a flow model based on polylinking system we introduce polylinking networks which is a flow model based on polylinking systems that generalizes the classical flow model of ford and fulkerson on acyclic networks and has applications in the context of wireless networks more precisely a flow model recently introduced by avestimehr et al proceedings of the allerton conference on communication control and computing 2007 used in the context of wireless information networks is a special case of the presented model we define a notion of source destination cut and derive a max flow min cut theorem additionally we present various properties of polylinking networks that can be seen as generalizations of properties for classical flows using submodular function minimization and submodular flow algorithms one can efficiently determine a maximum flow a minimum source destination cut as well as a minimum cost flow these algorithms lead to new efficient algorithms for the information flow model

paper pole assignment for distributed systems by finite dimensional control the question of pole assignment for a class of distributed systems by means of finite dimensional control is considered a finite dimensional compensator is usually designed based on a reduced order model and it is not a priori known what effect this will have on the original infinite dimensional system explicit formulas are derived which enable one to calculate the eigenvalues of the resulting closed loop system for a certain compensator design estimates are derived which can be used to guarantee stability a priori numerical results are also presented

backstepping control of coupled linear parabolic pdes with space and time dependent coefficients in this article the backstepping design of stabilizing state feedback controllers for coupled linear parabolic pdes with spatially varying distinct diffusion coefficients as well as space and time dependent reaction is presented the selected target system is a cascade of exponentially stable time invariant systems with time dependent couplings that is uniformly exponentially stable with a prescribed rate of convergence to determine the state feedback controller the kernel equations are derived which results in a set of coupled pdes for a time dependent and spatially varying kernel for this the method of successive approximations is extended from the time invariant case to the present problem the applicability of the method is demonstrated by the stabilization of two coupled unstable parabolic pdes with space and time dependent coefficients

symmetric duality with pseudo invexity in variational problems abstract weak and strong duality results are established under pseudo invexity hypotheses for symmetric dual variational problems self dual problems and static symmetric dual programs are included as special cases

a bound for the symmetric travelling salesman problem through matroid formulation abstract a new bound for the symmetric traveling salesman problem is proposed using a matroid theoretic formulation of the problem the resulting bound is shown to present a link between the well studied 1 tree and 2 matching bounds its potential is investigated

boundary control and estimation of reaction diffusion equations on the sphere under revolution symmetry conditions recently the problem of designing boundary controllers and observers for unstable linear constant coefficient reaction diffusion equation on n balls has been solved by means of the backstepping me

a backstepping approach to the output regulation of boundary controlled parabolic pdes in this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach thereby the outputs to be controlled are not required to be measurable and can be pointwise distributed or boundary quantities whereas the measurement is located at the boundary by solving the state feedback regulator problem in the backstepping coordinates regulator equations with a simple structure result so that their analysis and solution is facilitated the output feedback regulator design is completed by determining a finite dimensional reference observer and an infinite dimensional disturbance observer for the latter a backstepping approach is presented that consists of a triangular decoupling in the backstepping coordinates this allows a systematic design and the explicit derivation of directly verifiable existence conditions for the disturbance observer it is shown that for the resulting compensator the separation principle holds implying output regulation for the exponentially stable closed loop system with a prescribed stability margin the output regulation results of the article are illustrated by means of a parabolic system with an in domain pointwise controlled output

sufficiency and duality for multiobjective variational control problems with g invexity antczak introduced vector valued g invex functions in 2009 which is a new class of generalized convex functions for differentiable multiobjective programming problems in this paper we extend the vector valued g invex functions to multiobjective variational control problems by using the new concepts a number of sufficient optimality results and mond weir type duality results are obtained for multiobjective variational control programming problems

yield trajectory tracking for hyperbolic age structured population systems abstract for population systems modeled by age structured hyperbolic partial differential equations pdes that are bilinear in the input and evolve with a positive valued infinite dimensional state global stabilization of constant yield set points was achieved in prior work seasonal demands in biotechnological production processes give rise to time varying yield references for the proposed control objective aiming at a global attractivity of desired yield trajectories multiple non standard features have to be considered a non local boundary condition a pde state restricted to the positive orthant of the function space and arbitrary restrictive but physically meaningful input constraints moreover we provide control lyapunov functionals ensuring an exponentially fast attraction of adequate reference trajectories to achieve this goal we make use of the relation between first order hyperbolic pdes and integral delay equations leading to a decoupling of the input dependent dynamics and the infinite dimensional internal one furthermore the dynamic control structure does not necessitate exact knowledge of the model parameters or online measurements of the age profile with a galerkin based numerical simulation scheme using the key ideas of the karhunen loeve decomposition we demonstrate the controller s performance

fast inversion of triangular toeplitz matrices an algorithm requiring 0 n log n operations is proposed for the inversion of triangular toeplitz matrices this algorithm is faster than existing techniques even for relatively small values of n and can easily be written in fortran

parabolic evolution equations and nonlinear boundary conditions on etudie le probleme aux valeurs limites et initiales u 7b a t u f t u 7b b t u g t u 0 t t u 0 u 0 qui peut etre considere comme une contrepartie abstraite a des problemes paraboliques semilineaires

kt invex control problem abstract in this paper we introduce a new condition on functions of a control problem for which we define a kt invex control problem we prove that a kt invex control problem is characterized in order that a kuhn tucker point is an optimal solution we generalize optimality results of known mathematical programming problems we illustrate these results with examples

on the kronecker canonical form of singular mixed matrix pencils consider a linear time invariant dynamical system that can be described as f dot x t a x t b u t where a b and f are mixed matrices i e matrices having two kinds of nonzero coefficients fixed constants that account for conservation laws and independent parameters that represent physical characteristics the controllable subspace of the system is closely related to the kronecker canonical form of the mixed matrix pencil begin pmatrix a sf mid b end pmatrix under a physically meaningful assumption justified by the dimensional analysis we provide a combinatorial characterization of the sums of the minimal row column indices of the kronecker canonical form of mixed matrix pencils the characterization leads to a matroid theoretic algorithm for efficiently computing the dimension of the controllable subspace for the system with nonsingular f

on matching cover of graphs a k matching cover of a graph g g is a union of k k matchings of g g which covers v g v g the matching cover number of g g denoted by mc g m c g is the minimum number k k such that g g has a k k matching cover a matching cover of g g is optimal if it consists of mc g m c g matchings of g g in this paper we present an algorithm for finding an optimal matching cover of a graph on n n vertices in o n 3 o n 3 time if use a faster maximum matching algorithm the time complexity can be reduced to o nm o n m where m e g m e g and give an upper bound on matching cover number of graphs in particular for trees a linear time algorithm is given and as a by product the matching cover number of trees is determined

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

pde backstepping control of one dimensional heat equation with time varying domain in this work a pde backstepping based control law for one dimensional unstable heat equation with time varying spatial domain is developed the underlying parabolic partial differential equation pde with time varying domain is a model emerging from process control applications such as crystal growth the use of backstepping control methodology yields the inherent feature of a time varying pde describing the kernel of the associated volterra integral the well posedness of pde kernel is proven and a numerical method to compute the solution of pde kernel augmented with the error analysis to establish the accuracy of the proposed numerical method is demonstrated finally the explicit form of the full state feedback control law is given and appropriate simulation is provided for the application of temperature regulation in the czochralski crystal growth process

nonlinear boundary control of semilinear parabolic systems nonlinear boundary control problems for a class of semilinear parabolic systems are considered from the point of view of semigroup theory the method is based on some recent general results on parabolic evolution equations with nonlinear boundary conditions existence of optimal boundary controls is proved using the theory of measurable selections and the cesari property for multifunctions three results are presented covering relaxed controls and controls with state constraints this generalizes in a substantial way existing results on linear boundary control problems m c delfour and m sorine control of distributed parameter systems pergamon press oxford 1983 pp 87 90 i lasiecka appl math optim 6 1980 pp 287 383 p acquistapace et al siam j control optim 29 1991 pp 89 118 the result presented can be further extended to differential inclusions two examples are presented for illustration

backstepping control of coupled linear parabolic pides with spatially varying coefficients this paper considers the backstepping design of state feedback controllers for coupled linear parabolic partial integro differential equations pides of volterra type with distinct diffusion coefficients spatially varying parameters and mixed boundary conditions the corresponding target system is a cascade of parabolic pdes with local couplings allowing a direct specification of the closed loop stability margin the determination of the state feedback controller leads to kernel equations which are a system of coupled linear second order hyperbolic pides with spatially varying coefficients and rather unusual boundary conditions by extending the method of successive approximations for the scalar case to the considered system class the well posedness of these kernel equations is verified by providing a constructive solution procedure this results in a systematic method for the backstepping control of coupled parabolic pides as well as pdes the applicability of the new backstepping design method is confirmed by the stabilization of two coupled parabolic pides with dirichlet robin unactuated boundaries and a coupled neumann actuation

tracking control for boundary controlled parabolic pdes with varying parameters combining backstepping and differential flatness the combination of backstepping based state feedback control and flatness based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion convection reaction system with spatially and temporally varying parameters and nonlinear boundary input for this in a first step the backstepping transformation is utilized to determine a state feedback controller which transforms the original distributed parameter system into an appropriately chosen exponentially stable distributed parameter target system of a significantly simpler structure in a second step the flatness property of the target system is exploited in order to determine the feedforward controller which allows us to realize the tracking of suitably prescribed trajectories for the system output this results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion convection reaction system with varying parameters whose applicability and tracking performance is evaluated in simulation studies

recursive partial realization from the combined sequence of markov parameters and moments abstract in this paper we develop the recursive structure of partial realization from a two sided sequence of markov parameters and moments the specific feature of this recursive structure is that it accommodates sequences growing in two directions like in the two point pade approximation we present a recursive algorithm for the minimal partial realization from a sequence of markov parameters and moments that amounts to recursive lu factorization of a toeplitz behavior matrix leaping over nongeneric sections it turns out that this algorithm reveals a new continued fraction expansion which extends the classical cauer third form as a corollary various results related to toeplitz matrices two point pade approximations continued fractions etc are unified within this partial realization setting

output feedback boundary control of a heat pde sandwiched between two odes we present designs for exponential stabilization of an ordinary differential equation ode heat partial differential equation pde ode coupled system where the control actuation only acts in one ode the combination of pde backstepping and ode backstepping is employed in a state feedback control law and in an observer that estimates pde and two ode states using only one pde boundary measurement based on the state feedback control law and the observer the output feedback control law is then proposed the exponential stability of the closed loop system and the boundedness and exponential convergence of the control law are proved via lyapunov analysis finally numerical simulations validate the effectiveness of this method for the sandwiched system

boundary control of coupled reaction advection diffusion systems with spatially varying coefficients recently the problem of boundary stabilization for unstable linear constant coefficient coupled reaction diffusion systems was solved by means of the backstepping method the extension of this result to systems with advection terms and spatially varying coefficients is challenging due to complex boundary conditions that appear in the equations verified by the control kernels in this technical note we address this issue by showing that these equations are essentially equivalent to those verified by the control kernels for first order hyperbolic coupled systems which were recently found to be well posed the result therefore applies in this case allowing us to prove h 1 stability for the closed loop system it also unveils a previously unknown connection between backstepping kernels for coupled parabolic and hyperbolic problems

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

kt invexity in optimal control problems abstract we extend the notion of kt invexity from mathematical programming to the classical optimal control problem and show that this generalized invexity property is not only a sufficient condition of optimality for kt processes processes that obey kt conditions below but also a necessary condition

improved bounds for matroid partition and intersection algorithms we give bounds on total lengths of augmenting paths in standard implementations of the matroid partition and intersection algorithms and indicate how these observations can be used to improve the running times in certain applications for example for the matroid intersection algorithm on two r by n matrices the running time is shown to be o nr 2 log r we also give improved versions of the two algorithms when running times are measured in terms of calls to an independence oracle for example there is a matroid partition algorithm on o n n element matroids using o n 2 5 independence tests

on variational problems characterization of solutions and duality in this paper we introduce a new class of pseudoinvex functions for variational problems using this new concept we obtain a necessary and sufficient condition for a critical point of the variational problem to be an optimal solution illustrated with an example also weak strong and converse duality are established

duality and sufficiency in control problems with invexity recently mond chandra and husain 3 established duality results for a variational problem under more general convexity conditions called invex than mond and hanson 4 in a similar fashion the results of mond and hanson s for duality in control problems are extended to more general convex or invex functions it is also shown that for invex functions the necessary conditions for optimality in the control problem are also sufficient

backstepping based boundary observer for a class of time varying linear hyperbolic pides in this paper a luenberger type boundary observer is presented for a class of distributed parameter systems described by time varying linear hyperbolic partial integro differential equations first known limitations due to the minimum observation time for simple transport equations are restated for the considered class of systems then the backstepping method is applied to determine the unknown observer gain term by avoiding the framework of gevrey functions which is typically used for the time varying case it is shown that the backstepping method can be employed without severe limitations on the regularity of the time varying terms a modification of the underlying volterra transformation ensures that the observer error dynamics is equivalent to the behavior of a predefined exponentially stable target system the magnitude of the observer gain term can be traded for lower decay rates of the observer error after the theoretic results have been proven the effectiveness of the proposed design is demonstrated by simulation examples

finite dimensional control of distributed parameter systems by galerkin approximation of infinite dimensional controllers the galerkin method is presented as a way to develop finite dimensional controllers for linear distributed parameter systems dps the direct approach approximates the open loop dps and then generates the controller from this approximation the indirect approach approximates the infinite dimensional stabilizing controller conditions under which they produce equivalent controllers in the sense of closed loop stability are presented the indirect approach is shown to converge to the stable closed loop system consisting of dps and infinite dimensional controller conditions are presented on the behavior of the galerkin method for the open loop dps which guarantee closed loop stability for large enough finite dimensional approximations

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

robust distributed control of quasilinear reaction diffusion equations via infinite dimensional sliding modes abstract this paper investigates the problem of robust tracking control for quasilinear reaction diffusion partial differential equations subject to external unknown perturbations the considered class of equations is quite general and includes classical equations such as the heat equation or the fisher kpp equation as special cases global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite dimensional sliding mode controller extensive simulations support and validate the theoretical results

a direct approach to compensator design for distributed parameter systems we present a direct approach to finite order compensator design for distributed parameter systems i e one that is not based on reduced order modelling instead we use a parametrization around an initial compensator which displays both controller order and closed loop stability in a convenient way the main result is an existence theorem which holds for a wide class of linear time invariant systems parabolic delay damped hyperbolic the most important assumptions are bounded inputs and outputs finitely many unstable modes completeness of eigenvectors an example is included to illustrate the feasibility of our method for purposes of design

mittag leffler convergent backstepping observers for coupled semilinear subdiffusion systems with spatially varying parameters abstract the purpose of this paper is to investigate the observer based boundary output feedback control for subdiffusion processes governed by coupled semilinear time fractional diffusion systems tfdss with spatially varying parameters for this backstepping technique is used to mittag leffler stabilize the coupled semilinear observer error dynamic systems we then design an observer based output feedback controller at the right boundary to realize the mittag leffler stability of the closed loop systems at hand a numerical example is finally included to test our methods

on control design for pdes with space dependent diffusivity or time dependent reactivity in this paper the recently introduced backstepping method for boundary control of linear partial differential equations pdes is extended to plants with non constant diffusivity thermal conductivity and time varying coefficients the boundary stabilization problem is converted to a problem of solving a specific klein gordon type linear hyperbolic pde this pde is then solved for a family of system parameters resulting in closed form boundary controllers the results of a numerical simulation are presented for the case when an explicit solution is not available

boundary control of coupled reaction diffusion processes with constant parameters the problem of boundary stabilization is considered for some classes of coupled parabolic linear pdes of the reaction diffusion type with reference to n coupled equations each one equipped with a scalar boundary control input a state feedback law is designed with actuation at only one end of the domain and exponential stability of the closed loop system is proven the treatment is addressed separately for the case in which all processes have the same diffusivity and for the more challenging scenario where each process has its own diffusivity and a different solution approach has to be taken the backstepping method is used for controller design and particularly the kernel matrix of the transformation is derived in explicit form of series of bessel like matrix functions by using the method of successive approximations to solve the corresponding pde thus the proposed control laws become available in explicit form additionally the stabilization of an underactuated system of two coupled reaction diffusion processes is tackled under the restriction that only a scalar boundary input is available capabilities of the proposed synthesis and its effectiveness are supported by numerical studies made for three coupled systems with distinct diffusivity parameters and for underactuated linearized dimensionless temperature concentration dynamics of a tubular chemical reactor controlled through a boundary at low fluid superficial velocities when convection terms become negligible

multiobjective control problem with v invexity abstract a multiobjective control problem is considered duality results are obtained for mond weir type duals under v invexity assumptions and their generalizations

flatness based control of a nonlinear chemical reactor model the nonlinear model of a continuous stirred tank reactor is shown to be flat the flatness permits the design of suitable trajectories on the basis of the explicit stationary solution and the tracking of these trajectories asymptotically using quasi static state feedback linearization a nonlinear local observer with a time varying gain is designed allowing the realisation of the state feedback in the case of partial measurement of the state simulation results illustrate the tracking behavior of the closed loop with the observer

a necessary and sufficient condition for duality in multiobjective variational problems abstract in this paper we move forward in the study of duality and efficiency in multiobjective variational problems we introduce new classes of pseudoinvex functions and prove that not only it is a sufficient condition to establish duality results but it is also necessary moreover these functions are characterized in order that all kuhn tucker or fritz john points are efficient solutions recent papers are improved we provide an example to show this improvement and illustrate these classes of functions and results

nonsmooth continuous time optimization problems sufficient conditions we discuss sufficient conditions of optimality for nonsmooth continuous time nonlinear optimization problems under generalized convexity assumptions these include both first order and second order criteria

stabilization and structural assignment of dirichlet boundary feedback parabolic equations a parabolic equation defined on a bounded domain is considered with input acting on the boundary through the dirichlet b c expressed as a specified finite dimensional feedback of the solution the free system zero b c is assumed throughout to be unstable two main results are established first we provide in 2 a novel proof that fully solves the corresponding boundary feedback stabilization problem thereby removing an annoying assumption required by the technique of appl math optim 6 1980 pp 201 220 under certain natural algebraic conditions based on the finitely many unstable eigenvalues we establish the existence of general boundary vectors for which the corresponding feedback semigroup decays exponentially to zero in the l 2 omega operator norm or more generally in the h s omega operator norm 0 leqq s frac 1 2 however most of the paper is devoted to the second problem structural or spectral assignment which is a natural question relevant to the selfadj

on the extended luenberger type observer for semilinear distributed parameter systems the design of an extended luenberger observer is considered to solve the state observation problem for semilinear distributed parameter systems for this a backstepping based technique is proposed for the design of the output injection weights by making use of the extended linearization of the semilinear observer error system with respect to the observer state stability of both the linearized and the semilinear observer error dynamics is analyzed theoretically moreover an efficient sample and hold implementation is considered to improve the computational efficiency of the observer design simulation examples are provided for a bistable semilinear partial differential equation and the simplified model of a bioreactor with monod kinetics

flatness based boundary control of a class of quasilinear parabolic distributed parameter systems motion planning and control of a boundary controlled quasilinear parabolic partial differential equation in one spatial variable is considered the approach relies on a flatness property of the system namely that the system solution can be differentially parameterized in terms of a flat output which in the case considered is a boundary value such a parameterization allows straightforward motion planning and computation of a control law the approach is based on power series in the spatial variable and the convergence of these series is ensured by choosing the flat output to be a nonanalytic smooth function of appropriate gevrey class

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

stability analysis of linear partial differential equations with generalized energy functions we present a method for the stability analysis of a large class of linear partial differential equations pdes in one spatial dimension we rely on lyapunov analysis to establish the exponential stability of the systems under consideration the proposed test for the verification of the underlying lyapunov inequalities relies on the existence of solutions of a system of coupled differential equations we illustrate the application of this method using a pde actuated by a backstepping computed feedback law furthermore for the case of pdes defined by polynomial data we formulate a numerical methodology in the form of a convex optimization problem which can be solved algorithmically we show the effectiveness of the proposed numerical methodology using examples of different types of pdes

duality with invexity for a class of nondifferentiable static and continuous programming problems abstract the concept of invexity has allowed the convexity requirements in a variety of mathematical programming problems to be weakened we extend the duality theorems for a class of static nondifferentiable problems with wolfe type and mond weir type duals and further extend these for the continuous analogues

algebraic algorithms for matching and matroid problems we present new algebraic approaches for two well known combinatorial problems nonbipartite matching and matroid intersection our work yields new randomized algorithms that exceed or match the efficiency of existing algorithms for nonbipartite matching we obtain a simple purely algebraic algorithm with running time o n omega where n is the number of vertices and omega is the matrix multiplication exponent this resolves the central open problem of mucha and sankowski 2004 for matroid intersection our algorithm has running time o nr omega 1 for matroids with n elements and rank r that satisfy some natural conditions

symmetric duality with invexity in variational problems abstract weak and strong duality results are established under invexity hypotheses for symmetric dual variational problems without positivity constraints self dual problems and static symmetric dual programs are included as special cases

duality for a class of multiobjective control problems with generalized invexity abstract b mond and i smart j math anal appl 136 1988 325 333 defined a kind of invexity and discussed the duality and sufficiency in scalar control problems with such invexity d bhatia and p kumar j math anal appl 189 1995 676 692 defined another kind of invexity corresponding generalized invexity and discussed the duality for multiobjective control problems with such generalized invexity in this paper the duality results for multiobjective control problems with mond and smart s generalized invexity are discussed

exact and approximation algorithms for weighted matroid intersection in this paper we propose new exact and approximation algorithms for the weighted matroid intersection problem our exact algorithm is faster than previous algorithms when the largest weight is relatively small our approximation algorithm delivers a 1 epsilon approximate solution with a running time significantly faster than most known exact algorithms the core of our algorithms is a decomposition technique we decompose an instance of the weighted matroid intersection problem into a set of instances of the unweighted matroid intersection problem the computational advantage of this approach is that we can make use of fast unweighted matroid intersection algorithms as a black box for designing algorithms more precisely we show that we can solve the weighted matroid intersection problem via solving w instances of the unweighted matroid intersection problem where w is the largest given weight assuming that all given weights are integral furthermore we can find a 1 epsilon approximate solution via solving o epsilon 1 log r instances of the unweighted matroid intersection problem where r is the smaller rank of the two given matroids our algorithms make use of the weight splitting approach of frank j algorithms 2 4 328 336 1981 and the geometric scaling scheme of duan and pettie j acm 61 1 1 2014 our algorithms are simple and flexible they can be adapted to special cases of the weighted matroid intersection problem using specialized unweighted matroid intersection algorithms in addition we give a further application of our decomposition technique we solve efficiently the rank maximal matroid intersection problem a problem motivated by matching problems under preferences

duality for a class of multiobjective control problems abstract in this paper a class of multiobjective control problems is considered where the objective and constraint functions involved are f t x t t y t z t with x t rn y t rn and z t rm where x t and z t are the control variables and y t is the state variable under the assumption of invexity and its generalization duality theorems are proved through a parametric approach to related properly efficient solutions of the primal and dual problems

brief paper sliding mode boundary control of a parabolic pde system with parameter variations and boundary uncertainties this paper considers the stabilization problem of a one dimensional unstable heat conduction system rod modeled by a parabolic partial differential equation pde powered with a dirichlet type actuator from one of the boundaries by applying the volterra integral transformation a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties the associated lyapunov function is used for designing an infinite dimensional sliding manifold on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances it is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero a continuous control law satisfying the reaching condition is obtained by passing a discontinuous signum signal through an integrator

a dynamic compensator for in domain control of burgers equation this paper addresses the problem of output regulation control of a burgers equation under pointwise in domain actuation a dynamic compensator that generates the in domain control is developed for

backstepping forwarding control and observation for hyperbolic pdes with fredholm integrals an integral transform is introduced which allows the construction of boundary controllers and observers for a class of first order hyperbolic pides with fredholm integrals these systems do not have a strict feedback structure and thus the standard backstepping approach cannot be applied sufficient conditions for the existence of the backstepping forwarding transform are given in terms of spectral properties of some integral operators and more conservatively but easily verifiable in terms of the norms of the coefficients in the equations an explicit transform is given for particular coefficient structures in the case of strict feedback systems the procedure detailed in this paper reduces to the well known backstepping design the results are illustrated with numerical simulations

weakly efficient solutions and pseudoinvexity in multiobjective control problems abstract in this paper we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem called w kt pseudoinvexity and w fj pseudoinvexity we prove that all kuhn tucker or fritz john points are weakly efficient solutions if and only if these conditions are fulfilled we relate weakly efficient solutions to optimal solutions of weighting control problems we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

a fast accurate approximation method with multigrid solver for two dimensional fractional sub diffusion equation a fast accurate approximation method with multigrid solver is proposed to solve a two dimensional fractional sub diffusion equation using the finite difference discretization of fractional time derivative a block lower triangular toeplitz matrix is obtained where each main diagonal block contains a two dimensional matrix for the laplacian operator our idea is to make use of the block circulant approximation via fast fourier transforms so that the resulting task is to solve a block diagonal system where each diagonal block matrix is the sum of a complex scalar times the identity matrix and a laplacian matrix we show that the accuracy of the approximation scheme is of o because of the special diagonal block structure we employ the multigrid method to solve the resulting linear systems the convergence of the multigrid method is studied numerical examples are presented to illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver an approximation method is proposed to approximate the original block lower triangular toeplitz linear system sufficient condition is given to guarantee a high accuracy of the approximation method multigrid solver is employed to solve the resulting block diagonal linear system multigrid solver is proven to be linear convergence numerical examples illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver

flatness of heavy chain systems in this paper the flatness m fliess j levine p martin and p rouchon internat j control 61 1995 pp 1327 1361 m fliess j levine p martin and p rouchon ieee trans automat control 44 1999 pp 922 937 of heavy chain systems i e trolleys carrying a fixed length heavy chain that may carry a load is addressed in the partial derivatives equations framework we parameterize the system trajectories by the trajectories of its free end and solve the motion planning problem namely steering from one state to another state when considered as a finite set of small pendulums these systems were shown to be flat r m murray in proceedings of the ifac world congress san francisco ca 1996 pp 395 400 our study is an extension to the infinite dimensional case under small angle approximations these heavy chain systems are described by a one dimensional 1d partial differential wave equation dealing with this infinite dimensional description we show how to get the explicit parameterization of the chain trajectory using distributed and punctual advances and delays of its free end this parameterization results from symbolic computations replacing the time derivative by the laplace variable s yields a second order differential equation in the spatial variable where s is a parameter its fundamental solution is for each point considered along the chain an entire function of s of exponential type moreover for each we show that thanks to the liouville transformation this solution satisfies modulo explicitly computable exponentials of s the assumptions of the paley wiener theorem this solution is in fact the transfer function from the flat output the position of the free end of the system to the whole state of the system using an inverse laplace transform we end up with an explicit motion planning formula involving both distributed and punctual advances and delays operators

backstepping observers for linear pdes on higher dimensional spatial domains the extension of the backstepping based state observer design is considered for systems governed by parabolic pdes defined on a higher dimensional cuboidal spatial domain with the measured output being restricted to a single boundary hyperplane thereby a suitable coordinate and state transformation is employed which allows for the application of the backstepping method for the determination of a luenberger type state observer with observer corrections entering the pde and the boundary condition this ensures that the observer error dynamics follows the behavior of a predefined exponentially stable target system in view of a practical realization of the proposed observer approach the idealized system output previously assumed as measurable on the entire boundary hyperplane is reconstructed from a limited set of optimally located measurements by means of a least squares approximation the observer error convergence and the applicability of the proposed approach are confirmed analytically and are evaluated in numerical simulations

efficient solutions in v kt pseudoinvex multiobjective control problems a characterization in this paper we introduce a new condition on functionals involved in a multiobjective control problem for which we define the v kt pseudoinvex control problem we prove that a v kt pseudoinvex control problem is characterized so that a kuhn tucker point is an efficient solution we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

saddle point optimality criteria involving p b d invexity and p b d pseudoinvexity in interval valued optimisation problems in this paper under new generalised convexity assumptions we investigate some connections between an lu optimal solution of a variational control problem governed by interval valued multiple inte

sufficient optimality criteria and duality for multiobjective variational control problems with v invexity abstract the sufficient optimality criteria for a class of multiobjective variational control problems under the v invexity assumption are presented duality results are proved under a variety of v invexity assumptions multiobjective fractional variational control problems are also studied

computing pure nash and strong equilibria in bottleneck congestion games bottleneck congestion games properly model the properties of many real world network routing applications they are known to possess strong equilibria a strengthening of nash equilibrium to resilience against coalitional deviations in this paper we study the computational complexity of pure nash and strong equilibria in these games we provide a generic centralized algorithm to compute strong equilibria which has polynomial running time for many interesting classes of games such as e g matroid or single commodity bottleneck congestion games in addition we examine the more demanding goal to reach equilibria in polynomial time using natural improvement dynamics using unilateral improvement dynamics in matroid games pure nash equilibria can be reached efficiently in contrast computing even a single coalitional improvement move in matroid and single commodity games is strongly np hard in addition we establish a variety of hardness results and lower bounds regarding the duration of unilateral and coalitional improvement dynamics they continue to hold even for convergence to approximate equilibria

wiener hopf and spectral factorization of real polynomials by newton s method abstract we present a new method for factoring a real polynomial into the product of two polynomials which have their zeros inside and outside the unit circle respectively the approach is based on solving a nonlinear system by newton s method the jacobi matrix is a polynomial of a companion matrix and thus a bezoutian times the inverse of a triangular toeplitz matrix after getting deeper understanding of the displacement structure of the bezoutian each newton step can be reduced to a few applications of discrete fourier or cosine transforms and the lu decomposition of a conceived linear system with a cauchy like matrix these structural features are employed to design a fast algorithm which shows excellent numerical behavior for example in the case of the extremely ill conditioned test polynomial 2 z n k 0 n 1 z k 2 k 1 n z k of the degree 2 n 20000 we obtain the factorization after 22 newton steps with an error of 3 4 10 8 in the euclidean norm the execution time on a laptop being a couple of minutes the local quadratic convergence of our newton method is proved and explicit convergence balls are given on the basis of estimates for the lipschitz constant which occurs in kantorovich s theorem we also design and test two superfast versions of our method which for polynomials of degree 20000 typically need about half a minute to produce an initial coefficient vector and then perform the newton iteration within 1 s

backstepping observer based output feedback control for a class of coupled parabolic pdes with different diffusions abstract this paper aims to design a backstepping observer based output feedback controller for a class of coupled parabolic partial differential equations pdes with different diffusions the considered system is endowed with a sensor at the left boundary and an actuation at the right boundary firstly a backstepping observer is designed secondly compared to the existing literature a weaker condition is deduced to guarantee the stability of the plant system by means of a controller thirdly using the separation principle an observer based output feedback controller is set up based on the designed observer and controller finally the efficiency of the proposed method is shown by taking a simplified model of chemical tubular reactor

fast matrix rank algorithms and applications we consider the problem of computing the rank of an m n matrix a over a field we present a randomized algorithm to find a set of r rank a linearly independent columns in o vav p r field operations where vav denotes the number of nonzero entries in a and

efficiency in generalised v kt pseudoinvex control problems abstractin this paper strongly b v kt pseudoinvex multidimensional control problems are considered concretely we introduce a generalised condition on the functionals involved in a multidimensi

cooperative regenerating codes one of the design objectives in distributed storage system is the minimization of the data traffic during the repair of failed storage nodes by repairing multiple failures simultaneously and cooperatively rather than successively and independently further reduction of repair traffic is made possible a closed form expression of the optimal tradeoff between the repair traffic and the amount of storage in each node for cooperative repair is given we show that the points on the tradeoff curve can be achieved by linear cooperative regenerating codes with an explicit bound on the required finite field size the proof relies on a max flow min cut type theorem from combinatorial optimization for submodular flows two families of explicit constructions are given

boundary feedback stabilization of an unstable heat equation in this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut x t uxx x t a x u x t this equation can be viewed as a model of a heat conducting rod in which not only is the heat being diffused mathematically due to the diffusive term uxx but also the destabilizing heat is generating mathematically due to the term a u with a 0 we show that for any given continuously differentiable function a and any given positive constant l we can explicitly construct a boundary feedback control law such that the solution of the equation with the control law converges to zero exponentially at the rate of l this is a continuation of the recent work of boskovic krstic and liu ieee trans automat control 46 2001 pp 2022 2028 and balogh and krstic european j control 8 2002 pp 165 176

a note on polylinking flow networks this is a supplementary note on m x goemans s iwata and r zenklusen s paper that proposes a flow model based on polylinking systems their flow model is a series or tandem connection of polylinking systems we can consider an apparently more general model of a polylinking flow network which consists of an ordinary arc capacitated network endowed with polylinking systems on the vertex set one for each vertex of the network this is a natural apparent generalization of polymatroidal flow model of e l lawler and c u martel and of generalized polymatroidal flow model of r hassin we give a max flow min cut formula for the polylinking network flow problem and discuss some acyclic flow property of polylinking flows

boundary time varying feedbacks for fixed time stabilization of constant parameter reaction diffusion systems in this paper the problem of fixed time stabilization of constant parameter reaction diffusion partial differential equations by means of continuous boundary time varying feedbacks is considered moreover the time of convergence can be prescribed in the design the design of time varying feedbacks is carried out based on the backstepping approach using a suitable target system with a time varying coefficient one can state that the resulting kernel of the backstepping transformation is time varying and rendering the control feedback to be time varying as well explicit representations of the kernel solution in terms of generalized laguerre polynomials and modified bessel functions are derived the fixed time stability property is then proved a simulation example is presented to illustrate the main results

sufficiency and duality for multiobjective variational control problems with generalized f α ρ θ v convexity abstract zalmai introduced generalized f v convex functions a new class of functions that unifies several concepts of generalized convex functions in this article the generalized f v convex functions are extended to variational control problem by utilizing the new concepts we obtain sufficient optimality conditions and prove wolfe type and mond weir type duality results for multiobjective variational control programming problem