affine and bilinear systems on lie groups abstract in this paper we study affine and bilinear systems on lie groups we show that there is an intrinsic connection between the solutions of both systems such relation allows us to obtain some preliminary controllability results of affine systems on compact and solvable lie groups we also show that the controllability property of bilinear systems is very restricted and may only be achieved if the state space g is an euclidean space

reconstructing an unknown time dependent function in the boundary conditions of a parabolic pde this work investigates the parabolic inverse problem of reconstructing an unknown time dependent function in the boundary conditions from additional terminal integral or point observations a numerical scheme is developed for obtaining an approximate solution for this problem the method consists of reducing the solution of the inverse problem to a system of integral equations the properties of sinc function are then utilized for replacing the resulting integral equations by a system of linear algebraic equations several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method

identifying the diffusion coefficient by optimization from the final observation this paper deals with the inverse problem of determining a pair a u in the reaction diffusion equationu t au x x f x t with initial and boundary conditionsu x 0 email protected x u x x 0 u x x 1 0 from the final measurement data u x t z x which has important application in a large fields of applied science based on the optimal control framework the existence uniqueness and stability of the minimizer for the cost functional are established a necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced the gradient iteration algorithm is applied to the inverse problem and some numerical results are presented for various typical test examples

the method of central difference for the inverse time dependent heat source problem abstract this paper investigates the inverse problem of determining a heat source in a parabolic equation where data are given at some fixed location this problem is ill posed i e the solution if it exists does not depend continuously on the data a central difference regularization method is given and an order optimal stability estimate is obtained numerical results for several benchmark test problems indicate that the central difference regularization method is an accurate and flexible method to determine the unknown time dependent heat source

determination of a spacewise dependent heat source this paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time the spacewise dependent temperature measurement ensures that the inverse problem has a unique solution but this solution is unstable hence the problem is ill posed for this inverse problem we propose an iterative algorithm based on a sequence of well posed direct problems which are solved at each iteration step using the boundary element method bem the instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise

a mollification regularization method for the inverse spatial dependent heat source problem in this paper we consider the inverse problem of determining a heat source in a parabolic equation where data are given at a fixed time this problem is ill posed i e the solution if it exists does not depend continuously on the data the mollification method with gauss kernel is proposed to solve this problem an a priori error estimate between the exact solution and its regularized approximation is obtained moreover we also propose a new a posteriori parameter choice rule and get a good error estimate numerical results for several benchmark test problems indicate that the method is an accurate and flexible method to determine the unknown spatial dependent heat source

comments with reply on the controllability of planar bilinear systems by d e koditschek and k s narendra in the above titled study ibid vol ac 30 p 87 89 jan 1985 two classes of bilinear systems in the plane are examined and it is claimed that necessary and sufficient conditions for complete controllability of both classes are derived the commenter shows that the conditions for one of these classes are only sufficient a counterexample is given the authors briefly review their work and concede that the relevant theorem is incorrect

necessary and sufficient condition for global controllability of planar affine nonlinear systems in this correspondence we will investigate the global controllability of general planar affine nonlinear systems and present a simple necessary and sufficient condition for global controllability the analysis is carried out in detail which is based on some basic facts in planar topology such as the jordan curve theorem and in the geometrical theory of ordinary differential equations including the poincare bendixson theorem furthermore we will also discuss the global controllability for higher dimensional affine nonlinear system with a triangular like structure

identification of the pollution source from one dimensional parabolic equation models abstract consider an inverse source problem modeling the pollution source detection in a watershed the diffusion process due to the point source pollution is governed by a one dimensional linear parabolic equation with unknown source of the form t x s where s is the location and t the amplitude of point source applying a priori information about the source location and the analytic extension theory we prove the uniqueness from two interior measurements for the two kinds of boundary state one is a finite watershed model with zero neumann boundary data and the other is an infinite watershed model finally an implementable inversion algorithm together with some numerical examples are presented which shows the validity of our inversion scheme

identification of an unknown time dependent heat source term from overspecified dirichlet boundary data by conjugate gradient method the inverse problem of identifying the unknown time dependent heat source h t of the variable coefficient heat equation u t k x u x x f x h t with separable sources of the form f x h t from supplementary temperature measurement h t u 0 t at the left end of the rod is investigated the fourier method is employed to illustrate the comparison of spacewise f x and time dependent h t heat source identification problems an explicit formula for the frechet gradient of the cost functional j h u 0 h h l 2 0 t f 2 is derived via the unique solution of the appropriate adjoint problem the conjugate gradient algorithm based on the gradient formula for the cost functional is then proposed for numerical solution of the inverse source problem the algorithm is examined through numerical examples related to reconstruction of continuous and discontinuous heat sources h t when heat is transferred through non homogeneous as well as composite structures numerical analysis of the algorithm applied to the inverse source problem in typical classes of source functions is presented computational results obtained for random noisy output data show how the iteration number of the conjugate gradient algorithm can be estimated based on these results it is shown that this iteration number plays a role of a regularization parameter numerical results illustrate bounds of applicability of the proposed algorithm and also its efficiency and accuracy

identifying an unknown source in time fractional diffusion equation by a truncation method in this paper an inverse source problem for the time fractional diffusion equation is investigated we prove a conditional stability for this problem a truncation method is presented to deal with the ill posedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter numerical examples show that the proposed method is effective and stable

a meshless method for solving an inverse spacewise dependent heat source problem in this paper an effective meshless and integration free numerical scheme for solving an inverse spacewise dependent heat source problem is proposed due to the use of the fundamental solution as basis functions the method leads to a global approximation scheme in both spatial and time domains the standard tikhonov regularization technique with the generalized cross validation criterion for choosing the regularization parameter is adopted for solving the resulting ill conditioned system of linear algebraic equations the effectiveness of the algorithm is illustrated by several numerical examples

numerical solution for an inverse heat source problem by an iterative method abstract in this paper we consider a typical inverse heat source problem that is we determine two separable source terms in a heat equation from the initial and boundary data along with two additional measurements by a simple transformation the original problem is changed into a nonlinear problem and then we use an iterative method to solve it after giving an algorithm we prove some holder convergence rates for both the reconstructed heat source terms and the temperature distribution subject to certain bounds of the data numerical results show that our method is accurate and efficient

simultaneous inversion of the fractional order and the space dependent source term for the time fractional diffusion equation abstract in this paper a simultaneous identification problem of the spacewise source term and the fractional order for a time fractional diffusion equation is considered firstly under some assumption and with two different kinds of observation data for one dimensional and two dimensional time fractional diffusion equation the unique results of the inverse problem are proven by the laplace transformation method and analytic continuation technique then the inverse problems are transformed into tikhonov type optimization problems the existence of optimal solutions to the tikhonov functional is proven finally we adopt an alternating minimization algorithm to solve the optimization problems the efficiency and stability of the inversion algorithm are tested by several one and two dimensional examples

determination of a time dependent heat source under nonlocal boundary and integral overdetermination conditions abstract this paper investigates the inverse problem of finding a time dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions under some natural regularity and consistency conditions on the input data the existence uniqueness and continuously dependence upon the data of the solution are shown by using the generalized fourier method numerical tests using the crank nicolson finite difference scheme combined with an iterative method are presented and discussed

controllability aspects of quantum dynamics a unified approach for closed and open systems knowledge about to what extent quantum dynamical systems can be steered by coherent controls is indispensable for future developments in quantum technology the purpose of this paper is to analyze such controllability aspects for finite dimensional bilinear quantum control systems we use a unified approach based on lie algebraic methods from nonlinear control theory to revisit known and to establish new results for closed and open quantum systems in particular we provide a simplified characterization of different notions of controllability for closed quantum systems described by the liouville von neumann equation we derive new necessary and sufficient conditions for accessibility of open quantum systems modelled by the lindblad kossakowski master equation to this end we exploit a well studied topic of differential geometry namely the classification of all matrix lie groups which act transitively on the grassmann manifold or the punctured euclidean space for the special case of coupled spin 1 2 systems we obtain a remarkably simple characterization of accessibility these accessibility results correct and refine previous statements in the quantum control literature

an inverse problem of identifying the coefficient in a nonlinear parabolic equation abstract this paper deals with the determination of a pair p u in the nonlinear parabolic equation u t u x x p x f u 0 with initial and boundary conditions u x 0 x u x 0 u x 1 0 from the overspecified data u x t g x based on the optimal control framework the problem is transformed into a nonlinear optimization problem and the existence of the minimizer for the control functional is established the necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced since the optimal control problem is nonconvex one may not expect a unique solution in general however the local uniqueness and stability of the solution are proved which is also the main contribution of the paper

controllability properties of affine systems this paper deals with transitivity controllability of affine families of vector fields on a finite dimensional vector space v in particular we focus on affine families whose corresponding families of linear fields are transitive on v 0 and which in addition have no fixed points in v we show that such families are necessarily transitive on v and we also show that they remain transitive under small perturbations in general however affine families need not remain transitive under small perturbations for example small affine perturbations of transitive linear systems are not necessarily transitive since any affine system mathcal f naturally defines a system mathcal f r of right invariant vector fields on the semi direct product of v with gl v we also investigate transitivity properties mathcal f r our result is that if mathcal f is an affine family satisfying the preceding conditions then mathcal f r generates the full lie algebra on the semi direct product

simultaneous reconstruction of the spatially distributed reaction coefficient initial temperature and heat source from temperature measurements at different times abstract in many practical situations concerned with high temperatures pressures loads and or hostile environments certain properties of the physical medium geometry boundary and or initial conditions are not known and their direct measurement can be very inaccurate or even inaccessible in such situations one can adopt an inverse approach and try to infer the unknowns from some extra accessible measurements of other quantities that may be available however the simultaneous identification of several non constant physical properties along with initial and or boundary conditions is very challenging especially when it cannot be decoupled as it combines both nonlinear as well as ill posedness features one such new inverse problem concerning the identification of the space dependent reaction coefficient the initial temperature and the source term from measured temperatures at two instants t 1 t 2 and at the final time t where 0 t 1 t 2 t is investigated in this paper insight into the uniqueness of solution is gained by considering various particular cases moreover as in practice the input temperature data are usually noise polluted due to the errors that are inherently present their influence on the solution of inversion has to be assessed as such the least squares objective functional modelling the gap between the measured and computed data is minimized to obtain the quasi solution to the inverse problem and the frechet gradients are obtained the conjugate gradient method cgm with the fletcher reeves formula is applied to estimate the three unknown coefficients numerically numerical examples are illustrated to show that accurate and stable numerical solutions are obtained using the cgm regularized by the discrepancy principle

integration of fuzzy spatial relations in deformable models application to brain mri segmentation this paper presents a general framework to integrate a new type of constraints based on spatial relations in deformable models in the proposed approach spatial relations are represented as fuzzy subsets of the image space and incorporated in the deformable model as a new external force three methods to construct an external force from a fuzzy set representing a spatial relation are introduced and discussed this framework is then used to segment brain subcortical structures in magnetic resonance images mri a training step is proposed to estimate the main parameters defining the relations the results demonstrate that the introduction of spatial relations in a deformable model can substantially improve the segmentation of structures with low contrast and ill defined boundaries

similarity measure between fuzzy sets and between elements abstract two similarity measures are proposed one for the similarity between fuzzy sets and the other between elements in fuzzy sets with and example it is shown that the proposed measures can be used in the behavior analysis in an organization

solving an inverse parabolic problem by optimization from final measurement data we consider an inverse problem of reconstructing the coefficient q in the parabolic equation ut u q x u 0 from the final measurement u x t where q is in some subset of l1 the optimization method combined with the finite element method is applied to get the numerical solution under some assumption on q the existence of minimizer as well as the convergence of approximate solution in finite dimensional space is proven the new ingredient in this paper is that we do not need uniformly a priori bounds of h1 norm on q numerical implementations are also presented

controllability properties for finite dimensional quantum markovian master equations various notions from geometric control theory are used to characterize the behavior of the markovian master equation for n level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states it is shown that the system can be accessible but neither small time controllable nor controllable in finite time in particular if the generators of quantum dynamical semigroups are unital then the reachable sets admit easy characterizations as they monotonically grow in time the two level case is treated in detail

controllability of bilinear systems abstract the goal of this paper is to find conditions for the controllability of homogeneous in the state bilinear systems in state spaces of dimensions two and three the cases where the system matrices of such systems generate a lie algebra equal to the dimension of the state space are considered i e where the corresponding strictly bilinear system is controllable for the two dimensional case it turns out that there are only two situations when the strictly bilinear system is controllable but the homogeneous in the state bilinear system is not by checking the vector fields on the boundaries of the reachable sets obtained in these two situations one can easily determine whether the homogeneous in the state bilinear system is controllable or not provided the lie algebra of the system matrices has rank two this approach is extended to the three dimensional case and thus previously obtained results can be generalized

an inverse problem of identifying the coefficient of first order in a degenerate parabolic equation this work studies an inverse problem of determining the first order coefficient of degenerate parabolic equations using the measurement data specified at a fixed internal point being different from other ordinary parameter identification problems in parabolic equations in our mathematical model there exists degeneracy on the lateral boundaries of the domain which may cause the corresponding boundary conditions to go missing by the contraction mapping principle the uniqueness of the solution for the inverse problem is proved a numerical algorithm on the basis of the predictor corrector method is designed to obtain the numerical solution and some typical numerical experiments are also performed in the paper the numerical results show that the proposed method is stable and the unknown function is recovered very well the results obtained in the paper are interesting and useful and can be extended to other more general inverse coefficient problems of degenerate pdes

simultaneous reconstruction of space dependent heat transfer coefficients and initial temperature abstract many complex physical phenomena and engineering systems e g in heat exchanges reflux condensers combustion chambers nuclear vessels etc due to the high temperatures high pressures hostile environment involved possess certain properties which are inaccessible to measure and therefore their influence determination using inverse analysis is very important and desirable in this spirit the purpose of this paper is to mathematically formulate and analyse a new inverse problem in which given measurements of temperature at two different instants it is required to obtain the space dependent heat transfer coefficients htcs and the initial temperature this simultaneous identification is challenging since it is both nonlinear and ill posed the uniqueness of solution is established based on the max min principle for parabolic equations and the contraction mapping principle for the existence and uniqueness of a fixed point the novel inverse mathematical model that is proposed offers appropriate scientific guidance to the polymer heat transfer processing industry as to which data to measure provide in order to be able to reliably determine the desirable htcs along with the initial temperature which is in general unknown furthermore for the reconstruction the surface htc is determined separately whilst the variational formulation is introduced for the simultaneous determination of the domain htc and the initial temperature the frechet gradient of the minimizing objective functional is derived the numerical reconstruction process is based on the conjugate gradient method cgm regularized by the discrepancy principle accurate and stable numerical solutions are obtained even in the presence of noise in the input temperature data since noisy data are invented the study models realistic practical situations in which temperature measurements recorded using sensors or thermocouples are inherently contaminated with random noise

an inverse problem of determining the implied volatility in option pricing in the black scholes world there is the important quantity of volatility which cannot be observed directly but has a major impact on the option value in practice traders usually work with what is known as implied volatility which is implied by option prices observed in the market in this paper we use an optimal control framework to discuss an inverse problem of determining the implied volatility when the average option premium namely the average value of option premium corresponding with a fixed strike price and all possible maturities from the current time to a chosen future time is known the issue is converted into a terminal control problem by green function method the existence and uniqueness of the minimum of the control functional are addressed by the optimal control method and the necessary condition which must be satisfied by the minimum is also given the results obtained in the paper may be useful for those who engage in risk management or volatility trading

identification of discontinuous parameters in flow equations a problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered general theorems on existence and convergence of galerkin approximations are proved in l 1 setting classes of functions of bounded variation are discussed and the variation estimates are obtained a double discretization method with the variations constraints is used in two and three dimensional problems and the numerical experiments are presented

a note on the existence and stability of an inverse problem for a sis model abstract in this note we discuss the existence and stability of an inverse problem arising from the determination of the reaction coefficients for an sis model the study is motivated by a remark regarding the final discussion of the recent paper by xiang and liu 2015 the weak assumption of the work of h xiang and b liu is that the proofs of existence and stability results are valid only for the one dimensional case here we introduce an appropriate framework which is also valid in the multidimensional case and that generalizes the previous results

the method of simplified tikhonov regularization for dealing with the inverse time dependent heat source problem this paper investigates the inverse problem of determining a heat source using a parabolic equation where data are given at some fixed location the problem is ill posed i e the solution if it exists does not depend continuously on the data a simplified tikhonov regularization method is given and an order optimal stability estimate is obtained a numerical example shows that the regularization method is effective and stable

an inverse problem for computing a leading coefficient in the sturm liouville operator by using the boundary data abstract we consider an inverse problem for identifying a leading coefficient x in x y x q x y x h x which is known as an inverse coefficient problem for the sturm liouville operator we transform y x to u x t 1 t y x and derive a parabolic type pde in a fictitious time domain of t then we develop a lie group adaptive method lgam to find the coefficient function x when x is a continuous function of x we can identify it very well by giving boundary data of y y and the efficiency of lgam is confirmed by comparing the numerical results with exact solutions although the data used in the identification are limited we can provide a rather accurate solution of x

global exact quadratization of continuous time nonlinear control systems we consider a class denoted by cal q of the nonlinear control systems which can be densely represented as a subsystem of a certain kind of quadratic system namely a quadratic target we say that a system in cal q undergoes a globally exact quadratization here globally adds up to a slight extension of the notion of c infty immersion of systems namely a dense immersion which amounts to saying that it is defined on the whole manifold of the system states except possibly a zero measure set it is proven that the class cal q includes all systems characterized by vector fields whose components are analytic integral closed form functions icffs the result is first proven for algebraic system functions by means of a constructive proof and next extended up to analytic icffs for nonanalytic icffs a weaker result is proven as well also the case of a partially observed system is considered as well as the internal structure of every quadratic representation which is proven to be alwa

modeling and control of quantum systems an introduction the scope of this work is to provide a self contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems as well as a brief survey on the main approaches to control synthesis while part of the existing theory especially in the open loop setting stems directly from classical control theory most notably geometric control and optimal control a number of tools specifically tailored for quantum systems have been developed since the 1980s in order to take into account their distinctive features the probabilistic nature of atomic scale physical systems the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback design problems the relevant dynamical models for both closed and open quantum systems are presented along with the main results on their controllability and stability a brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies

the controllability of planar bilinear systems recent results concerning the controllability of planar bilinear systems are summarized the results are then used to characterize the controllability behavior of the homogeneous and general bilinear system in r 2

controllability in codimension one abstract local and global controlability of analytic affine control systems with an arbitrary number of controls are studied assuming strong accessibility of and codimension one of the lie algebra t generated by the input vector fields i e dim t p n 1 at every p m controls are assumed to have no a priori bound from the study of the set h where a necessary condition for local controllability at a point is verified and assuming some transversality relations an easy to verify geometric condition is proved h is a submanifold and is locally controllable at every point of h outside a codimension one submanifold a geometric sufficient condition for global controllability on simply connected manifolds is then obtained if every leaf of t intersects the manifold h and some transversality relations including those involved in the local condition are verified is globally controllable

an inverse radiative coefficient problem arising in a two dimensional heat conduction equation with a homogeneous dirichlet boundary condition in a circular section abstract in this study we investigate the well posedness of the solution of an optimal control problem related to a nonlinear inverse coefficient problem problems of this type have important applications in several fields of applied science unlike other terminal control problems the observation data are only given for a fixed direction rather than for the whole domain which may make the conjugate theory for parabolic equations ineffective moreover the coefficients in our model are singular so we propose some weighted sobolev spaces based on the optimal control framework the problem is transformed into an optimization problem and the existence of the minimizer is established after deducing the necessary conditions that must be satisfied by the minimizer we prove the uniqueness and stability of the minimizer following a minor modification of the cost functional and imposing some a priori regularity conditions on the forward operator we obtain the convergence of the minimizer for the noisy input data considered in this study the results obtained in this study are interesting and useful and they can be extended to more general parabolic equations with singular coefficients

on fuzzy distances and their use in image processing under imprecision abstract this paper proposesa classification of fuzzy distances with respect to the requirements needed for applications in image processing under imprecision we distinguish on the one hand distances that basically compare only the membership functions representing the concerned fuzzy objects and on the other hand distances that combine spatial distance between objects and membership functions to our point of view the second class of methods finds more general applications in image processing since these methods take into account both spatial information and information related to the imprecision attached to the image objects new distances based on mathematical morphology are proposed in this second class

local controllability of nonlinear systems abstract the local controllability of control systems with an arbitrary number of controls is considered first on an open set and then at a given point necessary conditions are derived concerning the lie algebra t generated by the input vector fields and applied to gradient systems the main results are a geometric sufficient condition for local controllability at a point and an equivalent condition based on the computation of lie brackets assuming t to be n 1 dimensional

recovery of a space dependent vector source in anisotropic thermoelastic systems abstract we investigate the theoretical and numerical determination of a space dependent vector source load in an anisotropic thermoelastic system of type iii from the knowledge of an additional final time measurement the uniqueness of a solution to this inverse source problem is proved for various assumptions made on the convolution kernel a convergent and stable iterative algorithm is proposed for the recovery of the unknown vector source in the linear case and at the same time a stopping criterion is also given three numerical experiments are considered to validate the properties of the proposed iterative procedure and the regularizing stabilizing character of the corresponding stopping criterion the numerical experiments carried out showed that it exists a certain limitation of the method with respect to the recovery of non symmetric sources

controllability of switched bilinear systems the controllability of switched bilinear systems sblss is considered three kinds of controllabilities including weak controllability approximate controllability and global controllability are investigated one by one sets of easily verifiable sufficient conditions are obtained for each case which are applicable to a large class of switched bilinear systems

a new numerical method for the inverse source problem from a bayesian perspective in this work a new numerical method for the inverse problem of determining a spacewise dependent heat source for a parabolic heat equation is developed we reconstruct the unknown heat source by an augmented tikhonov regularization a tr method derived from a bayesian perspective the a tr method could determine the regularization parameter and detect the noise level automatically numerical results for several benchmark test problems indicate that the a tr method is an accurate and flexible method to determine the unknown spacewise dependent heat source copyright 2010 john wiley sons ltd

on the controllability of piecewise linear hypersurface systems this paper investigates the global controllability of piecewise linear hypersurface systems which are defined as control systems that are subject to affine dynamics on each of the components of a finite polyhedral partition various new tools are developed for the study of the problem including a classification of the facets of the polyhedra in the partition necessary and sufficient conditions for complete controllability are obtained via the study of a suitably defined controllability connection matrix of polyhedra

n dimensional controllability with n 1 controls let m be a connected real analytic n dimensional manifold f g 1 g n 1 be complete real analytic vector fields on m which are linearly independent at some point of m and u 1 u n 1 be real valued controls consider the controllability of the system dot x t f x t sum min i 1 max n 1 u i t g i x t x 0 x 0 in m necessary and sufficient conditions are given so that this system is controllable on any simply connected domain d contained in m on which g 1 g n 1 are linearly independent these conditions depend on the computation of lie brackets at those points where f g 1 g n 1 are linearly dependent

approximate reflectional symmetries of fuzzy objects with an application in model based object recognition this paper is devoted to the study of reflectional symmetries of fuzzy objects we introduce a symmetry measure which defines the degree of symmetry of an object with respect to a given plane it is computed by measuring the similarity between the original object and its reflection the choice of an appropriate measure of comparison is based on the desired properties of the symmetry measure then an algorithm for computing the symmetry plane of fuzzy objects is proposed this is done using an optimization technique in the space of plane parameters finally we illustrate our approach with an application where the symmetry measure is used as an attribute in graph matching for model based object recognition

reachability of a set of facets for linear affine systems with n 1 inputs this note provides new necessary and sufficient conditions for an n dimensional linear affine system with n 1 inputs to reach an exit facet or set of exit facets of a simplex the conditions reduce the original np hard necessary and sufficient conditions to a set of at most n lp problems

on the characterization of the controllability property for linear control systems on nonnilpotent solvable three dimensional lie groups abstract in this paper we show that a complete characterization of the controllability property for linear control system on three dimensional solvable nonnilpotent lie groups is possible by the larc and the knowledge of the eigenvalues of the derivation associated with the drift of the system

local controllability along a reference trajectory abstract local controllability along a reference trajectory of analytic and smooth affine single input control systems without any a priori bounds on the control is considered and a geometric proof of a version of the hermes conjecture is given

similarity and symmetry measures for convex shapes using minkowski addition this paper is devoted to similarity and symmetry measures for convex shapes whose definition is based on minkowski addition and the brunn minkowski inequality this means in particular that these measures are region based in contrast to most of the literature where one considers contour based measures all measures considered in this paper are invariant under translations furthermore they can be chosen to be invariant under rotations multiplications reflections or the class of affine transformations it is shown that the mixed volume of a convex polygon and a rotation of another convex polygon over an angle spl theta is a piecewise concave function of spl theta this and other results of a similar nature form the basis for the development of efficient algorithms for the computation of the given measures various results obtained in this paper are illustrated by experimental data although the paper deals exclusively with the two dimensional case many of the theoretical results carry over almost directly to higher dimensional spaces

estimation of boundary condition of two dimensional nonlinear pde with application to continuous casting abstract solidification heat transfer process of billet is described by nonlinear partial differential equation pde due to the poor productive environment the boundary condition of this nonlinear pde is difficult to be fixed therefore the identification of boundary condition of two dimensional nonlinear pde is considered this paper transforms the identification of boundary condition into a pde optimization problem the lipchitz continuous of the gradient of cost function is proved based on the dual equation in order to solve this optimization problem this paper presents a modified conjugate gradient algorithm and the global convergence of which is analyzed the results of the simulation experiment show that the modified conjugate gradient algorithm obviously reduces the iterative number and running time due to the ill posedness of the identification of boundary condition this paper combines regularization method with the modified conjugate gradient algorithm the simulation experiment illustrates that regularization method can eliminate the ill posedness of this problem finally the experimental data of a steel plant illustrate the validity of this paper s method

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

a tikhonov type method for solving a multidimensional inverse heat source problem in an unbounded domain in this study we prove a stability estimate for an inverse heat source problem in the n dimensional case we present a revised generalized tikhonov regularization and obtain an error estimate numerical experiments for the one dimensional and two dimensional cases show that the revised generalized tikhonov regularization works well

stabilization of bilinear sparse matrix control systems using periodic inputs abstract in this brief paper using results from the theory of averaging of bilinear systems we provide a graph theoretic characterization for the existence of periodic control inputs that stabilize a sparse matrix system to the origin in particular we introduce a class of extensions to the directed graph corresponding to a given sparse matrix system which when contains a stable sparse matrix system implies that the original system is stabilizable using periodic inputs when this condition holds we provide a systematic procedure for designing such controllers our technical approach combines ideas from the theory of bilinear control systems and averaging theory with graph theoretic results

on global controllability of planar affine nonlinear systems with a singularity this paper is concerned with the global controllability of planar affine nonlinear systems with a singular point by using some recent developed methods a necessary and sufficient condition is obtained which can also be viewed as a generalization of the corresponding result in the book by nikitin s nikitin global controllability and stabilization of nonlinear systems world scientific publishing co pte ltd singapore 1994

a regularized optimization method for identifying the space dependent source and the initial value simultaneously in a parabolic equation in this paper a regularized optimization method is proposed for identifying the space dependent source and the initial value simultaneously in an inverse parabolic equation problem from two over specified measurements at different instants of time the solvability of the direct problem is presented and then the inverse problem is formulated into a regularized optimization problem for the stable identification of both the source term and the initial value based on a sequence of well posed direct problems solved by the finite element method a numerical scheme formulated into a linear system is proposed to implement the regularized optimization problem numerical results of three examples show that the proposed method is efficient and robust with respect to data noise

reachable sets and controllability of bilinear time invariant systems a qualitative approach this paper is concerned with a qualitative method for the study of reachable sets and controllability of bilinear time invariant systems a nonlinear decomposition technique which reduces the solution of the problem to the analysis of the qualitative behavior of a finite number of linear uncontrolled systems is introduced special consideration is given to the homogeneous bilinear systems with commutative matrices two and three dimensional examples are discussed

the reachable set of a linear endogenous switching system in this work switching systems are named endogenous when their switching pattern is controllable linear endogenous switching systems can be considered as a particular class of bilinear control systems the key idea is that both types of systems are equivalent to polysystems i e to systems whose flow is piecewise smooth the reachable set of a linear endogenous switching system can be studied consequently the main result is that in general it has the structure of a semigroup even when the lie algebra rank condition is satisfied since the logic inputs cannot reverse the direction of the flow the adaptation of existing controllability criteria for bilinear systems is straightforward

on the detection of the axes of symmetry of symmetric and almost symmetric planar images a simple algorithm is presented for finding all the axes of symmetry of symmetric and almost symmetric planar images having nonuniform gray level intensity images the technique which can also be used in conjunction with planar curves is based on the identification of the centroids of the given image and other related sets of points followed by a maximization of a specially defined coefficient of symmetry owing to the nature of the required procedures which are strictly based on the computation of mean values the method is not particularly affected by the presence of noise and is especially suited for application in conjunction with digitized figures

identifying the radiative coefficient of an evolutional type heat conduction equation by optimization method this paper studies an evolutional type inverse problem of identifying the radiative coefficient of heat conduction equation when the over specified data is given problems of this type have important applications in several fields of applied science being different from other ordinary inverse coefficient problems the unknown coefficient in this paper depends on both the space variable x and the time t based on the optimal control framework the inverse problem is transformed into an optimization problem and a new cost functional is constructed in the paper the existence uniqueness and stability of the minimizer of the cost functional are proved and the necessary conditions which must be satisfied by the minimizer are also given the results obtained in the paper are interesting and useful and can be extended to more general parabolic equations

application of the restrained optimal perturbation method to study the backward heat conduction problem in this paper a restrained optimal perturbation method is firstly proposed to solve the backward heat conduction problem the initial temperature distribution will be identified from the overspecified data a regularization term is introduced in the objective functional for overcoming the ill posedness of this problem spectral projected gradient algorithm is used to solve the optimal problem and we give the sensitivity analysis of the initial value the results of numerical experiments are also presented

two regularization strategies for an evolutional type inverse heat source problem this paper investigates an evolutional type inverse problem of determining an unknown heat source function in heat conduction equations when the solution is known in a discrete point set being different from other ordinary inverse source problems which often rely on only one variable the unknown coefficient in this paper depends not only on the space variable x but also on time t two regularization strategies which are called the time semi discrete scheme tsds and the integral reconstruction scheme irs respectively are proposed to deal with such a problem by the tsds the inverse problem is transformed into a sequence of stationary inverse problems and the unknown heat source is reconstructed layer by layer while the irs is to recover the source function from the situation as a whole both theoretical and numerical studies are provided two numerical algorithms on the basis of the landweber iteration are designed and some typical numerical experiments are performed in this paper the numerical results show that the proposed methods are stable and the unknown heat source is recovered very well

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

numerical reconstruction of heat fluxes this paper studies the reconstruction of heat fluxes on an inner boundary of a heat conductive system when the measurement of temperature in a small subregion near the outer boundary of the physical domain is available we will first consider two different regularization formulations for this severely ill posed inverse problem and justify their well posedness then we will propose two fully discrete finite element methods to approximate the resultant nonlinear minimization problems the existence and uniqueness of the discrete minimizers and convergence of the finite element solution are rigorously demonstrated a conjugate gradient method is formulated to solve the nonlinear finite element optimization problems numerical experiments are given to demonstrate the stability and effectiveness of the proposed reconstruction methods

solving the inverse problem of an sis epidemic reaction diffusion model by optimal control methods in this contribution a novel inverse problem on an sis epidemic reaction diffusion model is investigated by employing the optimal control methods by setting a proper regular cost functional and choosing the coefficients to be identified as control variables we embed the original inverse problem which is very difficult to solve into an optimal control problem the existence of the optimal controls and the first order necessary optimality condition satisfied by the optimal controls are established respectively in particular the local uniqueness and stability of the identification of the coefficients are proved by using analytical techniques

identification of parameters in distributed parameter systems by regularization identification of spatially varying parameters in distributed parameter systems from noisy data is an ill posed problem the concept of regularization widely used in solving linear fredholm integral equations is developed for the identification of parameters in distributed parameter systems a general regularization identification theory is first presented and then applied to the identification of parabolic systems the performance of the regularization identification method is evaluated by numerical experiments on the identification of a spatially varying diffusivity in the diffusion equation

the truncation method for identifying the heat source dependent on a spatial variable this paper deals with the ill posed problem of determining an unknown source depending only on the spatial variable in the heat equation in this problem the truncation method is employed to get the regularization solution moreover the holder type error estimate is also obtained between this regularization solution and the exact solution various typical examples are given to verify the efficiency and accuracy of the proposed method

identification of time dependent source terms and control parameters in parabolic equations from overspecified boundary data abstract this paper presents a semigroup approach for inverse source problems for the abstract heat equation when the measured output data is given in subject to the integral overspecification over the spatial domain the existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed such representation permits the derivation of sufficient conditions for the uniqueness of the solution also an approximation method based on the optimal homotopy analysis method oham is designed and the error estimates are discussed using graphical analysis moreover we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data the proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations the accuracy and stability of the method are discussed and compared with several finite difference techniques computational results show efficiency and high accuracy of the proposed algorithm

fuzzy morphisms between graphs a generic definition of fuzzy morphism between graphs gfm is introduced that includes classical graph related problem definitions as sub cases such as graph and subgraph isomorphism the gfm uses a pair of fuzzy relations one on the vertices and one on the edges each relation is a mapping between the elements of two graphs these two fuzzy relations are linked with constraints derived from the graph structure and the notion of association graph the theory extends the properties of fuzzy relation to the problem of generic graph correspondence we introduce two complementary interpretations of gfm from which we derive several interesting properties the first interpretation is the generalization of the notion of association compatibility the second is the new notion of edge morphism one immediate application is the introduction of several composition laws each property has a theoretical and a practical interpretation in the problem of graph correspondence that is explained throughout the paper special attention is paid to the formulation of a non algorithmical theory in order to propose a first step towards a unified theoretic framework for graph morphisms

symmetry identification of a 3 d object represented by octree an algorithm for identifying symmetry of a 3 d object given by its octree is presented and the symmetry degree a measure of object symmetry is proposed the algorithm is based on traversals of the octree obtained by the principal axis transform of an input octree an object can be in an arbitrary position and with arbitrary orientation within the octree space and a wide range of symmetries represented by groups of proper and improper rotations can be identified it is shown that the octree data structure supports these operations well especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry the operation of the algorithm is illustrated using some synthetic test objects the results which are composed of identified symmetry types and the corresponding symmetry degrees were satisfactory