parity space based fault detection for linear discrete time varying systems with unknown input in this paper a new approach to parity space based fault detection fd is put forward for linear discrete time varying ldtv systems the focus of our study is on solving the problem with heavy online computational burden the main contributions are two folds firstly the problem of parity space based fd is formulated as finding a minimum of quadratic form of unknown input secondly by applying projection in krein space a solution of optimal parity space based fd is obtained via recursively computing innovations it is shown that the reduction of computation cost is achievable especially with the increase of parity space order finally a numerical example is given to demonstrate the application of the proposed method

on l1 gain control of 2 d positive roesser systems with directional delays necessary and sufficient conditions abstract in this paper the problem of l 1 gain control is addressed for two dimensional 2 d positive roesser systems with directional delays a complete solution to the design problem is presented for the first time specifically by exploiting a new approach based on 2 d z transform an exact value of l 1 induced norm of the input output operator is obtained this analytical result is utilized to derive necessary and sufficient conditions under which a 2 d positive system with delays is asymptotically stable with a prescribed l 1 gain performance then by utilizing a vertex optimization approach necessary and sufficient conditions are established for the existence of a state feedback controller sfc that makes the closed loop system positive and stable subject to l 1 induced performance the proposed synthesis conditions are formulated in terms of linear programming lp which can be effectively solved by various convex algorithms to minimize the l 1 performance index

recursive state estimation for two dimensional shift varying systems with random parameter perturbation and dynamical bias abstract in this paper the state estimation problem is investigated for a class of two dimensional 2 d stochastic systems with shift varying parameters the stochasticity with the underlying system comes from three sources namely random parameter perturbations dynamical biases and additive white noises the measurement output is subject to the uniform quantization as a result of communication constraints on the sensors the purpose of the addressed problem is to recursively estimate the system states with prescribed estimation performance in spite of the stochastic disturbances and the uniform quantizations an augmented model is first constructed to combine the information about the state and the bias and the dynamical evolution is subsequently discussed furthermore through stochastic analysis and mathematical induction the estimator design algorithm is developed to acquire certain upper bound on the estimation error variance and such an upper bound is then minimized in the matrix trace sense moreover the boundedness issue of the estimation errors is investigated via matrix inversion lemma and inductive analysis technique finally the effectiveness of the proposed state estimation algorithm is validated on a typical 2 d system modeled by the well known darboux equation with extensive application potentials in industrial processes

entropy satisfying schemes for computing selection dynamics in competitive interactions in this paper we present entropy satisfying schemes for solving an integro differential equation that describes the evolution of a population structured with respect to a continuous trait in p e jabin and g raoul j math biol 63 2011 pp 493 517 solutions are shown to converge toward the so called evolutionary stable distribution esd as time becomes large using the relative entropy at the discrete level the esd is shown to be the solution to a quadratic programming problem and can be computed by any well established nonlinear programing algorithm the schemes are then shown to satisfy the entropy dissipation inequality on the set where initial data are positive and the numerical solutions tend toward the discrete esd in time an alternative algorithm is presented to capture the global esd for nonnegative initial data which is made possible due to the mutation mechanism built into the modified scheme a series of numerical tests are given to confirm both accuracy and the entropy satisf

the existence and design of functional observers for two dimensional systems abstract this paper is concerned with functional observers for two dimensional 2d systems described by the fornasini marchesini local state space second model a necessary and sufficient condition is given for the existence of asymptotic functional observers a more tractable necessary condition for the existence of asymptotic functional observers is also presented as it helps exclude those 2d systems for which there is no asymptotic functional observer a constructive design method is then proposed for the design of asymptotic functional observers using a rank condition on the given system matrices and a linear matrix inequality lmi technique two illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed method

unknown input observers for 2d state space models in this paper dead beat unknown input observers uios for two dimensional 2d state space models are investigated dead beat uios are observers which produce an exact estimate of the original system state trajectory after a finite number of evolution steps independently of the system and observer initial conditions and of the unknown disturbances that affect the system functioning necessary and sufficient conditions for the existence of dead beat uios are provided as well as a parameterization of all dead beat uio transfer matrices comparisons with luenberger type uios are also carried out and the extension of the paper results to the case of asymptotic uios with a given rate of convergence and to roesser models are finally discussed

finite frequency model reduction of two dimensional digital filters this technical note is concerned with the model reduction problem of two dimensional 2 d digital filters over finite frequency ranges the 2 d digital filter is described by the fornasini marchesini local state space fm lss model with the aid of the generalized kalman yakubovich popov gkyp lemma for 2 d systems sufficient conditions for the finite frequency model reduction problem are derived compared with full frequency methods the proposed finite frequency method can get a better approximation performance over finite frequency ranges an example is given to demonstrate the effectiveness of the proposed method

a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint we present a novel computational framework for diffusive reactive systems that satisfies the non negative constraint and maximum principles on general computational grids the governing equations for the concentration of reactants and product are written in terms of tensorial diffusion reaction equations we restrict our studies to fast irreversible bimolecular reactions if one assumes that the reaction is diffusion limited and all chemical species have the same diffusion coefficient one can employ a linear transformation to rewrite the governing equations in terms of invariants which are unaffected by the reaction this results in two uncoupled tensorial diffusion equations in terms of these invariants which are solved using a novel non negative solver for tensorial diffusion type equations the concentrations of the reactants and the product are then calculated from invariants using algebraic manipulations the novel aspect of the proposed computational framework is that it will always produce physically meaningful non negative values for the concentrations of all chemical species several representative numerical examples are presented to illustrate the robustness convergence and the numerical performance of the proposed computational framework we will also compare the proposed framework with other popular formulations in particular we will show that the galerkin formulation which is the standard single field formulation does not produce reliable solutions and the reason can be attributed to the fact that the single field formulation does not guarantee non negative solutions we will also show that the clipping procedure which produces non negative solutions but is considered as a variational crime does not give accurate results when compared with the proposed computational framework

a new scheme of fault detection for linear discrete time varying systems in this note a new scheme of fault detection fd is proposed for linear discrete time varying ldtv systems subject to l 2 norm bounded unknown inputs the basic idea is to find an optimal estimation of the l 2 norm of the unknown inputs including the unknown initial state variables this leads to a natural design of the fd system with the l 2 norm boundedness of the unknown inputs as a threshold and the l 2 norm of the unknown input estimate as the evaluation function to avoid heavy computational burden projection technique in krein space is applied which allows a recursive computation of the evaluation function it is shown that the achieved fd system satisfies both the worst case and best case sensitivity robustness ratio criteria and further applications to observer based fd lead to an alternative design of h infty h infty and or h h infty fault detection filter

robust reduction of a class of large scale linear programs a set of new tests for linear programming presolving analysis is described these tests are applicable for linear programs with box constraints and positive or zero coefficients partial applicability to general linear programming lp problems is discussed in a special section the aim is to detect and remove redundant rows and columns the tests are based on the solution of some auxiliary lp problems with one constraint and upper bounds on the variables a comparison with the klein holm numerical test is presented the tests are applied iteratively to the primal and dual lp problems the method is also applicable to lp problems with coefficients belonging to some range of uncertainty providing a robust procedure for scale reduction a detailed numerical example and results of numerical experiments are presented

preprocessing for quadratic programming techniques for the preprocessing of not necessarily convex quadratic programs are discussed most of the procedures extend known ones from the linear to quadratic cases but a few new preprocessing techniques are introduced the implementation aspects are also discussed numerical results are finally presented to indicate the potential of the resulting code both for linear and quadratic problems the impact of insisting that bounds of the variables in the reduced problem be as tight as possible rather than allowing some slack in these bounds is also shown to be numerically significant

brief paper unbiased minimum variance input and state estimation for linear discrete time systems this paper addresses the problem of simultaneously estimating the state and the input of a linear discrete time system a recursive filter optimal in the minimum variance unbiased sense is developed where the estimation of the state and the input are interconnected the input estimate is obtained from the innovation by least squares estimation and the state estimation problem is transformed into a standard kalman filtering problem necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed

presolving in linear programming most modern linear programming solvers analyze the lp problem before submitting it to optimization some examples are the solvers whizard tomlin and welch 1983 ob1 lustig et al 1994 osl forrest and tomlin 1992 sciconic 1990 and cplex bixby 1994 the purpose of the presolve phase is to reduce the problem size and to discover whether the problem is unbounded or infeasible in this paper we present a comprehensive survey of presolve methods moreover we discuss the restoration procedure in detail i e the procedure that undoes the presolve computational results on the netlib problems gay 1985 are reported to illustrate the efficiency of the presolve methods

robust h_ infty filtering for two dimensional uncertain linear discrete time varying systems a krein space based method a robust h infty filtering algorithm is proposed for two dimensional 2 d linear uncertain time varying systems in this study the considered 2 d systems are subject to unknown inputs measurement noises and time varying modeling uncertainties to appropriately deal with the system uncertainties a new problem formulation of robust h infty filter design for 2 d uncertain systems is first presented by introducing an alternative indefinite quadratic performance function in lieu of the standard h infty performance index then the robust 2 d h infty filter design is converted to an optimization problem of finding the positive minimum of the new indefinite quadratic performance function under certain conditions by relating this quadratic form to a specific 2 d state space model in krein space the krein space estimation theory is used to solve the reformulated optimization problem a recursive robust 2 d time varying h infty filter and its explicit condition for the existence are obtained through projection techniques in 2 d krein space one thermal process plant is used to illustrate the effectiveness of the proposed filter

a smoothing sqp framework for a class of composite l_q lq minimization over polyhedron the composite l q 0 q 1 minimization problem over a general polyhedron has received various applications in machine learning wireless communications image restoration signal reconstruction etc this paper aims to provide a theoretical study on this problem first we derive the karush kuhn tucker kkt optimality conditions for local minimizers of the problem second we propose a smoothing sequential quadratic programming framework for solving this problem the framework requires a approximate solution of a convex quadratic program at each iteration finally we analyze the worst case iteration complexity of the framework for returning an epsilon kkt point i e a feasible point that satisfies a perturbed version of the derived kkt optimality conditions to the best of our knowledge the proposed framework is the first one with a worst case iteration complexity guarantee for solving composite l q minimization over a general polyhedron

two integrable couplings of a generalized d kaup newell hierarchy and their hamiltonian and bi hamiltonian structures abstract we enlarge the spectral problem of a generalized d kaup newell d kn spectral problem solving the enlarged zero curvature equations we produce integrable couplings a reduction of the spectral matrix leads to a second integrable coupling system next bilinear forms that are symmetric ad invariant and non degenerate on the given non semisimple matrix lie algebra are computed to employ the variational identity the variational identity is then applied to the original enlarged spectral problem of a generalized d kn hierarchy and the reduced problem hamiltonian structures are presented as well as a bi hamiltonian formulation of the reduced problem both hierarchies have infinitely many commuting high order symmetries and conserved densities i e are liouville integrable

generalized kalman yakubovich popov lemma for 2 d fm lss model this paper is concerned with the generalized kalman yakubovich popov kyp lemma for 2 d fornasini marchesini local state space fm lss systems by carefully analyzing the feature of the states in 2 d fm lss models a linear matrix inequality lmi characterization for a rectangular finite frequency region is constructed and then by combining this characterization with s procedure a generalized kyp lemma is proposed for 2 d fm lss models as applications of the developed kyp lemma new conditions are further derived for designing controllers guaranteeing finite frequency positive realness of the closed loop systems where both state feedback and dynamic output feedback control laws are considered finally two illustrative examples clearly show the effectiveness of the proposed results the main contribution of the paper is trifold 1 a novel characterization for a finite frequency region has been developed 2 a generalized kyp lemma has been proposed including the existing bounded realness and positive realness results as special cases and 3 systematic methods for finite frequency positive real control of 2 d systems have been presented

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

formal optimization of some reduced linear programming problems it is often possible and profitable to reduce or presolve linear programs in particular there are frequently constraints which force many of the variables to be at bound unfortunately the solution found by the simplex method for such reduced models is not usually formally optimal in the sense that nonoptimal dual values may be present when the original problem is restored furthermore the restored full problem is now totally degenerate and may require many iterations to achieved formal optimality

the fornasini marchesini and the roesser models algebraic methods for recasting this paper is devoted to giving a new method for recasting the fornasini marchesini model of the two dimensional system to the roesser form endowed with an important feature that the dimensions of both models are the same the two dimensional similarity transformation and spectral transformations of the transfer function variables are used for this purpose both the standard and singular cases are considered

a sufficient condition on the exponential stability of two dimensional 2 d shift variant systems in this paper we consider a class of two dimensional 2 d shift variant systems based on the bound on the deviation of parameters a sufficient condition is derived which ensures exponential stability with different decaying rates along the two directions an example is presented to illustrate the result

filtering design for two dimensional markovian jump systems with state delays and deficient mode information this paper is concerned with the problem of h filtering for a class of two dimensional markovian jump linear systems described by the fornasini marchesini local state space model the systems under consideration are subject to state delays and deficient mode information in the markov chain the description of deficient mode information is comprehensive that simultaneously includes the exactly known partially unknown and uncertain transition probabilities by invoking the properties of the transition probability matrix together with the convexification of uncertain domains a new h performance analysis criterion for the filtering error system is firstly derived then via some matrix inequality linearisation procedures two approaches for the filter synthesis are proposed it is shown that both the full order and reduced order filters can be constructed by solving a set of linear matrix inequalities finally simulation studies are provided to illustrate the effectiveness of the proposed design methods

unbiased minimum variance estimation for systems with unknown exogenous inputs a new method is developed for the state estimation of linear discrete time stochastic systems in the presence of an unknown disturbance the filter obtained is optimal in the unbiased minimum variance sense the necessary and sufficient conditions for the existence and the stability of the filter are given

near optimal control for time varying linear discrete systems with additive nonlinearities and random gains in this technical note the near optimal control problem is investigated for a class of time varying linear discrete systems subject to additive nonlinearities and random gains first certain upper bound on the cost function is proposed to quantify the control performance subsequently in virtue of the time varying discrete riccati like recursions drlrs the near optimal control strategy is designed such that this upper bound is minimized over the finite horizon to reflect the steady state behavior of the dynamic system the upper bound of the derived time varying drlrs is also analyzed over the infinite horizon by resorting to the semidefinite programming method finally a numerical example is provided to verify the validity and advantages of the proposed methodology

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

unbiased minimum variance fault and state estimation for linear discrete time varying two dimensional systems the fault and state estimation problem is addressed for a class of linear discrete time varying two dimensional systems subject to state and measurement noises two estimators are proposed to compute the estimation of the system state and or fault recursively both of which are unbiased with minimum variance through formulating the estimation problem as the solvability problem of the corresponding matrix equations of estimator gains and system constraint the necessary and sufficient condition of the existence and the solution for the proposed estimators are given an example is used to demonstrate the effectiveness of the proposed estimators