrivial solutions of kirchhoff type problems via the yang index abstract we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the yang index and critical groups

classification of doubly periodic minimal surfaces of genus zero we prove that if the quotient surface of a properly embedded doubly periodic minimal surface in 3 has genus zero then the surface is one of the classical scherk examples

exponential convergence of recursive least squares with exponential forgetting factor this paper demonstrates that provided the system input is persistently exciting the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent further it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary the result holds for stable finite dimensional linear time invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail

adding one handle to half plane layers in this paper we build properly embedded singly periodic minimal surfaces which have infinite total curvature in the quotient by the period these surfaces are constructed by adding a handle to the toroidal half plane layers defined by h karcher the technics that use is to solve a jenkins serrin problem over a strip domain and to consider the conjugate minimal surface to the graph

existence of a positive solution to kirchhoff type problems without compactness conditions abstract the existence of a positive solution to a kirchhoff type problem on r n is proved by using variational methods and the new result does not require usual compactness conditions a cut off functional is utilized to obtain the bounded palais smale sequences

adaptive rls algorithms under stochastic excitation strong consistency analysis abstract this paper deals with the analysis of a general rls identification algorithm with forgetting factor almost sure exponential convergence of the estimates to the true parametrization is established for disturbance free systems under a persistent excitation condition of stochastic type

identification of time delays using a polynomial identification method abstract an algorithm for the exact least squares identification of an approximate continuous time time delay system is derived and its operation verified by simulation

discrete time adaptive control utilizing prior information we present schemes for discrete time adaptive control of a linear time invariant system which is partially known along with an analysis of their convergence properties

symmetry of some entire solutions to the allen cahn equation in two dimensions abstract in this paper we prove even symmetry and monotonicity of certain solutions of allen cahn equation in a half plane we also show that entire solutions with finite morse index and four ends must be evenly symmetric with respect to two orthogonal axes a classification scheme of general entire solutions with finite morse index is also presented using energy quantization

on ground states for the kirchhoff type problem with a general critical nonlinearity abstract in this paper we consider the following kirchhoff type problem a b r 3 u 2 u f u in r 3 u h 1 r 3 u 0 in r 3 where a b 0 are constants and f has a critical growth the aim of this paper is to study the existence of ground state solutions for kirchhoff type equations with a general nonlinearity in the critical growth without the assumption of the monotonicity of the function t f t t 3 moreover we will show that the mountain pass value gives the least energy level and also obtain a mountain pass solution

uniqueness of the riemann minimal examples we prove that a properly embedded minimal surface in r 3 of genus zero with infinite symmetry group is a plane a catenoid a helicoid or a riemann minimal example we introduce the language of hurwitz schemes to understand the underlying moduli space of surfaces in our setting

an embedded minimal surface with no symmetries we construct embedded minimal surfaces of finite total curvature in euclidean space by gluing catenoids and planes we use weierstrass representation and we solve the period problem using the implicit function theorem as a corollary we obtain the existence of minimal surfaces with no symmetries

sufficiency of excitation in the context of adaptive identification and adaptive control of linear systems the concept of a sufficiently exciting input play a key role in this note necessary and sufficient conditions are presented for an input function of a single input linear stationary system to be sufficiently exciting these conditions are independent of the stability properties of the linear system

high energy solutions of systems of kirchhoff type equations in rn in the present paper five new critical point theorems on the product spaces are given and three existence theorems for the sequence of high energy solutions for the systems of kirchhoff type equations are studied

identification of partially known systems abstract the concepts of partially known system identification are introduced and the advantages of a method whereby process information can be utilized in a linear transfer function representation of the system are highlighted and discussed in particular an algorithm for identifying a single unknown physical system parameter associated with a linear system is given it is assumed that the system is polynomial as opposed to linear in the physical parameter the bond graph representation is used as the basis for deriving a system dependent algorithm for each partially known system the method is illustrated by simulated examples

on some generalizations of landau s theorem applicable to analysis of adaptive systems a generalization of landau s theorem concerning the properties of a class of adaptive algorithms is given this generalization enables us firstly to establish an exponential convergence result for some special algorithms and secondly to establish the properties used in the stability analysis of adaptive control schemes for a broader class of algorithms than has been done before

useful redundancy in parameter and time delay estimation for continuous time models in this paper we propose an algorithm to estimate the parameters including time delay of continuous time systems based on instrumental variable identification methods to overcome the multiple local minima of the cost function associated with the estimation of a time delay system we utilize the useful redundancy technique specifically the cost function is filtered through a set of low pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem numerical examples are presented to demonstrate the effectiveness of the proposed algorithm

identification for systems with bounded noise in this paper we present a set membership identification algorithm for systems with unknown but bounded disturbance the algorithm contains a weighting factor which is selected according to whether the new observed data contains sufficient information the proposed approach ensures that the estimation error is bounded and nonincreasing furthermore it is shown that the parameter estimates provided by the algorithm will converge to a region containing the true parameters and its upper bound is also given

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

adaptive rls algorithms under stochastic excitation l sup 2 convergence analysis a very general class of rls recursive least squares algorithms having a forgetting factor is considered the basic assumptions are that the data generation mechanism is free of disturbances and that the observation vector is a stochastic process satisfying a phi mixing condition a stochastic characterization of persistent excitation is first given then it is proved that the algorithm is exponentially convergent in the mean square sense

infinitely many radial solutions for kirchhoff type problems in rn abstract in this paper we concern with a class of kirchhoff type problems in r n by using the fountain theorem we obtain three existence results of infinitely many radial solutions for the problem

bounded state solution of degenerate kirchhoff type problem with a critical exponent abstract in the present paper we investigate the following degenerate kirchhoff type problem b r n u 2 d x u v x u u 2 2 u in r n u d 1 2 r n where b is a positive constant v l n 2 r n is a given nonnegative function and 2 is the critical exponent quite a few papers have been published about the degenerate kirchhoff type problem with a critical exponent moreover this degenerate problem in r n n 5 has never been considered so far we obtain some sufficient conditions on the existence of bounded state solution for this degenerate problem as to the cases where n 5 it is the first time to consider the degenerate problem

infinitely many positive solutions for kirchhoff type problems abstract this paper is concerned with the existence of infinitely many positive solutions to a class of kirchhoff type problem a b u 2 d x u f x u in and u 0 on where is a smooth bounded domain of r n a b 0 0 and f r r is a caratheodory function satisfying some further conditions we obtain a sequence of a e positive weak solutions to the above problem tending to zero in l with f being more general than that of k perera z zhang nontrivial solutions of kirchhoff type problems via the yang index j differential equations 221 2006 246 255 z zhang k perera sign changing solutions of kirchhoff type problems via invariant sets of descent flow j math anal appl 317 2006 456 463

bound state solutions of kirchhoff type problems with critical exponent abstract in the present paper we consider the following kirchhoff type problems a b r 3 u 2 d x u v x u u 5 in r 3 u d 1 2 r 3 where a 0 b 0 and v l 3 2 r 3 is a given nonnegative function if v 3 2 is suitable small we prove that this problem has at least one bound state solution

the nehari manifold for a kirchhoff type problem involving sign changing weight functions abstract this paper examines a class of kirchhoff type equations that involve sign changing weight functions using nehari manifold and fibering map the existence of multiple positive solutions is established

analysis of the kalman filter based estimation algorithm an orthogonal decomposition approach in this paper we shall provide new analysis on some fundamental properties of the kalman filter based parameter estimation algorithms using an orthogonal decomposition approach based on the excited subspace a theoretical analytical framework is established based on the decomposition of the covariance matrix which appears to be very useful and effective in the analysis of a parameter estimation algorithm with the existence of an unexcited subspace the sufficient and necessary condition for the boundedness of the covariance matrix in the kalman filter is established the idea of directional tracking is proposed to develop a new class of algorithms to overcome the windup problem based on the orthogonal decomposition approach two kinds of directional tracking algorithms are proposed these algorithms utilize a time varying covariance matrix and can keep stable even in the case of unsufficient and or unbounded excitation

a globally convergent adaptive pole placement algorithm without a persistency of excitation requirement this paper presents an indirect adaptive control scheme for deterministic plants which are not necessarily minimum phase global convergence is established for the scheme in the sense that the closed loop poles are asymptotically assigned for the given data sequence and the system input and output remain bounded for all time a key feature of the scheme is that no persistency of excitation condition is required the algorithm uses recursive least squares with variable forgetting factor normalized regression vectors and a matrix gain with constant trace

fractional kirchhoff type equation with hardy littlewood sobolev critical exponent abstract in this paper we consider the following fractional kirchhoff type equation a b r n r n u x u y 2 x y n 2 s d x d y s u i u 2 h u 2 h 2 u in r n where n 3 s 0 1 a 0 b 0 0 n and 2 h n n 2 s is the hardy littlewood sobolev critical exponent and i is the riesz potential we establish the existence nonexistence and multiplicity of nontrivial solutions to above equation

existence and concentration result for the kirchhoff type equations with general nonlinearities in this paper we study the existence and concentration behaviors of positive solutions to the kirchhoff type equations varepsilon 2 m left varepsilon 2 n int mathbf r n nabla u 2 mathrm d x right delta u v x u f u quad rm in mathbf r n quad u in h 1 mathbf r n n geqq 1 where m and v are continuous functions under suitable conditions on m and general conditions on f we construct a family of positive solutions u varepsilon varepsilon in 0 tilde varepsilon which concentrates at a local minimum of v after extracting a subsequence ek

optimal finite dimensional recursive identification in a polynomial output mapping class abstract a time varying polynomial output equation expressing an implicit dependence of the observed signal on the parameter vector admits a finite dimensional recursive representation for the optimal on line estimator both continuous and discrete observations result in the differential systems which give the estimate deterministic exponentially weighted least squares is applied exponential stability of the identifier and convergence to the true parameter value are shown two examples are presented a continuous application originates in a ph control process the discrete identification is applied in a dynamic arma type model which is quadratic in the parameter

convergence analysis of the least squares identification algorithm with a variable forgetting factor the time varying linear systems abstract this paper studies the convergence of the least squares identification algorithm with a variable forgetting factor the evolution of the parameter estimator with respect to initial conditions actual parameter changes and stochastic perturbations is analysed bounds on the deterministic and stochastic parts of their estimator error are found and their relation to a persistent excitation condition is discussed this relation explains the possibility of having bursting phenomena during the identification process special attention is paid to the consistency of these results with the classical ones obtained for the ordinary least squares algorithm when the forgetting factor tends to unity

the classification of doubly periodic minimal tori with parallel ends let k be the space of properly embedded minimal tori in quotients of r 3 by two independent translations with any fixed even number of parallel ends after an appropriate normalization we prove that k is a 3 dimensional real analytic manifold that reduces to the finite coverings of the examples defined by karcher meeks and rosenberg in 9 10 15 the degenerate limits of surfaces in k are the catenoid the helicoid and three 1 parameter families of surfaces the simply and doubly periodic scherk minimal surfaces and the riemann minimal examples

the classical theory of minimal surfaces we present here a survey of recent spectacular successes in classical minimal surface theory we highlight this article with the theorem that the plane the helicoid the catenoid and the one parameter family frtgt2 0 1 of riemann minimal examples are the only complete properly embedded minimal planar domains in r 3 the proof of this result depends primarily on work of colding

ground state solutions for kirchhoff type equations with asymptotically 4 linear nonlinearity this paper is concerned with the following kirchhoff type equation a b v 2 v f x v in v 0 on assuming that the primitive of f is asymptotically 4 linear as v a homeomorphism between the nehari manifold and a subset of unit sphere is constructed based on some observations and new techniques inspired by recent work of szulkin and weth 2010 ground state solutions for the equation above are obtained as well as infinitely many pairs of nontrivial solutions for case f x v is odd with respect to v

the existence of nontrivial solutions for the critical kirchhoff type problem in rn abstract in this paper we study the problem 0 1 a b r n u 2 d x u v x u f u g x u 2 1 in r n where n 3 a b 0 when n 3 and 0 is small under suitable conditions on v f and g we prove 0 1 has two nontrivial solutions when n 4 and g x 1 we also obtain the existence and non existence results

recursive least squares identification algorithms with incomplete excitation convergence analysis and application to adaptive control the convergence properties of a fairly general class of adaptive recursive least squares algorithms are studied under the assumption that the data generation mechanism is deterministic and time invariant first the open loop identification case is considered by a suitable notion of excitation subspace the convergence analysis of the identification algorithm is carried out with no persistent excitation hypothesis i e it is proven that the projection of the parameter error on the excitation subspace tends to zero while the orthogonal component of the error remains bounded the convergence of an adaptive control scheme based on the minimum variance control law is then dealt with it is shown that under the standard minimum phase assumption the tracking error converges to zero whenever the reference signal is bounded furthermore the control variable turns out to be bounded

minimal surfaces with the area growth of two planes the case of infinite symmetry we prove that a connected properly immersed minimal surface in with infinite symmetry group and area growth constant less than is a plane a catenoid or a scherk singly periodic minimal surface as a consequence the scherk minimal surfaces are the only connected periodic minimal desingularizations of the intersections of two planes

brief paper identification of continuous time systems with multiple unknown time delays by global nonlinear least squares and instrumental variable methods this paper considers the identification problem of multiple input single output miso continuous time systems with unknown time delays of the inputs from sampled input output data an iterative global separable nonlinear least squares gsepnls method which estimates the time delays and transfer function parameters separably is derived to significantly reduce the possibility of convergence to a local minimum by using the stochastic global optimization techniques furthermore the gsepnls method is modified to a novel global separable nonlinear instrumental variable gsepniv method to remove the biases of the estimates in the presence of high measurement noise simulation results show that the proposed algorithms work quite well

existence and multiplicity of non trivial solutions for schrodinger kirchhoff type equations with radial potential abstract in the present paper the following schrodinger kirchhoff type problem p a b r n u 2 d x u v x u q x f u in r n u x 0 as x is studied four existence theorems of nontrivial solutions and a sequence of high energy solutions for problem p are obtained by the mountain pass theorem and symmetric mountain pass theorem

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

brief a directional forgetting algorithm based on the decomposition of the information matrix a novel algorithm for directional forgetting is proposed based on a matrix decomposition method which is developed in this paper this algorithm performs exponential forgetting according to the direction of the data vector thus preventing the problem known as estimator windup which is a characteristic of the standard exponential forgetting algorithm

paper discrete time adaptive control for deterministic time varying systems there is currently considerable interest in the application of recently developed self tuning control algorithms to real control problems however there exist few algorithms which will work for other than slow time varying systems a new algorithm which is able to successfully control unknown systems with quite rapidly varying parameters is presented several simulation results are also presented a convergence proof in the linearly time varying parameter case is given

existence results of positive solutions of kirchhoff type problems abstract in the present paper we use variational methods to prove two existence results of positive solutions of the following kirchhoff type problems a b u 2 u f x u in u 0 on one deals with the asymptotic behaviors of f near zero and infinity and the other deals with 4 superlinear of f at infinity

a novel approach for stabilizing recursive least squares filters a novel approach for stabilizing recursive least squares rls filters is presented the approach relies on a detailed fixed point analysis which provides two important benefits the analysis reveals a bias in the error propagation mechanism providing an analytical basis for instability problems the analysis then indicates which specific roundoff errors are causing instability these roundoff errors are then biased in such a way that the overall filter is biased towards stable performance experimental results indicate that stability can be achieved with negligible loss in least squares performance

approximate n player nonzero sum game solution for an uncertain continuous nonlinear system an approximate online equilibrium solution is developed for an n player nonzero sum game subject to continuous time nonlinear unknown dynamics and an infinite horizon quadratic cost a novel actor critic identifier structure is used wherein a robust dynamic neural network is used to asymptotically identify the uncertain system with additive disturbances and a set of critic and actor nns are used to approximate the value functions and equilibrium policies respectively the weight update laws for the actor neural networks nns are generated using a gradient descent method and the critic nns are generated by least square regression which are both based on the modified bellman error that is independent of the system dynamics a lyapunov based stability analysis shows that uniformly ultimately bounded tracking is achieved and a convergence analysis demonstrates that the approximate control policies converge to a neighborhood of the optimal solutions the actor critic and identifier structures are implemented in real time continuously and simultaneously simulations on two and three player games illustrate the performance of the developed method

schrodinger kirchhoff equation involving double critical nonlinearities abstract in this paper we are interested in weak solutions of the following schrodinger kirchhoff equation involving double critical nonlinearities a b r 3 u 2 u u 2 s 1 1 x s 1 u 2 s 2 1 x s 2 in r 3 0 u d 1 2 r 3 u 0 in r 3 where a b are two positive constants 2 s 2 3 s and 0 s 1 s 2 2 a natural strategy is to search the weak solutions of the equation as critical points of a suitable functional via variational methods but by dilation invariance we see that the functional doesn t satisfy p s condition we will make use of several techniques to recover compactness our results show that the higher order term dominates lower order term and there exist multi scale characteristics in this nonlinear problem

the classification of singly periodic minimal surfaces with genus zero and scherk type ends given an integer k 2 let s k be the space of complete embedded singly periodic minimal surfaces in r 3 which in the quotient have genus zero and 2k scherk type ends surfaces in s k can be proven to be proper a condition under which the asymptotic geometry of the surfaces is well known it is also known that s 2 consists of the 1 parameter family of singly periodic scherk minimal surfaces we prove that for each k 3 there exists a natural one to one correspondence between s k and the space of convex unitary nonspecial polygons through the map which assigns to each m s k the polygon whose edges are the flux vectors at the ends of m a special polygon is a parallelogram with two sides of length 1 and two sides of length k 1 as consequence s k reduces to the saddle towers constructed by karcher

singular perturbed kirchhoff type problem with critical exponent abstract in the present paper we consider the following kirchhoff type problem with critical exponent e 2 a e b r 3 u 2 d x u v x u f u in r 3 u h 1 r 3 by variational methods we show the existence of the positive solutions concentrating around global minima of the potential v x as e 0 we do not need the monotonicity of the function f 3

persistency of excitation in the presence of possibly unbounded signals this note develops an explicit characterization of the concept of persistency of excitation for time invariant linear systems in the presence of possibly unbounded signals this result can be used to establish exponential convergence for a range of adaptive control algorithms a feature of our proof is a particular technique for dealing with the initial condition response

digital parameter adaptive control of processes with unknown dead time simultaneous estimation of process parameters and process time delay is achieved by applying a modification of the recursive least squares method for an extended process model the order of the numerator polynomial is increased by an upper limit of the time delay the estimation of the actual time delay email protected and the calculation of the final process model is done in every step by fitting the impulse response of a model with an assumed order email protected and time delay email protected to the impulse response of the estimated extended process model by combining this method with a feedback control algorithm parameter adaptive control algorithms result and they can be applied to processes with unknown parameters and unknown constant or time varying time delays

robust adaptive control conditions for global stability an input output approach is presented for analyzing the global stability and robustness properties of adaptive controllers to unmodeled dynamics the concept of a tuned system is introduced i e the control system that could be obtained if the plant were known comparing the adaptive system to the tuned system results in the development of a generic adaptive error system passivity theory is used to derive conditions which guarantee global stability of the error system associated with the adaptive controller and ensure boundedness of the adaptive gains specific bounds are presented for certain significant signals in the control systems limitations of these global results are discussed particularly the requirement that a certain operator be strictly positive real spr a condition that is unlikely to hold due to unmodeled dynamics

some uniqueness and nonexistence theorems for embedded minimal surfaces thanks to the works of callahan costa hoffman karcher meeks rosenberg wei etc see for example 1 2 3 5 8 11 12 16 20 we dispose now of a large number of properly embedded minimal surfaces in the euclidean space ir other than the classical examples all those surfaces can be viewed as minimal surfaces with finite total curvature properly embedded in complete flat three manifolds the most basic invariants associated to a surface of this type are its topology and its periodicity it is an interesting problem to decide if the simplest examples like the catenoid the helicoid the scherk s surfaces or the riemann example can be characterized in terms of some of these invariants in the non periodic case there are two important uniqueness theorems in this direction the first one obtained by schoen 17 characterizes the catenoid as the only complete minimal surface embedded

the critical neumann problem of kirchhoff type in this paper we study the critical neumann problem of kirchhoff type by using the variational method and the concentration compactness argument the existence and multiplicity of nontrivial solutions are obtained

sign changing solutions of kirchhoff type problems via invariant sets of descent flow we obtain sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow

sign changing and multiple solutions of kirchhoff type problems without the p s condition abstract the existence of nontrivial solutions of kirchhoff type equations is an important nonlocal quasilinear problem in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4 superlinear kirchhoff type problems without the p s condition one concerning the existence of a nontrivial solution and the other one concerning the existence of sign changing solutions and multiple solutions a b u 2 u f x u in u 0 on

positive solutions for the kirchhoff type problem involving general critical growth part i existence theorem involving general critical growth abstract in this paper we consider the following kirchhoff type problem a r 3 u 2 d x b r 3 u 2 d x u b u f u in r 3 u h 1 r 3 u 0 in r 3 where 0 is a parameter a b are positive constants and f reaches the critical growth without the ambrosetti rabinowitz condition we prove the existence of positive solutions for the kirchhoff type problem with a general critical nonlinearity we also study the asymptotics of solutions as 0 numerical solutions for related problems will be discussed in the second part

on exponential convergence and robustness of least squares identification abstract robustness and convergence properties of exponentially weighted least squares identification are studied it is shown that exponential convergence in the noiseless case can be obtained for a class of increasing or decreasing regression vectors the rate of change of the limits in the regressors affect the convergence rates which are explicitly given it is demonstrated that for a sub class of regressors decreasing in the norm exponential convergence without the noise does not guarantee robustness subject to a bounded noise instead exponential divergence of the estimate is shown in a specific case

new existence and multiplicity of nontrivial solutions for nonlocal elliptic kirchhoff type problems abstract in the present paper we study the existence and multiplicity of nontrivial solutions for nonlocal elliptic kirchhoff type problems a b u 2 d x u f x u in u 0 on where a b 0 are real numbers some new existence and multiplicity results of nontrivial solutions are obtained by means of the mountain pass theorem and a cut off technique one known result is improved

existence and multiplicity of solutions for kirchhoff type equations abstract in this paper the existence and multiplicity of weak solutions are obtained for a class of kirchhoff type problems with dirichlet boundary value conditions by using the mountain pass theorem the local linking theorem the fountain theorem and the symmetric mountain pass lemma in critical point theory

bounded error identification of time varying parameters by rls techniques the performance of the recursive least squares algorithm with constant forgetting factor in the identification of time varying parameters is studied in a stochastic framework it is shown that the mean square tracking error keeps bounded if and only if the so called covariance matrix of the algorithm is l sup 1 bounded then a feasibility range for the forgetting factor is worked out in correspondence of which the covariance matrix and therefore the tracking error keeps bounded

nonlinear perturbations of a periodic kirchhoff equation in rn abstract this paper is concerned with the existence of positive solutions for the following class of nonlocal problem m r n u 2 d x r n v x u 2 d x u v x u f u u in r n where 5 for n 3 and 1 for n 1 2 is a positive parameter and 0 1 moreover m v and f are continuous functions satisfying some conditions

recursive estimation of time delay in sampled systems abstract this paper presents a new identification method based on standard recursive least squares for the estimation of time delay in linear sampled systems the algorithm relies on the fact that if the continuous time model has a delay or anticipation shorter than one sampling time then a real negative zero arises in the corresponding sampled system by inspection of the phase contribution of this zero the value of the delay is recursively updated a frequency domain analysis is also performed to examine the characteristics of the algorithm simulation results illustrate the performances of the time delay estimation algorithm

adaptive identification via prediction error directional forgetting factor convergence analysis the prediction error directional forgetting factor algorithm suitably incorporates the features of the directional forgetting and prediction error forgetting algorithms under the assumption that the data generation mechanism is deterministic and subject to a constant parameter it is shown that the algorithm is convergent but not exponentially convergent furthermore a modification is proposed that leads to an exponentially convergent algorithm

a modified ew els algorithm for system with bounded disturbances inclusion abstract this paper presents a new estimation algorithm which is essentially a modification of the exponentially weighted recursive least squares algorithm ew rls for systems with bounded disturbances assuming knowledge of a disturbance upper bound the algorithm s derivation is performed by minimizing a cost function weighted by two factors one is fixed by the user and exponentially weights the arriving information the other is time varying and data dependent the purpose of the latter is to ensure algorithm stability faced with the bounded disturbances from this proposal results a very simple algorithm which completely depends on the significant information and stops when the data are meaningless it is also shown that if the signals are persistently exciting the convergence of the algorithm is exponentially fast an application of the algorithm to the problem of estimating the friction forces in servo mechanisms under structural bounded errors is also presented

a priori bounds for positive solutions of kirchhoff type equations abstract let be a bounded smooth domain in r n assume that 0 2 1 2 a 0 and b 0 we consider the following dirichlet problem of kirchhoff type equation 0 1 a b u 2 2 u u p 1 u h x u u in u 0 on with p 0 2 1 where 2 for n 2 and 2 n 2 n 2 for n 3 under suitable conditions of h x u u see a h 1 and h 2 in section 3 we get a priori estimates for positive solutions to problem 0 1 by making use of these estimates and the continuous method we further get some existence results for positive solutions to problem 0 1 when 0 p 1 or 2 1 p 2 effects of the term a b u 2 2 on the solution set of problem 0 1 can be seen in an example given in section 2

convergence and exponential convergence of identification algorithms with directional forgetting factor abstract in this paper the convergence properties of the rls algorithm with directional forgetting df are extensively analyzed the assumption is made that the data generation mechanism is deterministic the main conclusions are that df is simply convergent but not exponentially convergent the exponential convergence can be achieved by means of a suitable modification of df