nonlinear kolmogorov equations in infinite dimensional spaces the backward stochastic differential equations approach and applications to optimal control solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control

generalized variational like inequalities for pseudomonotone type ii operators in this paper we shall prove some existence results of solutions for a new class of generalized variational like inequalities with eta h pseudomonotone type ii operators defined on noncompact sets in hausdorff topological vector spaces c 2005 elsevier ltd all rights reserved

existence and uniqueness for a non coercive lubrication problem the purpose of this paper is to study a mathematical model of hydrodynamic lubrication when cavitation takes place the obtained equation is a non linear degenerate partial differential equation

generalised quasi variational inequalities for upper semi continuous operators on non compact sets suppose that e is a topological vector space and x is a non empty subset of e let s x 2 x and t x e be two maps then the quasi variational

the split levinson algorithm the classical levinson algorithm for computing the predictor polynomial relative to a real positive definite toeplitz matrix is shown to be redundant in complexity it can be broken down into two simpler algorithms either of which needs only to be processed this result can be interpreted in the framework of the theory of orthogonal polynomials on the real line as follows the symmetric and antisymmetric parts of the predictors relative to the sequence of toeplitz matrices constitute two families of polynomials orthogonal on the interval 1 1 with respect to some even weight functions it turns out that the recurrence relations for these orthogonal polynomials can be used efficiently to compute the desired predictor the resulting split levinson algorithm requires roughly one half the number of multiplications and the same number of additions as the classical levinson algorithm a simple derivation of cybenko s method for computing the pisarenko frequencies is obtained from the recurrence relations underlying the split levinson algorithm

global regular solutions of second order hamilton jacobi equations in hilbert spaces with locally lipschitz nonlinearities abstract this paper is devoted to the study of a second order hamilton jacobi equation in infinite dimensions with a locally lipschitz continuous hamiltonian h related with a stochastic optimal control problem driven by white noise in an earlier paper the author studied the case of globally lipschitz continuous hamiltonian h this paper is concerned with the case of locally lipschitz continuous h that include e g the quadratic case which appears very frequently in the applications existence uniqueness and c 2 regularity of a local solution follow by methods given previously the heart of the work is the proof of a priori estimates of the c 1 norm of the local solution this has been done by studying properties of nonlinear transition semigroups and by a careful application of them to our problem the results have been applied to a stochastic optimal control problem proving existence of feedback optimal controls

variational conclusions of set valued bifunctions on convex subsets of banach spaces with applications in this paper variational conclusions of set valued bifunctions on convex subsets of banach spaces are investigated and several new results are obtained the results are applied to the fixed point theory and variational inequalities we obtain two fixed point theorems and existence theorems of solutions of variational inequalities

wide sense stability of discrete and continuous time linear systems in the complex case canonical reflection coefficients are used to determine the number of roots appearing on the unit circle and their multiplicities for a stable polynomial with no zero outside the unit circle a criterion so that a stable polynomial has no multiple zeros on the unit circle is then deduced and transposed to the continuous time linear systems in the complex case

optimal control of a stochastic delay heat equation with boundary noise and boundary control in this paper a controlled stochastic delay heat equation with neumann boundary noise and boundary control is considered the existence and uniqueness of the mild solution for the associated hamilton jacobi bellman equations are obtained by means of the backward stochastic differential equations which is applied to the optimal control problem

generalized bi quasi variational inequalities for quasi pseudo monotone type i operators on non compact sets in this paper the authors prove some existence results for solutions for a new class of generalized bi quasi variational inequalities gbqvi for quasi pseudo monotone type i and strongly quasi pseudo monotone type i operators defined on non compact sets in locally convex hausdorff topological vector spaces in obtaining these results on gbqvi for quasi pseudo monotone type i and strongly quasi pseudo monotone type i operators we shall use chowdhury and tan s generalized version of ky fan s minimax inequality as the main tool

a pointwise criterion for controller robustness abstract we present a pointwise criterion for controller robustness with respect to stability the term point here refers to complex frequency in the right half plane the proposed test is based on the concept of the minimal angle between subspaces determined by the plant and the compensator the test leads to separate balls of uncertainty at each frequency and may therefore help to reduce conservativeness in the analysis of robustness

tabular method for determining root distribution of delta operator formulated real polynomials a tabular method for the investigation of real polynomial root distribution with respect to the circle spl verbar c 1 spl delta spl verbar 1 spl delta in the complex plane is presented such a procedure is useful in stability considerations of spl delta operator formulated discrete time systems with sampling time spl delta in particular when the characteristic polynomial contains literal coefficients we show that direct verification of stability may be preferable over techniques that utilize transformations when the sampling frequency is fast relative to the system bandwidth in addition as sampling frequency increases the relationship with the well known routh hurwitz table becomes apparent

on the mechanism of recursive stability test algorithms most stability test procedures are based on a recursion relation that starting from a given characteristic polynomial generates a sequence of polynomials pi s of descending degree i the zero distribution with respect to the boundary of the stability region the imaginary axis in the case of continuous time systems of each polynomial in the sequence is related to that of the preceding polynomial and to the value of a single parameter to explain the operation of each method the right hand side pcirc i s of the recursion is expressed as a suitable combination of the even and odd parts of pi i possibly multiplied by low powers of s it is shown how for suitable values of the combination parameters pcirc i s admits a given factor r s the next polynomial pcirc i 1 s in the sequence is obtained by factoring out r s from pcirc i s this approach not only allows us to point out the common nature of standard stability criteria but also to conceive new methods of comparable complexity

stochastic optimal control problems and parabolic equations in banach spaces we consider stochastic optimal control problems in banach spaces these problems are related to nonlinear controlled equations with dissipative nonlinearity and are treated via the backward stochastic differential equation approach which also allows us to solve in a mild sense hamilton jacobi bellman equations in banach spaces we apply the results to controlled stochastic heat and wave equations with a cost functional that is well defined on continuous functions and to delay equations in spaces of p integrable functions

coercivity conditions and variational inequalities various coercivity conditions appear in the literature in order to guarantee solutions for the variational inequality problem we show that these conditions are equivalent to each other and that they are not only sufficient but also necessary for the set of solutions to be non empty and bounded

adaptive linear barycentric rational finite differences method for stiff odes abstract it is our purpose to introduce a simple multistep method based on linear barycentric rational interpolation for solving ordinary differential equations also we design an adaptive version having one free parameter which is used to improve the stability properties numerical experiments of the constructed methods on some well known stiff problems indicate efficiency and capability of the methods in solving stiff problems

a circular stability test for general polynomials abstract we extend a new stability test proposed recently for discrete system polynomials 1 to polynomials with complex coefficients the method is based on a three term recursion of a conjugate symmetric sequence of polynomials the complex version has the same relative improved efficiency as the real version in comparison to the classical schur cohn formulation for counting the number of zeros of a polynomial with respect to the unit circle furthermore if desirable the complex text can be carried out using only real polynomials and arithmetic

direct bilinear routh stability criteria for discrete systems the bilinear transformation is applied to routh conditions for hurwitz polynomials to obtain a variety of equivalent direct z plane continued fraction cf expansions and stability conditions for discrete system polynomials efficient computational algorithms are provided they can be used to test the stability of a discrete system and to determine the number of zeros of unstable system polynomials outside the unit circle the many new cf forms may be also applicable to the design of bilinear transformed sampled data ladder filters

nonzero solutions for a class of set valued variational inequalities in reflexive banach spaces in this paper we study the existence of nonzero solutions for a class of set valued variational inequalities involving set contractive mappings by using the fixed point index approach in reflexive banach spaces some new existence theorems of nonzero solutions for this class of set valued variational inequalities are established

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions part i the case of bounded stochastic evolutions on etudie des equations elliptiques degenerees d ordre 2 non lineaires de la forme f d 2 u du u x 0 dans h ou h est un espace de hilbert separable x un point generique dans h u une fonction de h r

a class of operator equilibrium problems in this paper we consider a class of operator equilibrium problems oep for short with operator solutions and derive a minty type lemma for this class of problems further using this lemma and kkm theorem we establish some existence theorems for oep the theorems presented in this paper generalize improve and unify many known results

splitting of some s domain stability test algorithms some classic s domain algorithms are first expressed in a unified form from this all possible split forms are then derived and classified in particular attention is focused on two families of algorithms which include the standard routh algorithm and an s domain levinson like algorithm respectively the related split forms are analysed and compared their complexity can be reduced by suitably choosing some scaling factors it turns out that the usual form of the routh algorithm which is intrinsically split and the simplified version of the split levinson like algorithm are substantially equivalent and superior to any other possible split algorithm

a discrete stability equation theorem and method of stable model reduction a method to derive stable reduced order models for a stable discrete time invariant system is presented the method is based on a unit circle stability criterion this criterion is the r plane equivalent of a stability criterion for continuous time systems and is proven by using the bilinear transformation the resulting model reduction method forms the discrete analogue of the stability equation and michailov s methods for the simplification of continous time systems that were recently suggested in various closely related versions

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

immittance domain levinson algorithms several computationally efficient versions of the levinson algorithm for solving linear equations with toeplitz and quasi toeplitz matrices are presented motivated by a new stability test the new versions require half the number of multiplications and the same number of additions as the conventional form of the levinson algorithm the saving is achieved by using three term rather than two term recursions and propagating them in an impedance admittance or immittance domain rather than the conventional scattering domain one of the recursions coincides with recent results of p delsarte and y genin ieee trans acoust speech signal proc vol assp 34 p 470 8 june 1986 on split levinson algorithms for symmetric toeplitz matrices where the efficiency is gained by using the symmetric and skew symmetric versions of the usual polynomials this special structure is lost in the quasi toeplitz case but one still can obtain similar computational reductions by suitably using three term recursions in the immittance domain

generalized bi quasi variational inequalities abstract let e f be hausdorff topological vector spaces over the field which is either the real field or the complex field let f e be a bilinear functional and let x be a non empty subset of e given a multi valued map s x 2x and two multi valued maps m t x 2f the generalized bi quasi variational inequality gbqvi problem is to find a point y x such that y s y and inf w t y re w y x 0 for all x s y and for all m y in this paper two general existence theorems on solutions of gbqvis are obtained which simultaneously unify sharpen and extend existence theorems for multi valued versions of hartman stampacchia variational inequalities proved by browder and by shih and tan variational inequalities due to browder existence theorems for generalized quasi variational inequalities achieved by shih and tan theorems for monotone operators obtained by debrunner and flor fan and browder and the fan glicksberg fixed point theorem

optimal control problems for stochastic delay evolution equations in banach spaces we consider the optimal control for a banach space valued stochastic delay evolution equation the existence and uniqueness of the mild solution for the associated hamilton jacobi bellman equations are obtained by means of backward stochastic differential equations an application to optimal control of stochastic delay partial differential equations is also given

a note on the new 1 d and 2 d stability theorems for discrete systems an interesting theorem on the stability of 1 d discrete systems has been presented in 1 and it has been extended to the 2 d case in 2 in this correspondence after showing that the conditions stated by the theorems of 1 and 2 are only necessary we introduce another condition inclusion of which makes the above stability theorems necessary and sufficient

generalized quasi variational inequalities on non compact sets with pseudo monotone operators abstract in this paper we first generalize a ky fan minimax inequality then we obtain two foundational quasi variational inequalities which play a key role throughout this paper we shall use these results to obtain some general theorems on solutions of the generalized quasi variational inequalities gqvi on a paracompact set x in a hausdorff locally convex space e where the set valued operator t x 2 e is either strongly pseudo monotone or pseudo monotone

second order hamilton jacobi equations in infinite dimensions some second order hamilton jacobi equations connected to stochastic optimal control problems for infinite dimensional systems driven by a white noise are studied a direct method to prove existence and uniqueness of mild solutions is developed then this solution is identified as the value function of the related stochastic control problem and a feedback formula for optimal controls is derived

comparison between some stability criteria of discrete time filters routh s algorithm is written in the form of polynomial recursion and transposed for testing stability in the wide sense of discrete time linear systems the algorithm obtained is a three term recursion of symmetric polynomials this recursion easily gives both the coefficients appearing in the continued fraction expansion associated to a given polynomial in the z domain and a computation scheme for the bilinear transformation of polynomials finally this recursion is compared to other algorithms already known for testing stability

the existence and uniqueness of the solution for nonlinear kolmogorov equations abstract by means of backward stochastic differential equations the existence and uniqueness of the mild solution are obtained for the nonlinear kolmogorov equations associated with stochastic delay evolution equations applications to optimal control are also given

a stability test for continuous systems abstract a test for determining the zero distribution of a real polynomial with respect to the imaginary axis is presented it is based on the construction of a sequence of polynomials of descending degree which draws on the levinson algorithm the proof of the stability criterion which is based on intuitive geometrical considerations is very simple and the computational complexity is not greater than that for the routh test the critical situations that may arise are also examined and some examples are given

nonconvexity of the stability domain of digital filters the stability of a causal digital filter with a rational transfer function h z is completely specified by the location of its poles with respect to the unit circle uc the set of points a corresponding to stable filters i e to polynomials p with roots inside the uc is called the stability domain sigma of digital filters results are established that concern the convexity of sigma the denominator of a rational digital filter of nth order is a polynomial represented by a point a of the n dimensional space of its coefficients it is shown that for n or 3 sigma is not convex and especially if point a belongs to sigma and a satisfies 0

a direct routh stability method for discrete system modelling the routh approximation method which has been suggested for the reduction of stable discrete time linear systems to guarantee stable models uses the bilinear transformation a stability theorem in the z plane is presented which is shown to be an equivalent of the routh criterion an efficent method that avoids the bilinear transformation is presented by which the routh disrete models are derived directly in the z plane

immittance versus scattering domain fast algorithms for non hermitian toeplitz and quasi toeplitz matrices abstract the classical algorithms of schur and levinson are efficient procedures to solve sets of hermitian toeplitz linear equations or to invert the corresponding coefficient matrices they propagate pairs of variables that may describe incident and scattered waves in an associated cascade of layered media model and thus they can be viewed as scattering domain algorithms it was recently found that a certain transformation of these variables followed by a change from two term to three term recursions results in reduction in computational complexity in the abovementioned algorithms roughly by a factor of two the ratio of such pairs of transformed variables can be interpreted in the above layered media model as an im pedance or ad mittance hence the name immittance domain variables this paper provides extensions for previous immittance schur and levinson algorithms from hermitian to non hermitian matrices it considers both toeplitz and quasi toeplitz matrices matrices with certain hidden toeplitz structure and compares two and three term recursion algorithms in the two domains the comparison reveals that for non hermitian matrices the algorithms are equally efficient in both domains this observation adds new comprehension to the source and value of algorithms in the immittance domain the immittance algorithms like the scattering algorithms exploit the quasi toeplitz structure to produce fast algorithms however unlike the scattering algorithms they can respond also to symmetry of the underlying matrix when such extra structure is present and yield algorithms with improved efficiency

path dependent hamilton jacobi equations in infinite dimensions abstract we propose notions of minimax and viscosity solutions for a class of fully nonlinear path dependent pdes with nonlinear monotone and coercive operators on hilbert space our main result is well posedness existence uniqueness and stability for minimax solutions a particular novelty is a suitable combination of minimax and viscosity solution techniques in the proof of the comparison principle one of the main difficulties the lack of compactness in infinite dimensional hilbert spaces is circumvented by working with suitable compact subsets of our path space as an application our theory makes it possible to employ the dynamic programming approach to study optimal control problems for a fairly general class of delay evolution equations in the variational framework furthermore differential games associated to such evolution equations can be investigated following the krasovski subbotin approach similarly as in finite dimensions

extensions of the stability criterion for arma filters using the lattice representation of an arma filter it is well known that the necessary and sufficient condition so that the poles are inside the unit circle is k i where the k i s are the reflection coefficients the filter is said to be wide sense stable if no pole is located outside the unit circle and it is interesting to characterize this stability by an appropriate necessary and sufficient condition to establish this condition the concept of canonical reflection coefficient is introduced which eliminates the problems appearing when the levinson recursion is not inversible some examples are discussed and a simple and practical test for wide sense stability is given

multi objective parameter identification of euler bernoulli beams under axial load abstract identification of physical parameters of the partial differential equation describing transverse vibrations of an axially loaded euler bernoulli beam ebb is proposed via a multi objective optimization formulation and solved by a genetic algorithm conflicting objectives such as performance and stability are specifically formulated and optimized simultaneously stability is quantified in terms of the solution s time growth factor physical parameter sets in the resulting pareto front approximation represent best trade offs with respect to the multiple objectives to compute output error performance objectives the ebb equation is discretized via finite differences in space and time and reformulated to a state space system identifiability is verified by checking regularity of the so called fisher information matrix the identification methodology is capable of determining material parameters including damping as well as the axial load from few spatially concentrated measurements its features are demonstrated and successfully validated on specific simulation data and measurement data obtained from a laboratory testbed