first and second order necessary conditions for stochastic optimal controls abstract the main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach the control system is governed by a stochastic differential equation in which both drift and diffusion terms may contain the control variable and the set of controls is allowed to be nonconvex only one adjoint equation is introduced to derive the first order necessary condition while only two adjoint equations are needed to state the second order necessary conditions for stochastic optimal controls

pointwise second order necessary conditions for stochastic optimal controls part i the case of convex control constraint this paper is the first part of our series of work to establish pointwise second order necessary conditions for stochastic optimal controls in this part both drift and diffusion terms may contain the control variable but the control region is assumed to be convex under some assumptions in terms of the malliavin calculus we establish the desired necessary conditions for stochastic singular optimal controls in the classical sense

numerical analysis for a macroscopic model in micromagnetics the macroscopic behavior of stationary micromagnetic phenomena can be modeled by a relaxed version of the landau lifshitz minimization problem in the limit of large and soft magnets omega it is reasonable to exclude the exchange energy and convexify the remaining energy densities the numerical analysis of the resulting minimization problem begin align min e 0 bf m text amongst bf m omega to mathbb r d text with bf m x le1 text for almost every x in omega end align for d 2 3 faces difficulties caused by the pointwise side constraint bf m le1 and an integral over the whole space mathbb r d for the stray field energy this paper involves a penalty method to model the side constraint and reformulates the exterior maxwell equation via a nonlocal integral operator mathcal p acting on functions exclusively defined on omega the discretization with piecewise constant discrete magnetizations leads to edge oriented boundary integrals the implementation of which and related numerical quadrature are discussed as are adaptive algorithms for automatic mesh refinement a priori and a posteriori error estimates provide a thorough rigorous error control of certain quantities three classes of numerical experiments study the penalization empirical convergence rates and performance of the uniform and adaptive mesh refining algorithms

pointwise second order necessary optimality conditions for the mayer problem with control constraints this paper is devoted to second order necessary optimality conditions for the mayer optimal control problem when the control set u is a closed subset of mathbb r m we show that in the absence of endpoint constraints if an optimal control bar u cdot is singular and integrable then for almost every t such that bar u t is in the interior of u both the goh and a generalized legendre clebsch condition hold true moreover when the control set is a convex polytope similar conditions are verified on the tangent subspace to u at bar u t for almost all t s such that bar u t lies on the boundary partial u of u the same conditions are valid also for u having a smooth boundary at every t where bar u cdot is singular and locally lipschitz and bar u t in partial u in the presence of a smooth endpoint constraint these second order necessary optimality conditions are satisfied whenever the mayer problem is calm and the maximum principle is abnormal if it is

non coercive first order mean field games abstract we study first order evolutive mean field games where the hamiltonian are non coercive this situation occurs for instance when some directions are forbidden to the generic player at some points we establish the existence of a weak solution of the system via a vanishing viscosity method and mainly we prove that the evolution of the population s density is the push forward of the initial density through the flow characterized almost everywhere by the optimal trajectories of the control problem underlying the hamilton jacobi equation as preliminary steps we need to prove that the optimal trajectories for the control problem are unique at least for a e starting points and that the corresponding unique optimal control has a feedback expression in terms of the intrinsic gradient of the value function

the frisch scheme in dynamic system identification abstract the use of the frisch scheme in the identification of linear dynamic systems is investigated in order to describe the whole family of models that can explain given input output noisy sequences unlike the algebraic case it is shown that in general only a single model is compatible with the data these results are first proposed for single input single output systems and then generalized to the multivariable case

brief paper on the identifiability of errors in variables models with white measurement errors we discuss identifiability of dynamic siso errors in variables eiv models with white measurement errors although this class of models turns out to be generically identifiable it has been pointed out that in certain circumstances there may be two eiv models which are indistinguishable from external input output experiments this lack of global identifiability may be prejudicial to identification and needs better understanding the identifiability conditions found in the literature guarantee uniqueness under certain coprimality assumptions on the rational transfer function of the ideal true system and the spectral density of the noiseless true input unfortunately these conditions are not testable since they concern precisely the unknowns of the problem which are not available to the experimenter we provide new identifiability conditions which are instead expressible in terms of the external description of the observable signals namely their joint power spectral densities

accuracy analysis of the frisch scheme for identifying errors in variables systems several estimation methods have been proposed for identifying errors in variables systems where both input and output measurements are corrupted by noise one of the promising approaches is the so called frisch scheme this paper provides an accuracy analysis of the frisch scheme applied to system identification the estimates of the system parameters and the noise variances are shown to be asymptotically gaussian distributed an explicit expression for the covariance matrix of the asymptotic distribution is given as well numerical simulations support the theoretical results a comparison with the cramer rao lower bound is also given in the examples and it is shown that the frisch scheme gives a performance close to the cramer rao bound for large signal to noise ratios snrs

a simplified form of the bias eliminating least squares method for errors in variables identification this note considers the bias eliminating least squares bels method for identifying the errors in variables systems with white input noise and colored output noise a simplified form of the bels algorithm is proposed that is proved to be equivalent to the existing one some expositions of this simplified bels expression are also given the new relation is a form of linear iv equations which will not only reduce the computational load but also simplify the analysis of the properties of the bels estimates

a reduced theory for thin film micromagnetics micromagnetics is a nonlocal nonconvex variational problem its minimizer represents the ground state magnetization pattern of a ferromagnetic body under a specified external field this paper identifies a physically relevant thin film limit and shows that the limiting behavior is described by a certain reduced variational problem our main result is the 0 convergence of suitably scaled three dimensional micromagnetic problems to a two dimensional reduced problem this implies in particular convergence of minimizers for any value of the external field the reduced problem is degenerate but convex as a result it determines some but not all features of the ground state magnetization pattern in the associated thin film limit c 2002 wiley periodicals inc

regularity properties of optimal controls a class of optimal control problems is considered involving integral cost functions and linear dynamics broad verifiable hypotheses he are known under which the problems have solutions these must be supplemented for standard optimality conditions in the form of a maximum principle to apply new regularity properties of optimal controls when merely hypotheses he are in force are established a byproduct is a maximum principle governing optimal controls under such circumstances where the ostate function is possibly unbounded criteria for minimizing controls to be essentially bounded are also deduced

variational approach to second order sufficient optimality conditions in optimal control we consider a bolza optimal control problem with convex pure state constraints and general control constraints and propose new second order sufficient optimality conditions for a weak local minimum that can be applied in a general framework in particular the reference control may be merely measurable and the dynamics may be discontinuous in the time variable our approach is based on a new decomposition result for control constraints involving second order tangents

the classical problem of the calculus of variations in the autonomous case relaxation and lipschitzianity of solutions we consider the problem of minimizing b a l x t x t dt x a a x b b under the assumption that the lagrangian l is continuous and satisfies a growth assumption that does not imply superlinear growth we provide a result on the relaxation of the functional and show that a solution to the minimum problem is lipschitzian

existence and lipschitz regularity of solutions to bolza problems in optimal control in this paper we investigate the existence and lipschitz continuity of optimal trajectories for the autonomous bolza problem in control theory the main feature of our results is that they relax the usual fast growth condition for the lagrangian furthermore we show that optimal solutions do satisfy the maximum principle

errors in variables system identification using structural equation modeling errors in variables eiv identification refers to the problem of consistently estimating linear dynamic systems whose output and input variables are affected by additive noise various solutions have been presented for identifying such systems in this study eiv identification using structural equation modeling sem is considered two schemes for how eiv single input single output siso systems can be formulated as sems are presented the proposed formulations allow for quick implementation using standard sem software by simulation examples it is shown that compared to existing procedures here represented by the covariance matching cm approach sem based estimation provide parameter estimates of similar quality

degenerate optimal control problems with state constraints standard necessary conditions for optimal control problems with pathwise state constraints supply no useful information about minimizers in a number of cases of interest e g when the left endpoint of state trajectories is fixed at x0 and x0 lies in the boundary of the state constraint set in these cases a nonzero but nevertheless trivial set of multipliers exists we give conditions for the existence of nontrivial multipliers a feature of these conditions is that they allow nonconvex velocity sets and measurably time dependent data the proof techniques are based on refined estimates of the distance of a given state trajectory from the set of state trajectories satisfying the state constraint originating in the dynamic programming literature

regularity and necessary conditions for a bolza optimal control problem abstract we consider a bolza optimal control problem whose lagrangian possibly extended valued may be discontinuous in the state and control variable so that optimal solutions are not supposed to necessarily satisfy the maximum principle given an optimal trajectory control pair we prove that it satisfies a new erdmann du bois reymond type condition and show that from this condition it is possible to derive boundedness properties of the optimal control and a lipschitz regularity result for the optimal state arc just imposing general growth assumptions allowing some almost linear growth behaviors

lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands the study of regularity properties for minimizers of problems of the form min u u dt u e iv q r u a a u b b 1 1 has been undertaken for a long time in calculus of variations and a number of results are by now available on this subject when f t s z is a smooth coercive function problem 1 1 was considered by tonelli see 18 19 who proved that every minimizer u t of the problem 1 1 is locally lipschitz on a relatively open set of full measure in a b under some additional assumptions on f it is also possible to prove global regularity theorems see for instance cesari 3 chap 2 sect 61 in recent years much attention has been devoted to problems of the form l l on the one hand in weakening the hypotheses of tonelli s regularity results and on the other in finding counterexamples of nonregular minimizers for coercive functionals with respect to this last subject we recall that it has been shown see ball and mizel l and clarke and vinter 6 that there exist polynomial functions f t s z such that for suitable c 0 and p

a generalized instrumental variable estimation method for errors in variables identification problems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper it is shown how a number of common methods for errors in variables methods can be put into a general framework resulting into a generalized instrumental variable estimator give various computational aspects of give are presented and the asymptotic distribution of the parameter estimates is derived

speech enhancement combining optimal smoothing and errors in variables identification of noisy ar processes in the framework of speech enhancement several parametric approaches based on an a priori model for a speech signal have been proposed when using an autoregressive ar model three issues must be addressed 1 how to deal with ar parameter estimation indeed due to additive noise the standard least squares criterion leads to biased estimates of ar parameters 2 can an estimation of the variance of the additive noise for each speech frame be obtained a voice activity detector is often used for its estimation 3 which estimation rules and techniques filtering smoothing etc can be considered to retrieve the speech signal our contribution in this paper is threefold first we propose to view the identification of the noisy ar process as an errors in variables problem this blind method has the advantage of providing accurate estimations of both the ar parameters and the variance of the additive noise second we propose an alternative algorithm to standard kalman smoothing based on a constrained minimum variance estimation procedure with a lower computational cost third the combination of these two steps is investigated it provides better results than some existing speech enhancement approaches in terms of signal to noise ratio snr segmental snr and informal subjective tests

identification of dynamic errors in variables models this paper deals with the identifiability of scalar dynamic errors in variables models characterized by rational spectra the hypothesis of causality for the underlying dynamic system is taken into account by making use of stochastic realization theory and of the structural properties of state space representations it is shown that under mild assumptions the model is uniquely identified

a connection between the maximum principle and dynamic programming for constrained control problems we consider the mayer optimal control problem with dynamics given by a nonconvex differential inclusion whose trajectories are constrained to a closed set and obtain necessary optimality conditions in the form of the maximum principle together with a relation between the costate and the value function this additional relation is applied in turn to show that the maximum principle is nondegenerate we also provide a sufficient condition for the normality of the maximum break principle to derive these results we use convex linearizations of differential inclusions and convex linearizations of constraints along optimal trajectories then duality theory of convex analysis is applied to derive necessary conditions for optimality in this way we extend the known relations between the maximum principle and dynamic programming from the unconstrained problems to the constrained case

certain models from uncertain data the algebraic case abstract the problem of deriving possible linear relations from data affected by additive noise has received remarkable attention in recent years particularly regarding the assumptions prejudices behind the procedures leading to unique models unlike traditional approaches leading to unique solutions least squares maximum likelihood etc the frisch scheme belonging to the family of errors in variables ev schemes leads to a whole family of models compatible with a set of noisy data and is considered as mildly affected by prejudices this paper shows how also under the assumptions of the frisch scheme it is possible to obtain a unique model from uncertain data and also to derive the actual amount of noise when the noiseless data are linked by a single linear relation the more general ev case of non independent additive noises is then considered and it is shown how also under these assumptions it is possible to obtain the unique set of parameters linking the noiseless data and how the family of compatible noise covariance matrices is defined in this case by the infinite elements of a linear variety

subspace algorithms for the identification of multivarible dynamic errors in variables models abstract we consider the problem of identifying multivariable finite dimensional linear time invariant systems from noisy input output measurements apart from the fact that both the measured input and output are corrupted by additive white noise the output may also be contaminated by a term which is caused by a white input process noise furthermore all these noise processes are allowed to be correlated with each other we shall develop a solution to this problem in the framework of subspace identification and we shall show that our algorithms give consistent estimates when the system is operating in open or closed loop two realistic simulation studies are presented to demonstrate the practical applicability of the proposed algorithms 1997 elsevier science ltd

frisch scheme identification for dynamic diagonal bilinear models the article addresses the problem of dynamic system identification in the errors in variables framework for a class of discrete time time invariant input output bilinear models when subjected to a white input signal the proposed algorithm is based on an extension of the bias compensated least squares method and utilises the frisch scheme equations to determine the parameter vector together with the variances of the input and output noise sequences the appropriateness of the approach is analysed and its performance evaluated when compared to other errors in variables identification techniques by means of a monte carlo simulation the results obtained demonstrate the accuracy of the proposed method and the performance in terms of noise robustness is also observed

novel parameter estimation of autoregressive signals in the presence of noise this paper proposes a new method for estimating the parameters of an autoregressive ar signal from observations corrupted by white noise the feature of the new method is that the observation noise variance estimate is converted into the only solution of a nonlinear equation to yield unbiased estimate of the ar parameters moreover a convergent newton iterative algorithm with a deterministic initial point is presented for efficient implementation of the proposed new estimation method as a result the proposed new method can minimize the error of estimating the variance of the observation noise since more accurate estimates of this observation noise variance can be attained at earlier stages the proposed method can achieve a good performance in estimating the ar signal parameters numerical results demonstrate that the proposed new algorithm is more effective in terms of accuracy and robustness against noise than conventional algorithms

a priori error estimates for hp penalty bem for contact problems in elasticity the purpose of the paper is to obtain a priori error estimates for the hp version of penalty galerkin bem applied to frictionless contact problems in elasticity the error analysis is divided into two parts at first we consider the error caused by the approximation of the variational inequality or lagrange multiplier formulation with the penalty problem under additional regularity assumptions we derive a linear convergence rate with respect to the penalty parameter then the discretization error between the solution of the penalty problem and its galerkin approximation is considered we show two types of the best approximation property which is similar to the cea s lemma but the estimate depends on the penalty parameter finally we derive an a priori estimate for the error between the exact solution u of the variational inequality and the boundary element galerkin solution of the penalty problem for u h 3 2 c n we obtain the convergence rate o h p 1 when choosing the penalty parameter e c h p 1 for arbitrary fixed 0 1 and c 0

effective simulation of a macroscopic model for stationary micromagnetics the effective behaviour of stationary micromagnetic phenomena is modelled by a convexified landau lifshitz minimization problem for the limit of large and soft magnets x without the exchange energy the numerical simulation of the resulting minimization problem has to overcome difficulties caused by the pointwise side restriction jmj 6 1 and the stray field energy on the unbounded domain r d a penalty method models the side restriction and the exterior maxwell equation is recast via a nonlocal integral operator p as shown in numer anal macrosc model micromagnet submitted for publication analysis numerik und simulation eines relaxierten modellproblems zum mikromagnetismus doctoral thesis vienna university of technology 2003 the discretization leads to a nonlocal problem with piecewise constant ansatz and test functions and dense stiffness matrices with closed form formula for their entries this paper addresses the numerical solution with newton raphson schemes and the scientific computation of effective micromagnetic simulations 2004 published by elsevier b v

necessary conditions in stochastic linear quadratic problems and their applications abstract stochastic linear quadratic optimal control problems are considered a unified approach is proposed to treat the necessary optimality conditions of closed loop optimal strategies and open loop optimal controls notice that the former notion does not rely on initial wealth while the later one does our conclusions of closed loop optimal strategies are directly derived by suitable variational methods the approach to which is different from 12 11 moreover the necessary conditions for closed loop optimal strategies happen to be sufficient which takes us by surprise finally two applications are given as illustration

lipschitz continuity of optimal controls for state constrained problems this paper provides new conditions under which optimal controls are lipschitz continuous for dynamic optimization problems with functional inequality constraints a control constraint expressed in terms of a general closed convex set and a coercive cost function it is shown that the linear independence condition on active state constraints present in the earlier literature can be replaced by a less restrictive positive linear independence condition that requires linear independence merely with respect to nonnegative weighting parameters smoothness conditions on the data imposed in earlier work are also relaxed the new conditions for lipschitz continuity of optimal controls are obtained by a detailed analysis of the implications of first order optimality conditions in the form of a nonsmooth maximum principle

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

an upper bound on the number of linear relations identified from noisy data by the frisch scheme abstract the frisch scheme is one of many approaches to the identification of linear relations from noisy data solution of the associated matrix optimization problem leads to the identification of a maximal number of such relations to date no general solution procedure is known here an upper bound on the maximal number of relations that can be identified is presented the upper bound is derived using the theory of schur complements in conjunction with a result for the case where only one relation can be identified the possibility of developing a completely general solution procedure using these ideas is also briefly discussed

linear estimates for trajectories of state constrained differential inclusions and normality conditions in optimal control abstract we consider solutions to a differential inclusion x f x constrained to a compact convex set here f is a compact possibly non convex valued lipschitz continuous multifunction whose convex closure co f satisfies a strict inward pointing condition at every boundary point x given a reference trajectory x taking values in an e neighborhood of we prove the existence of a second approximating trajectory x 0 t which satisfies the linear estimate x x ac 0 t k e if one of the following two cases occurs i the initial datum x 0 x 0 is given but lies in a compact set containing only points where the boundary is smooth ii the initial point x 0 of the approximating trajectory x can be chosen arbitrarily subsequently we employ these linear ac estimates to establish conditions for normality of the generalized euler lagrange condition for optimal control problems with state constraints in which we have an integral term in the cost we finally provide an illustrative example which underlines the fact that if conditions i and ii above are not satisfied then we can find a degenerate minimizer

extended accuracy analysis of a covariance matching approach for identifying errors in variables systems a system identification method for errors in variables problems based on covariance matching was recently proposed in the first step a small amount of covariances of noisy input output data are computed and then a parametric model is fitted to these covariances in this paper the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances as an important byproduct an efficient algorithm is presented for computing the covariance matrix of the computed input output covariances

fem bem coupling for the large body limit in micromagnetics we present and analyze a coupled finite element boundary element method for a model in stationary micromagnetics the finite element part is based on mixed conforming elements for two and three dimensional settings we show well posedness of the discrete problem and present an a priori error analysis for the case of lowest order elements

the turnpike property in finite dimensional nonlinear optimal control turnpike properties have been established long time ago in finite dimensional optimal control problems arising in econometry they refer to the fact that under quite general assumptions the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces the first and the last of which being transient short time arcs and the middle piece being a long time arc staying exponentially close to the optimal steady state solution of an associated static optimal control problem we provide in this paper a general version of a turnpike theorem valuable for nonlinear dynamics without any specific assumption and for very general terminal conditions not only the optimal trajectory is shown to remain exponentially close to a steady state but also the corresponding adjoint vector of the pontryagin maximum principle the exponential closedness is quantified with the use of appropriate normal forms of riccati equations we show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method or a shooting method in particular we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector not at the initial time but at the middle of the trajectory

a covariance matching approach for identifying errors in variables systems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper a covariance matching approach is proposed to solve the identification problem it applies for general types of input signals the method utilizes a small set of covariances of the measured input output data this property applies also for some other methods such as the frisch scheme and the bias eliminating least squares method algorithmic details for the proposed method are provided user choices for example specification of which input output covariances to utilize are discussed in some detail the method is evaluated by using numerical examples and is shown to have competitive properties as compared to alternative methods

investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints in this paper we study the degeneracy phenomenon in optimal control problems with state constraints it is shown that this phenomenon occurs because of the incompleteness of the standard variants of pontryagin s maximum principle for problems with state constraints a new maximum principle containing additional information about the behavior of the hamiltonian at the endtimes is developed we also obtain some sufficient and necessary conditions for nondegeneracy and pointwise nontriviality of the maximum principle the results obtained pertain to optimal control problems with systems described by differential inclusions and ordinary differential equations

an integral type constraint qualification to guarantee nondegeneracy of the maximum principle for optimal control problems with state constraints abstract for optimal control problems involving ordinary differential equations and functional inequality state constraints the maximum principle may degenerate producing no useful information about minimizers this is known as the degeneracy phenomenon several non degenerate forms of the maximum principle valid under different constraint qualifications have been proposed in the literature in this paper we propose a new constraint qualification under which a nondegenerate maximum principle is validated in contrast with existing results our constraint qualification is of an integral type an advantage of the proposed constraint qualification is that it is verified on a larger class of problems with nonsmooth data and convex velocity sets

an indirect method in the calculus of variations this article presents a new approach to the issue of the existence of solutions to the basic problem in the calculus of variations the method is indirect and applies to certain classes of problems with slow or no growth in addition to those satisfying the traditional coercivity condition the proof hinges upon showing with the help of nonsmooth analysis that a certain value function is constant examples are given to illustrate the applicability of the results and the necessity of the hypotheses

normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints abstract there has been a longstanding interest in deriving conditions under which dynamic optimization problems are normal that is the necessary conditions of optimality nco can be written with a nonzero multiplier associated with the objective function this paper builds upon previous results on nondegenerate nco for trajectory constrained optimal control problems to provide even stronger normal forms of the conditions the nco developed may address problems with nonsmooth less regular data the particular case of calculus of variations problems is here explored to show a favorable comparison with existent results

variational approach to second order optimality conditions for control problems with pure state constraints for optimal control problems with set valued control constraints and pure state constraints we propose new second order necessary optimality conditions in addition to the usual second order derivative of the hamiltonian these conditions contain extra terms involving second order tangents to the set of feasible trajectory control pairs at the extremal process under consideration the second order necessary optimality conditions of the present work are obtained by using a variational approach in particular we present a new second order variational equation this approach allows us to make direct proofs as opposed to the classical way of obtaining second order necessary conditions by using an abstract infinite dimensional optimization problem no convexity assumptions on the constraints are imposed and optimal controls are required to be merely measurable

invariants and canonical forms for systems structural and parametric identification the basic definitions regarding invariant functions and canonical forms for an equivalence relation on a generic set are first recalled with reference to observable state space models and to the equivalence relation induced by a change of basis it is then shown how the image of a complete set of independent invariants for the considered equivalence relation can be used to parametrize a subset of canonical forms in the given set then the set of polynomial input output models of the type p z y t q z u t and the equivalence relation induced by the premultiplication of p and q by a unimodular matrix are considered and canonical forms parametrized by a complete set of independent invariants introduced since the two sets of canonical forms share common sets of complete independent invariants very simple algebraical links between state space and input output canonical forms can be deduced the previous results are used to design efficient algorithms solving the problem of the canonical structural and parametric realization and identification of generic input output sequences generated by a linear discrete time invariant multivariable system the results obtained in the identification of a real process are then reported

the set of observationally equivalent errors in variables models abstract linear dynamic errors in variables or factor models with uncorrelated noise components are considered we give a description of the set of all noise spectra which are oberservationally equivalent with respect to the second moments of observations

nonoccurrence of the lavrentiev phenomenon for many optimal control problems in this paper we study nonoccurrence of the lavrentiev phenomenon for a large class of nonconvex optimal control problems identified with the corresponding complete metric space of integrands mathcal m which satisfy a growth condition common in the literature and are lipschitzian on bounded sets we establish that for most elements of mathcal m in the sense of baire category the infimum on the full admissible class of trajectory control pairs is equal to the infimum on a subclass of trajectory control pairs whose controls are bounded by a certain constant

numerical quadratic energy minimization bound to convex constraints in thin film micromagnetics we analyze the reduced model for thin film devices in stationary micromagnetics proposed in desimone et al r soc lond proc ser a math phys eng sci 457 2016 2983 2991 2001 we introduce an appropriate functional analytic framework and prove well posedness of the model in that setting the scheme for the numerical approximation of solutions consists of two ingredients the energy space is discretized in a conforming way using raviart thomas finite elements the non linear but convex side constraint is treated with a penalty method this strategy yields a convergent sequence of approximations as discretization and penalty parameter vanish the proof generalizes to a large class of minimization problems and is of interest beyond the scope of thin film micromagnetics

pointwise second order necessary conditions for stochastic optimal controls part ii the general case this paper is the second part of our series of work to establish pointwise second order necessary conditions for stochastic optimal controls in this part we consider the general cases i e the control region is allowed to be nonconvex and the control variable enters into both the drift and the diffusion terms of the control systems by introducing four variational equations and four adjoint equations which are quite different from the case of convex control constraint we obtain the desired necessary conditions for stochastic singular optimal controls in the sense of the pontryagin type maximum principle

transformations between input output multistructural models properties and applications some general properties of recently introduced inputs output multistructural overlapping models are analysed and compared with the properties of the well known input output canonical forms algorithms for the transformation of a generic input output model to a multi structural one and for transformation between adjacent multistructural models are then proposed the use of the models in on line multivariate identification is also discussed and a numerical example given

first and second order necessary optimality conditions for controlled stochastic evolution equations with control and state constraints abstract the purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints the control acts both in the drift and diffusion terms and the control region is a nonempty closed subset of a separable hilbert space we employ some classical set valued analysis tools and theories of the transposition solution of vector valued backward stochastic evolution equations and the relaxed transposition solution of operator valued backward stochastic evolution equations to derive these optimality conditions the correction part of the second order adjoint equation which does not appear in the first order optimality condition plays a fundamental role in the second order optimality condition

comparing some classes of bias compensating least squares methods three different classes of bias compensating least squares identification methods are compared and shown to be identical it is also discussed how the user parameters in the classes can be chosen to achieve optimal accuracy of the parameter estimates

normality of the maximum principle for nonconvex constrained bolza problems we consider a bolza optimal control problem with state constraints it is well known that under some technical assumptions every strong local minimizer of this problem satisfies first order necessary optimality conditions in the form of a constrained maximum principle in general the maximum principle may be abnormal or even degenerate and so does not provide a sufficient information about optimal controls in the recent literature some sufficient conditions were proposed to guarantee that at least one maximum principle is nondegenerate cf a v arutyanov s m aseev investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints siam j control optim 35 1997 930 952 f rampazzo r b vinter a theorem on existence of neighbouring trajectories satisfying a state constraint with applications to optimal control ima 16 4 1999 335 351 f rampazzo r b vinter degenerate optimal control problems with state constraints siam j control optim 39 4 2000 989 1007 our aim is to show that actually conditions of a similar nature guarantee normality of every nondegenerate maximum principle in particular we allow the initial condition to be fixed and the state constraints to be nonsmooth to prove normality we use j yorke type linearization of control systems and show the existence of a solution to a linearized control system satisfying new state constraints defined in turn by linearization of the original set of constraints along an extremal trajectory

on the lavrentiev phenomenon for multiple integral scalar variational problems abstract we prove the non occurrence of lavrentiev gaps between lipschitz and sobolev functions for functionals of the form i u f u u u when r n r is lipschitz and belongs to a wide class of open bounded sets in r n containing lipschitz domains the lagrangian f is assumed to be either convex in both variables or a sum of functions f s a s g b s with g convex and s a s g 0 b s satisfying a non oscillatory condition at infinity we thus derive the non occurrence of the lavrentiev phenomenon for unnecessarily convex functionals of the gradient no growth conditions are assumed

local differentiability of distance functions recently clarke stern and wolenski characterized in a hilbert space the closed subsets c for which the distance function dc is continuously differentiable everywhere on an open tube of uniform thickness around c here a corresponding local theory is developed for the property of dc being continuously differentiable outside of c on some neighborhood of a point x c this is shown to be equivalent to the prox regularity of c at x which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation additional characterizations are provided in terms of dc being locally of class c 1 or such that dc 2 is convex around x for some 0 prox regularity of c at x corresponds further to the normal cone mapping nc having a hypomonotone truncation around x and leads to a formula for pc by way of nc the local theory also yields new insights on the global level of the clarke stern wolenski results and on a property of sets introduced by shapiro as well as on the concept of sets with positive reach considered by federer in the finite dimensional setting

a new variational inequality in the calculus of variations and lipschitz regularity of minimizers abstract we consider a problem of the calculus of variations of the form p minimize i x a b t x t x t d t x a x b subject to x w 1 m a b r n x t c a e x t t a b where a b r n r n r is borel measurable c is a cone is a nonempty subset of r n and is an arbitrary extended valued function we prove that if t t x satisfies a nonsmooth version of cesari s condition s then any local minimizer of p in the ac norm is lipschitz whenever is coercive the proof is obtained via a new variational inequality formulated here that holds under the extended condition s just borel measurability if is autonomous for a e t in a b w t x t x t v v t x t x t p t v 1 v 0 where p t is an absolutely continuous arc the derivative of which belongs to a suitable subdifferential of x t x t a e on a b the proof of the directional weierstrass type condition w is based on clarke s nonsmooth recent versions of the maximum principle

brief identification of static errors in variables models the rank reducibility problem the problem of identifying linear static relations from noisy data is investigated under the assumptions of the frisch scheme the work presents an attempt to simplify the search for solutions of the related rank reducibility problem the proposed approach is based on a relaxation of the original problem by means of algebraic manipulations of the non linear equations which characterize the solution set it is shown that this method can be advantageously used when particular conditions regarding the number of variables and the number of linear relations are satisfied

numerical analysis of relaxed micromagnetics by penalised finite elements some micromagnetic phenomena in rigid ferro magnetic materials can be modelled by a non convex minimisation problem typically minimising sequences develop finer and finer oscillations and their weak limits do not attain the infimal energy solutions exist in a generalised sense and the observed microstructure can be described in terms of young measures a relaxation by convexifying the energy density resolves the essential macroscopic information the numerical analysis of the relaxed problem faces convex but degenerated energy functionals in a setting similar to mixed finite element formulations the lowest order conforming finite element schemes appear instable and nonconforming finite element methods are proposed an a priori and a posteriori error analysis is presented for a penalised version of the side restriction that the modulus of the magnetic field is bounded pointwise residual based adaptive algorithms are proposed and experimentally shown to be efficient

nondegenerate necessary conditions for nonconvex optimal control problems with state constraints standard versions of the maximum principle for optimal control problems with pathwise state inequality constraints are satisfied by a trivial set of multipliers in the case when the left endpoint is fixed and lies in the boundary of the state constraint set and so give no useful information about optimal controls recent papers have addressed the problem of overcoming this degenerate feature of the necessary conditions in these papers it is typically shown that if a constraint qualification is imposed requiring existence of inward pointing velocities then sets of multipliers exist in addition to the trivial ones a simple new approach for deriving nondegenerate necessary conditions is presented which permits relaxation of hypotheses previously imposed concerning data regularity and convexity of the velocity set

optimal sampled data controls with running inequality state constraints pontryagin maximum principle and bouncing trajectory phenomenon sampled data control systems have steadily been gaining interest for their applications in automatic engineering where they are implemented as digital controllers and recently results have been obtained in optimal control theory for nonlinear sampled data control systems and certain generalizations in this paper we derive a pontryagin maximum principle for general nonlinear finite dimensional optimal sampled data control problems with running inequality state constraints in particular we obtain a nonpositive averaged hamiltonian gradient condition with the adjoint vector being a function of bounded variations our proof is based on the ekeland variational principle in general optimal control problems with running inequality state constraints are difficult to solve using numerical methods due to the discontinuities the jumps and the singular part of the adjoint vector however in our case we find that under certain general hypotheses the adjoint vector only experiences jumps at most at the sampling times and moreover the trajectory only contacts the running inequality state constraints at most at the sampling times we call this behavior a bouncing trajectory phenomenon and it constitutes the second major focus of this paper finally taking advantage of the bouncing trajectory phenomenon we numerically solve three examples with different kinds of constraints and in several dimensions