homotopy perturbation method for quadratic riccati differential equation and comparison with adomian s decomposition method abstract in this paper a homotopy perturbation method is proposed to solve quadratic riccati differential equation comparisons are made between adomian s decomposition method adm and the exact solution and the proposed method the results reveal that the proposed method is very effective and simple

a further note on the robustness of output feedback control methods to modeling errors in an earlier note it was shown that designing a nonstrictly proper output feedback compensator using a model that neglects parasitic elements might lead to an unstable closed loop system even when the neglected modes are asymptotically stable the purpose of this note is to show that this instability phenomenon might take place even when the reduced order design model is strictly proper

a characterization of decentralized fixed modes in terms of transmission zeros a simple development is given to show that a linear time invariant plant has a decentralized fixed mode at if and only if is a transmission zero of certain subsystems of the plant

solving a singular system of two nonlinear odes abstract in this paper a new method is given in order to solve a singular system of two nonlinear ordinary differential equations having multiple solutions and we may give a special solution by imposing an additional condition representation of the exact solution is given in the form of series in the reproducing kernel space its approximate solution is obtained by truncating the series the error of the approximate solution is monotone decreasing in the sense of w 2 0 1 and the intrinsic merit of the method given in the paper lies in its speedy convergence some numerical examples are studied to demonstrate the accuracy of the present method

a continuous method for nonlocal functional differential equations with delayed or advanced arguments abstract in the previous works the authors presented the reproducing kernel method rkm for solving various differential equations however to the best of our knowledge there exist no results for functional differential equations the aim of this paper is to extend the application of reproducing kernel theory to nonlocal functional differential equations with delayed or advanced arguments and give the error estimation for the present method some numerical examples are provided to show the validity of the present method

he s homotopy perturbation method for a boundary layer equation in unbounded domain by means of he s homotopy perturbation method hpm an approximate solution of a boundary layer equation in unbounded domain is obtained comparison is made between the obtained results and those in open literature the results show that the method is very effective and simple

lq suboptimal decentralised controllers with disturbance rejection property for hierarchical systems this article is concerned with decentralised output regulation of hierarchical systems subject to input and output disturbances it is assumed that the disturbance can be represented as the output of an autonomous linear time invariant lti system with an unknown initial state the primary objective is to design a decentralised controller with the property that not only does it reject the degrading effect of the disturbance on the output to achieve a satisfactory steady state performance it also results in a small linear quadratic lq cost function implying a good transient behaviour to this end the underlying problem is treated in two phases in the first step a number of modified systems are defined in terms of the original system the problem of designing an lq centralised controller which stabilises all the modified systems and rejects the disturbance in the original system is considered and it is shown that this centralised controller can be found efficiently by solving a linear matrix ine

new method based on the hpm and rkhsm for solving forced duffing equations with integral boundary conditions this paper investigates the forced duffing equation with integral boundary conditions its approximate solution is developed by combining the homotopy perturbation method hpm and the reproducing kernel hilbert space method rkhsm hpm is based on the use of the traditional perturbation method and the homotopy technique the hpm can reduce nonlinear problems to some linear problems and generate a rapid convergent series solution in most cases rkhsm is also an analytical technique which can solve powerfully linear boundary value problems therefore the forced duffing equation with integral boundary conditions can be solved using advantages of these two methods two numerical examples are presented to illustrate the strength of the method

solving integro differential equations with cauchy kernel a simple method for solving the fredholm singular integro differential equations with cauchy kernel is proposed based on a new reproducing kernel space using a transformation and modifying the traditional reproducing kernel method the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space the advantage of the approach lies in the fact that on the one hand by improving the definition of traditional inner product the representation of new reproducing kernel function becomes simple and requirement for image space of operator is weakened comparing with traditional reproducing kernel method on the other hand the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives some examples are displayed to demonstrate the validity and applicability of the proposed method

elimination of fixed modes in decentralized systems by means of sampling abstract in this contribution it is shown that fixed modes in continuous time decentralized control systems can be eliminated by the use of sampling criteria are derived which distinguish the fixed modes which are still present in the sampled data system from those which are eliminated

a computational method for solving one dimensional variable coefficient burgers equation abstract the burgers equation is a simple one dimensional model of the navier stoke equation in this paper the exact solution to one dimensional variable coefficient burgers equation is obtained in the reproducing kernel space w 2 3 the exact solution is represented in the form of series the n term approximation u n t x to exact solution u t x is proved to converge to the exact solution moreover the approximate error of u n t x is monotone decreasing some numerical examples have been studied to demonstrate the accuracy of the present method results obtained by the method have been compared with the exact solution of each example and are found to be in good agreement with each other

crank nicolson finite difference method for two dimensional diffusion with an integral condition a finite difference method which is based on the 5 5 crank nicolson cn scheme is developed for solving the heat equation in two dimensional space with an integral condition replacing one boundary condition the fully implicit method developed here is unconditionally stable and it has reasonable accuracy while the conditionally stable fully explicit schemes use less amount of central processor cpu time the unconditional stability of the scheme developed in this article for every diffusion number is significant some numerical tests are presented and the accuracy obtained and the cpu time required are reported error estimates derived in the maximum norm are tabulated

time complexity of decentralized fixed mode verification given an interconnected system this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode dfm it is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system it is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication this work concludes that the identification of distinct dfms by means of a deterministic algorithm rather than a randomized one is computationally very easy although the existing algorithms for solving this problem would wrongly imply that it is cumbersome this note provides not only a complexity analysis but also an efficient algorithm for tackling the underlying problem

design of distributed lti observers for state omniscience consider that an autonomous linear time invariant lti plant is given and that each member of a network of lti observers accesses a portion of the output of the plant the dissemination of information within the network is dictated by a pre specified directed graph in which each vertex represents an observer this paper proposes a distributed estimation scheme that is a natural generalization of consensus in which each observer computes its own state estimate of the plant using only the portion of the output vector accessible to it and the state estimates of other observers that according to the graph are available to it unlike straightforward high order solutions in which each observer broadcasts its measurements throughout the network the average dimension of the state of each observer in the proposed scheme does not exceed the order of the plant plus one we determine necessary and sufficient conditions for the existence of a parameter choice for which the proposed scheme attains asymptotic omniscience of the state of the plant at all observers the conditions reduce to certain detectability requirements that imply that if omniscience is not possible under the proposed scheme then it is not viable under any other scheme including higher order lti nonlinear and time varying ones subject to the same graph

on the characterization of fixed modes in decentralized control characterizations of decentralized fixed modes in terms of remnant zeros are presented a novel criterion for testing the fixed modes is obtained the result can be used to derive an existing algebraic criterion through a simple rank evaluation of certain matrices

generic well posedness of minimization problems with mixed smooth constraints abstract in this paper we study mathematical programming problems with mixed smooth constraints in a banach space and show that most of the problems in the baire category sense are well posed our result is a generalization of a result of a d ioffe et al a variational principle for problems with functional constraints siam j optim 12 2001 461 478 obtained for finite dimensional banach spaces it is also an extension of our recent result a j zaslavski generic well posedness of minimization problems with mixed continuous constraints nonlinear anal doi 10 1016 j na 2005 10 032 which was obtained for mathematical programming problems with continuous constraints

an efficient computational method for second order boundary value problems of nonlinear differential equations we will discuss a class of boundary value problems bvps of nonlinear differential equations in the reproducing kernel space the existence of the solution and a iterative method are established for the kind of problems some examples are displayed to demonstrate the computation efficiency of the method

solving singular boundary value problems of higher even order in this paper we present a new algorithm to solve a kind of singular boundary value problems of higher even order based on the theory of numerical analysis in the reproducing kernel space w 2 2 m 3 0 1 singular boundary value problem of sixth order has been discussed for the problem u 6 x a x u 4 x b x u x c x u x f x 0

almost every convex or quadratic programming problem is well posed we provide an abstract principle aimed at proving that classes of optimization problems aretypically well posed in the sense that the collection of ill posed problems within each class is s porous as a consequence we establish typical well posedness in the above sense for unconstrained minimization of certain classes of functions e g convex and quasi convex continuous as well as of convex programming with inequality constraints we conclude the paper by showing that the collection of consistent ill posed problems of quadratic programming of any fixed size has lebesgue measure zero in the corresponding euclidean space

decentralized stabilization and pole assignment for general proper systems considered is the problem of finding existence conditions and a controller synthesis procedure using decentralized control for assigning the poles of a linear time invariant proper system described by a state space model c a b d where no assumption is made regarding the structure of d this problem has direct application to the decentralized stabilization problem decentralized robust servomechanism problem etc and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block diagonal structure

a measure for the decentralized assignability of eigenvalues abstract the results of 7 are generalized to produce a continuous measure of how close a mode is to being a decentralized fixed mode 13 implications of this measure on controller design are also explored

a variational principle for problems with functional constraints in this paper we show that in several important classes of optimization problems like mathematical programming with k smooth data quadratic programming in a hilbert space convex programming in a banach space semi infinite programming and optimal control of linear systems with quadratic cost most of the problems in the baire category sense are well posed this is derived from a general variational principle for problems with functional constraints

fully implicit finite differences methods for two dimensional diffusion with a non local boundary condition three new fully implicit methods which are based on the 5 5 crank nicolson method the 5 5 n h noye hayman implicit method and the 9 9 n h implicit method are developed for solving the heat equation in two dimensional space with non local boundary conditions the latter is fourth order while the others are second order while the implicit methods developed here like the scheme based on the standard implicit backward time centered space btcs method use a large amount of central processor cpu time the high accuracy of the new fourth order fully implicit scheme is significant like the btcs method the new methods are also unconditionally stable

numerical solution of one dimensional burgers equation using reproducing kernel function this paper presents a numerical method for one dimensional burgers equation by the hopf cole transformation and a reproducing kernel function abbreviated as rkf the numerical solution is given as explicit integral expressions with the rkf at each time step so that the computation is fully parallel the stability and error estimates are derived numerical results for some test problems are presented and compared with the exact solutions some numerical results are also compared with the results obtained by other methods the present method is easily implemented and effective

a new algorithm for a class of singular boundary value problems abstract in this paper we present a new algorithm to solve a class of singular boundary value problems in the reproducing kernel space w 2 3 0 1 the algorithm is efficiently applied to solving some model problems with the comparison between the numerical solutions and the exact solutions it is demonstrated by the numerical examples that this algorithm is of high precision

the exact solution of a class of volterra integral equation with weakly singular kernel abstract in this paper the weakly singular volterra integral equations with an infinite set of solutions are investigated among the set of solutions only one particular solution is smooth and all others are singular at the origin the numerical solutions of this class of equations have been a difficult topic to analyze and have received much previous investigation the aim of this paper is to present a numerical technique for giving the approximate solution to the only smooth solution based on reproducing kernel theory applying weighted integral we provide a new definition for reproducing kernel space and obtain reproducing kernel function using the good properties of reproducing kernel function the only smooth solution is exactly expressed in the form of series the n term approximate solution is obtained by truncating the series meanwhile we prove that the derivative of approximation converges to the derivative of exact solution uniformly the final numerical examples compared with other methods show that the method is efficient

technical communique a graph theoretic method to find decentralized fixed modes of lti systems this paper deals with the decentralized pole assignability of interconnected systems by means of linear time invariant lti controllers a simple graph theoretic approach is proposed to identify the distinct decentralized fixed modes dfms of the system i e the unrepeated modes which cannot be moved by means of a lti decentralized controller the state space representation of the system is transformed to the decoupled form using a proper change of coordinates for any unrepeated mode a matrix is then computed which resembles the transfer function matrix of the system at some point in the complex plane a bipartite graph is constructed accordingly in terms of the computed matrix now the problem of verifying if this mode is a dfm of the system reduces to checking if the constructed graph has a complete bipartite subgraph with a certain property the sole restriction of this work is that it is only capable of identifying the distinct dfms of a system however it is axiomatic that most of the modes of the real world systems are normally distinct the primary advantage of the present paper is its simplicity compared to the existing ones which often require evaluating the rank of several matrices

extrapolation method of iterated collocation solution for two dimensional nonlinear volterra integral equations in this paper we study the numerical solution of two dimensional nonlinear volterra integral equation by collocation and iterated collocation method asymptotic error expansion of iterated collocation solution is obtained using richardson s extrapolation we show that the accuracy of numerical solution in the iterated collocation method can be improved greatly some numerical examples are given to illustrate this theory

robust stabilizability verification of polynomially uncertain lti systems this paper investigates the stabilizability of uncertain linear time invariant lti systems via structurally constrained controllers first an lti uncertain system is considered whose state space matrices depend polynomially on the uncertainty vector defined over some region it is shown that if the system is stabilizable by a structurally constrained controller in one point belonging to the region then it is stabilizable by a controller with the same structure in all points belonging to the region except for those located on an algebraic variety thus if a system is stabilizable via a constrained controller at the nominal point then it is almost always stabilizable at any operating point around the nominal model it is also shown how this algebraic variety or the dominant subvariety of it can be computed efficiently the results obtained in this paper encompass a broad range of the existing results in the literature on robust stability of the lti systems in addition to new ones

solving singular two point boundary value problem in reproducing kernel space in this paper we present a new method for solving singular two point boundary value problem for certain ordinary differential equation having singular coefficients its exact solution is represented in the form of series in reproducing kernel space in the mean time the n term approximation u n x to the exact solution u x is obtained and is proved to converge to the exact solution some numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

iterative solution of nonlinear equations with strongly accretive operators abstract let e be a real banach space with a uniformly convex dual suppose t e e is a strongly accretive map with bounded range such that for each e the equation tx has a solution in e it is proved that each of the two well known fixed point iteration methods the mann and ishikawa iteration methods under suitable conditions converges strongly to a solution of the equation tx furthermore our method shows that such a solution is necessarily unique explicit error estimates are given our results resolve in the affirmative an open problem j math anal appl 151 no 2 1990 460 and generalize important known results

densely defined selections of multivalued mappings rather general suficient conditions are found for a given multivalued mapping f x y to possess an upper semicontinuous and compactvalued selection g which is defined on a dense g subset of the domain of f the case when the selection g is single valued and continuous is also investigated the results are applied to prove some known as well as new results concerning generic differentiability of convex functions lavrentieff type theorem generic well posedness of optimization problems and generic nonmultivaluedness of metric projections and antiprojections

the exact solution for solving a class nonlinear operator equations in the reproducing kernel space in this paper the author will introduce the sobolev space w 1 2 w n firstly and then give the reproducing properties of the space w 1 2 w n as these results of those a class of the nonlinear operator equation n i 1 m i j 1 a i ju f is transformed to the n dimensional linear operator equation au f finally we also give the exact solution of this nonlinear operator equation

solving singular nonlinear second order periodic boundary value problems in the reproducing kernel space abstract in this paper we present a new method for solving a singular nonlinear second order periodic boundary value problem its analytical solution is represented in the form of series in the reproducing kernel space in the mean time the n term approximation u n x to the analytical solution u x is obtained and is proved to converge to the analytical solution some numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method indicate the method is simple and effective

brief paper control of continuous time lti systems by means of structurally constrained controllers this paper deals with the characterization of the fixed modes of multi channel systems with respect to linear time invariant lti structurally constrained controllers fixed modes can be found numerically for any lti system with respect to any given control structure using a random number generator the existing analytical methods however are not capable of characterizing the fixed modes in the most general case of non strictly proper systems with non block diagonal i e overlapping control structure efficiently the notion of a decentralized overlapping fixed mode dofm is introduced in this paper to address the above problem in the most general case to this end the knowledge of the overlapping control structure is translated into a bipartite graph whose vertices correspond to the input and output vectors of various control channels an efficient technique is applied to the obtained graph to identify the dofms of the system it is to be noted that a system is stabilizable via an appropriate lti decentralized overlapping controller if and only if it does not have any unstable dofm moreover it is shown how those modes which are not dofms can be placed freely in the complex plane using a proper lti decentralized overlapping controller the efficacy of this work is demonstrated through an example

on decentralized dynamic pole placement and feedback stabilization in this paper we study the feedback control problem using an r channel decentralized dynamic feedback control scheme we will develop the theory in the behavioral framework using this framework we introduce an algebraic parameterization of the space of all possible feedback compensators having a bounded mcmillan degree and we show that this parameterization has the structure of an algebraic variety we define the pole placement map for this problem and we give exact conditions when this map is onto and almost onto finally we provide new necessary and sufficient conditions which guarantee that the set of stabilizable plants is a generic set

second order boundary value problems with integral boundary conditions abstract in this paper we investigate the existence of positive solutions of nonlocal second order boundary value problems with integral boundary conditions

how to solve nonlinear operator equation a v2 cv f in this paper we discuss the problems of how to solve linear operator equation in hilbert spaces and a kind of nonlinear operator equation a v 2 cv f in reproducing kernel space w 2 1 a b for linear operator equation we obtain a criterion about the existence of solutions if it has solutions we get the analytic representation of its minimum norm solution and the structure of its solution space for nonlinear operator equation a v 2 cv f by using the method of solving linear operator equation one exact solution is given besides we obtain the representation of its solution set final examples show our methods are effective

how to solve the equation aubu cu f in this paper we first discuss the problem of how to solve a continuous linear operator equation in separable hilbert space we give the necessary and sufficient condition for the existence of solution and the method to decide the existence for solutions of the equation is also given if the solution exists we give the representation and approxima of the minimal normal solution of the equation and formula are obtained we conduct some research of how to solve the operator equation aubu cu f we give the factorization method and characteristic value method to solve such an equation

generic well posedness of minimization problems with mixed continuous constraints in this paper we study mathematical programming problems with mixed constraints in a banach space and show that most of the problems in the baire category sense are well posed our result is a generalization of a result of ioffe et al siam j optim 12 2001 461 478 obtained for finite dimensional banach spaces

error estimation for the reproducing kernel method to solve linear boundary value problems in the previous works the authors presented the reproducing kernel method rkm for solving various boundary value problems however an effective error estimation for this method has not yet been discussed the aim of this paper is to fill this gap in this paper we shall give the error estimation for the reproducing kernel method to solve linear boundary value problems

the exact solution and stability analysis for integral equation of third or first kind with singular kernel in this paper we give representation of exact solution for integral equation of third or first kind with singular kernel by the form of series in the reproducing kernel space the n term approximate to the exact solution is obtained by truncating the series and the error is monotone decreasing with increasing item of the n term approximate solution the solution is stable in the reproducing kernel space some numerical examples are studied to demonstrate the accuracy of the present method

on algebraic properties of general proper decentralized abstract the new concepts of the decentralized output feedback variable polynomial the decentralized output feedback cycle index of general proper systems and the geometric multiplicities of decentralized fixed modes are introduced their computational methods and some algebraic properties are presented it is shown that the decentralized output feedback cycle index of a general proper system is equal to one when the system has no fixed modes or equal to the maximum of the geometric multiplicities of its decentralized fixed modes it is also shown that almost all decentralized output feedback can be used to make the zeros of the decentralized variable polynomial distinct and disjoint from any given finite set of points on the complex plane

a numerical method for singularly perturbed turning point problems with an interior layer the objective of this paper is to present a numerical method for solving singularly perturbed turning point problems exhibiting an interior layer the method is based on the asymptotic expansion technique and the reproducing kernel method rkm the original problem is reduced to interior layer and regular domain problems the regular domain problems are solved by using the asymptotic expansion method the interior layer problem is treated by the method of stretching variable and the rkm four numerical examples are provided to illustrate the effectiveness of the present method the results of numerical examples show that the present method can provide very accurate approximate solutions

optimal periodic feedback design for continuous time lti systems with constrained control structure this paper aims to design a high performance controller with any predefined structure for continuous time lti systems the control law employed is the generalized sampled data hold function gshf which can have any special form e g polynomial exponential piecewise constant etc the gshf is first written as a linear combination of a set of basis functions obtained in accordance with its desired form and structure the objective is to find the coefficients of this linear combination such that a prespecified linear quadratic performance index is minimized a necessary and sufficient condition for the existence of such gshf is first obtained in the form of matrix inequality which can be solved by using the existing methods to obtain a set of stabilizing initial values for the coefficients or to conclude the non existence of such structurally constrained gshf an efficient algorithm is then presented to compute the optimal coefficients from their initial values so that the performance index is minimi

brief paper simultaneous lq control of a set of lti systems using constrained generalized sampled data hold functions in this paper sampled data control of a set of continuous time lti systems is considered it is assumed that a predefined guaranteed continuous time quadratic cost function which is in fact the sum of the performance indices for all systems is given the main objective here is to design a decentralized periodic output feedback controller with a prespecified form e g polynomial piecewise constant exponential etc which minimizes the above mentioned guaranteed cost function this problem is first formulated as a set of matrix inequalities and then by using a well known technique it is reformulated as a lmi problem the set of linear matrix inequalities obtained provides necessary and sufficient conditions for the existence of a decentralized optimal simultaneous stabilizing controller with the prespecified form rather than a general form moreover an algorithm is presented to solve the resultant lmi problem finally the efficiency of the proposed method is demonstrated in two numerical examples

a new adi technique for two dimensional parabolic equation with an integral condition abstract nonclassical parabolic initial boundary value problems arise in the study of several important physical phenomena this paper presents a new approach to treat complicated boundary conditions appearing in the parabolic partial differential equations with nonclassical boundary conditions a new fourth order finite difference technique based upon the noye and hayman n h alternating direction implicit adi scheme is used as the basis to solve the two dimensional time dependent diffusion equation with an integral condition replacing one boundary condition this scheme uses less central processor time cpu than a second order fully implicit scheme based on the classical backward time centered space btcs method for two dimensional diffusion it also has a larger range of stability than a second order fully explicit scheme based on the classical forward time centered space ftcs method the basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyeet this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference methods the results of numerical experiments for the new method are presented the central processor times needed are also reported error estimates derived in the maximum norm are tabulated

variational principles and well posedness in optimization and calculus of variations the concluding result of the paper states that variational problems are generically solvable and even well posed in a strong sense without the convexity and growth conditions always present in individual existence theorems this and some other generic well posedness theorems are obtained as realizations of a general variational principle extending the variational principle of deville godefroy zizler

iterative reproducing kernel hilbert spaces method for riccati differential equations this paper presents iterative reproducing kernel hilbert spaces method irkhsm to obtain the numerical solutions for riccati differential equations with constant and variable coefficients representation of the exact solution is given in the w 2 2 0 x reproducing kernel space numerical solution of riccati differential equations is acquired by interrupting the n term of the exact solution also the error of the numerical solution is monotone decreasing in terms of the norm of w 2 2 0 x the outcomes from numerical examples show that the present iterative algorithm is very effective and convenient

nonlinearly weighted l1 solvability of the first kind fredholm integral equation abstract the fredholm integral equation of the first kind is a well known example of linear ill posed problems and of functional equations that do not admit of a direct analytical solution in terms of their data we show that a variational perturbation of the kernel k v x v x in an inverse problem space dual to the solution space can yield for the integral equation a maximum a posteriori direct primal solution x x i this dual space l 1 c k happens to be a certain restriction of a nonlinearly covariantly weighted l 1 space it is proved that the emerging analytical primal solution must satisfy an equivalent regularizing urysohn nonlinear integral equation with a movable bifurcation point and that it belongs also in a certain nonlinearly weighted l 1 i space invoked by l 1 c k an analytical explanation is advanced for a possible autotransformability between the first kind and second kind fredholm integral equations as a result of perturbations of k only in the dual space

the combined reproducing kernel method and taylor series for handling nonlinear volterra integro differential equations with derivative type kernel abstract the reproducing kernel method is applied to volterra nonlinear integro differential equations in this technique the nonlinear term is replaced by its taylor series the exact solution is represented in the form of series in the reproducing hilbert kernel space the approximation solution is expressed by n term summation of reproducing kernel functions some numerical examples are solved in two different spaces and parameters of n measurements of the experimental data is an indications of stability and convergence on the reproducing kernel

overlapping control systems with optimal information exchange this paper deals with the stabilizability of interconnected systems via linear time invariant lti decentralized controllers given a controllable and observable system with some distinct decentralized fixed modes dfms it is desired to find a suitable control structure in terms of information flow for it since a decentralized controller consists of a number of non interacting local controllers the objective here is to establish certain interactions between the local controllers in order to eliminate the undesirable dfms this objective is achieved by translating the knowledge of the system into some bipartite graphs then the notions of minimal sets and maximal subgraphs are introduced which lead to a simple combinatorial algorithm for solving the underlying problem the efficacy of the results obtained is demonstrated by an illustrative example

technical communique fixed modes in multivariable systems using constrained controllers a general expression is derived relating an arbitrary output feedback controller to the resulting closed loop characteristic polynomial in terms of suitably defined zero polynomials of the system this expression is then used to characterize the fixed modes of a multivariable system with respect to controllers of any desired structure

structurally constrained controller synthesis for general proper plants with application to vehicle platooning abstractthis paper considers the problem of synthesizing a static output feedback sof subject to arbitrary information structure constraints in particular the plants can be non strictly proper in such a case the existing methods are hardly applicable except few special cases a general approach that significantly differs from the existing methods is proposed that is able to deal with the most general case with the feature that both finite frequency and full frequency h infinity performance specifications can be addressed in a unified manner sufficient solvability conditions are derived in terms of a set of finite frequency positive real and strictly positive real conditions of linear matrix inequalities lmis form some frequency dependent matrices are introduced into the design with the merit of making the conditions less restrictive several numerical examples are given that demonstrate the efficacy of the proposed approach including applications to vehicle platooning

a finite difference method for the singularly perturbed problem with nonlocal boundary condition the purpose of this paper is to present a finite difference method for numerical solutions of singularly perturbed boundary value problem for second order ordinary differential equation with nonlocal boundary condition by the method of integral identities with the use exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form an exponentially fitted difference scheme on an uniform mesh is developed which is shown to be original e uniformly first order accurate in the discrete maximum norm for original problem numerical results are presented which illustrate the theoretical results

solving a nonlinear system of second order boundary value problems in this paper a method is presented to obtain the analytical and approximate solutions of linear and nonlinear systems of second order boundary value problems the analytical solution is represented in the form of series in the reproducing kernel space in the mean time the approximate solution un x is obtained by the n term intercept of the analytical solution and is proved to converge to the analytical solution some numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method indicate the method is simple and effective

stepwise stability for the heat equation with a nonlocal constraint the authors prove the stepwise stability for a finite difference scheme for the heat equation with an integral constraint the resulting matrix is nonsymmetric and does not have the usual band structure the proof is based on the method of matrix analysis the eigenvalues of several matrices are found explicitly or their location described precisely this method relies upon the relationship of the characteristic polynomials of these matrices with orthogonal polynomials

the exact solution of nonlinear operator equation aubu cu f abstract this paper is intended to discuss the problems of solving system of linear operator equations and a kind of nonlinear operator equation a u b u c u f for system of linear operator equations we obtain a criterion about the existence of solutions if it has solutions we get the analytic representation of its minimum norm solution and the structure of its solution space for nonlinear operator equation a u b u c u f with the help of the discussion on how to solve the system of linear operator equations the exact solution is given besides we obtain the representation of all its solutions

the epi distance topology continuity and stability results with applications to convex optimization problems let i x denote the proper lower semicontinuous convex functions on a banach space x equipped with the completely metrizable topology of uniform convergence of distance functions on bounded sets we show subject to some standard constraint qualifications that the operations of addition and restriction are continuous these results are applied to convex well posed optimization problems as well as to convergence of approximated solutions in infinite dimensional convex programming to linear functionals exposing convex sets and to metric projections also for any given function in i x we obtain results regarding the convergence of its inf convolution with smoothing kernels

modified homotopy perturbation method for nonlinear equations and comparison with adomian decomposition method abstract in this paper we present some efficient numerical algorithms for solving nonlinear equations based on newton raphson method by using modified homotopy perturbation method the modified adomian decomposition method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method appl math comput 145 2003 887 893 is compared with new algorithms some numerical illustrations are given to show the efficiency of algorithms

typical convex program is very well posed in this paper we consider the collection of convex programming problems with inequality and equality constraints in which every problem of the collection is obtained by linear perturbations of the cost function and right hand side perturbation of the constraints while the core cost function and the left hand side constraint functions are kept fixed the main result shows that the set of the problems which are not well posed is porous in a certain strong sense our results concern both the infinite and finite dimensional case in the last case the conclusions are significantly sharper

structurally fixed modes a notion of structurally fixed modes is introduced in the framework of decentralized control systems to identify the modes that cannot be shifted by decentralized feedback regardless of the numerical values of system parameters in this way a qualitative characterization of decentralized fixed modes is provided which is suitable for delineating decentrally stabilizable systems the characterization leads naturally to the notion of fixed modes with respect to arbitrary feedback structure constraints

comparison of homotopy perturbation method and homotopy analysis method comparison of homotopy perturbation method hpm and homotopy analysis method is made revealing that the former is more powerful than the later furthermore the hpm is further developed in this paper by applying the modern perturbation methods

brief paper robust controllability and observability degrees of polynomially uncertain systems this paper deals with the class of polynomially uncertain continuous time linear time invariant lti systems whose uncertainties belong to a semi algebraic set the objective is to determine the minimum of the smallest singular value of the controllability or observability gramian over the uncertainty region this provides a quantitative measure for the robust controllability or observability degree of the system to this end it is shown that the problem can be recast as a sum of squares sos problem in the special case when the uncertainty region is polytopic the corresponding sos formulation can be simplified significantly one can apply the proposed method to any large scale interconnected system in order to identify those inputs and outputs that are more effective in controlling the system in a robust manner this enables the designer to simplify the control structure by ignoring those inputs and outputs whose contribution to the overall control operation is relatively weak a numerical example is presented to demonstrate the efficacy of the results

an algebraic characterization of quotient decentralized fixed modes in the control of linear time invariant lti decentralized systems a decentralized fixed mode dfm is one which is immovable using an lti decentralized controller however some dfms can be moved using more complicated decentralized controllers the ones which cannot are labelled quotient dfms qdfms since they arise from a related quotient system the classical algorithm used to compute the qdfms requires two steps a partitioning of the sub systems using graph theory followed by the application of standard tools from decentralized control here the goal is to provide a more direct approach to computing them

discrete time control of continuous systems with approximate decentralized fixed modes in this paper the discrete time control of decentralized continuous time systems which have approximate decentralized fixed modes is studied it is shown that under certain conditions discrete time controllers can improve the overall performance of the decentralized control system when a linear time invariant continuous time controller is ineffective in order to obtain these conditions a quantitative measure for different types of approximate fixed modes in a decentralized system is given in this case it is shown that discrete time zero order hold zoh controllers and in particular that generalized sampled data hold functions gshf can significantly improve the overall performance of the resultant closed loop system the proposed sampled data controller is in fact a linear time varying controller for the continuous time system

application of homotopy perturbation and variational iteration methods to nonlinear heat transfer and porous media equations perturbation methods depend on a small parameter which is difficult to be found for real life nonlinear problems to overcome this shortcoming two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this article one is he s variational iteration method vim and the other is the homotopy perturbation method hpm the vim is to construct correction functionals using general lagrange multipliers identified optimally via the variational theory and the initial approximations can be freely chosen with unknown constants the hpm deforms a difficult problem into a simple problem which can be easily solved nonlinear convective radiative cooling equation nonlinear heat equation porous media equation and nonlinear heat equation with cubic nonlinearity are used as examples to illustrate the simple solution procedures comparison of the applied methods with exact solutions reveals that both methods are tremendously effective