non linear systems abstract we review the general properties of non linear systems and show the basic techniques used universally to study the symmetry breaking and bifurcation properties we exemplify these characteristics by using a turing system that is general enough as to present many of the universal features of non linear systems we then show some interesting applications to various problems that we have treated in the past

approximation algorithms for supply chain planning and logistics problems with market choice we propose generalizations of a broad class of traditional supply chain planning and logistics models that we call supply chain planning and logistics problems with market choice instead of the traditional setting we are given a set of markets each specified by a sequence of demands and associated with a revenue decisions are made in two stages in the first stage one chooses a subset of markets and rejects the others once that market choice is made one needs to construct a minimum cost production plan set of facilities to satisfy all of the demands of all the selected markets the goal is to minimize the overall lost revenues of rejected markets and the production facility opening and connection costs these models capture important aspects of demand shaping within supply chain planning and logistics models we introduce a general algorithmic framework that leverages existing approximation results for the traditional models to obtain corresponding results for their counterpart models with market choice more specifically any lp based approximation for the traditional model can be leveraged to a frac 1 1 e 1 alpha approximation algorithm for the counterpart model with market choice our techniques are also potentially applicable to other covering problems

a fractal procedure for monotonicity preserving interpolation interpolation subject to strip condition on first derivative is considered with a fif shape parameters involved in the fif controls shape of the curve near left and right end points some traditional rational splines emerge as special cases of the fif derivative of the monotonic rational fif may be nondifferentiable in a finite or dense subset of interval this paper is concerned with interpolation subject to a strip condition on the first order derivative using a class of rational cubic fractal interpolation functions fifs this facilitates the fif to generate monotonic curves for a given set of monotonic data the proposed monotonicity preserving rational fif subsumes and supplements a classical monotonic rational cubic spline in models leading to the monotonicity preserving interpolation problem wherein the first order derivative of the constructed interpolant is to be nondifferentiable in a finite or dense subset of the interpolation interval the developed fractal scheme is well suited in contrast to its classical nonrecursive counterpart it is shown that the present fractal interpolation scheme has o h 4 accuracy provided the original function belongs to c 4 i and the parameters involved in the fif are appropriately chosen

improved algorithms for economic lot size problems many problems in inventory control production planning and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by a s manne 1958 and by h m wagner and t m whitin 1958 the manne wagner whitin model and its variants have been studied widely in the operations research and management science communities and a large number of algorithms have been proposed for solving various problems expressed in terms of this model most of which assume concave costs and rely on dynamic programming in this paper we show that for many of these concave cost economic lot size problems the dynamic programming formulation of the problem gives rise to a special kind of array called a monge array we then show how the structure of monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems we focus on uncapacitated problems i e problems without bounds on production inventory or backlogging capacitated problem

computing non stationary s s policies using mixed integer linear programming abstract this paper addresses the single item single stocking location non stationary stochastic lot sizing problem under the s s control policy we first present a mixed integer non linear programming minlp formulation for determining near optimal s s policy parameters to tackle larger instances we then combine the previously introduced minlp model and a binary search approach these models can be reformulated as mixed integer linear programming milp models which can be easily implemented and solved by using off the shelf optimization software computational experiments demonstrate that optimality gaps of these models are less than 0 3 of the optimal policy cost and computational times are reasonable

on the existence of a common quadratic lyapunov function for a rank one difference abstract suppose that a and b are real hurwitz matrices and that their difference a b is rank one then a and b have a common quadratic lyapunov function if and only if the product ab has no real negative eigenvalue this result is due to shorten and narendra who showed that it follows as a consequence of the kalman yacubovich popov lemma and the solution of the lur e problem here we present a new and independent proof based on results from convex analysis and the theory of moments

perturbation results for the estrada index in weighted networks the logarithm of the estrada index has been proposed recently as a spectral measure to character efficiently the robustness of complex networks in this paper we explore the estrada index in weighted networks and develop various perturbation results based on spectral graph theory it is shown that the robustness of a network may be enhanced even when some edge weights are reduced this is of particular theoretical and practical significance to network design and optimization

the linear quadratic regulator for periodic hybrid systems abstract the main objective of this paper is to characterize feedback control laws that are optimal with respect to a quadratic cost functional in the framework of linear hybrid systems undergoing time driven periodic jumps namely the so called hybrid linear quadratic regulator lqr problem the optimal solution to the hybrid lqr problem is determined both in the case of finite horizon and infinite horizon optimal control problems by introducing a hybrid periodic extension of the classic differential and difference riccati equations thus leading to the notion of monodromy riccati equation interestingly due to the periodic nature of the discrete time events the computation of the optimal feedback hinges upon the solution of a differential rather than algebraic riccati equation also in the infinite horizon case hence yielding a time varying periodic control law necessary and sufficient conditions that ensure asymptotic stability of the closed loop system are provided and discussed in detail in the case of infinite horizon optimal control problems

routing properties of supercubes abstract usually each vertex of the s 1 dimensional hypercube is labeled with a unique integer k with 0 k 2 s 1 1 the supercube s n of n nodes with 2 s n 2 s 1 is constructed by merging nodes u and u 2 s with n u 2 s 1 1 in the s 1 dimensional hypercube into a single node labeled as u 2 s and leaving other nodes in the s 1 dimensional hypercube unchanged in this paper we give the exact distance between any two nodes of supercube and present a new shortest path routing algorithm on s n then we show how to construct s n disjoint paths between any two nodes of the supercube where s n is the connectivity of s n finally we compute the wide diameter and the fault diameter of s n we show that both the wide diameter and the fault diameter are equal to s 2 if n 2 s 1 2 i 1 0 i s 1 and s 1 otherwise

robust solutions of linear programming problems contaminated with uncertain data optimal solutions of linear programming problems may become severely infeasible if the nominal data is slightly perturbed we demonstrate this phenomenon by studying 90 lps from the well known netlib collection we then apply the robust optimization methodology ben tal and nemirovski 1 3 el ghaoui et al 5 6 to produce robust solutions of the above lps which are in a sense immuned against uncertainty surprisingly for the netlib problems these robust solutions nearly lose nothing in optimality

a survey of the theory of hypercube graphs abstract we present a comprehensive survey of the theory of hypercube graphs basic properties related to distance coloring domination and genus are reviewed the properties of the n cube defined by its subgraphs are considered next including thickness coarseness hamiltonian cycles and induced paths and cycles finally various embedding and packing problems are discussed including the determination of the cubical dimension of a given cubical graph

optimality of s s policies in inventory models with markovian demand this paper is concerned with a generalization of classical inventory models with fixed ordering costs that exhibit s s policies in our model the distribution of demands in successive periods is dependent on a markov chain the model includes the case of cyclic or seasonal demand the model is further extended to incorporate some other realistic features such as no ordering periods and storage and service level constraints both finite and infinite horizon nonstationary problems are considered we show that s s policies are also optimal for the generalized model as well as its extensions

common eigenvectors of two matrices abstract a computable criterion is given for two square matrices to possess a common eigenvector as well as a criterion for one matrix to have an eigenvector lying in a given subspace some applications are discussed

bergeʼs maximum theorem for noncompact image sets abstract this note generalizes berge s maximum theorem to noncompact image sets it also clarifies the results from feinberg kasyanov and zadoianchuk 2013 7 on the extension to noncompact image sets of another berge s theorem that states semi continuity of value functions here we explain that the notion of a k inf compact function introduced there is applicable to metrizable topological spaces and to more general compactly generated topological spaces for hausdorff topological spaces we introduce the notion of a k n inf compact function n stands for nets in k inf compactness which coincides with k inf compactness for compactly generated and in particular for metrizable topological spaces

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

a unifying approximate dynamic programming model for the economic lot scheduling problem we formulate the well known economic lot scheduling problem elsp with sequence dependent setup times and costs as a semi markov decision process using an affine approximation of the bias function we obtain a semi infinite linear program determining a lower bound for the minimum average cost rate under a very mild condition we can reduce this problem to a relatively small convex quadratically constrained linear problem by exploiting the structure of the objective function and the state space this problem is equivalent to the lower bound problem derived by dobson dobson g 1992 the cyclic lot scheduling problem with sequence dependent setups oper res 40 736 749 and reduces to the well known lower bound problem introduced in bomberger bomberger ee 1966 a dynamic programming approach to a lot size scheduling problem management sci 12 778 784 for sequence dependent setups we thus provide a framework that unifies previous work and opens new paths for future research on tighter lower bounds

dwell time based stabilisation of switched linear delay systems using clock dependent lyapunov krasovskii functionals dwell time stability conditions of the switched delay systems are derived using multiple clock dependent lyapunov krasovskii functionals the corresponding conditions are approximated by both using

hybrid control for switched linear systems with average dwell time this technical note presents a hybrid control scheme for the output feedback control of switched linear systems with average dwell time the proposed hybrid controller consists of a standard switching output feedback control law and a supervisor enforcing a reset rule for the switching controller states at each switching instant this hybrid control scheme provides an efficient and systema tic way for designing average dwell time switched linear control systems in the sense that the boundary condition can be incorporated into the synthesis problem in a convex formulation specifically bo th full order and reduced order controllers with guaranteed stability and optimal weighted h1 performance will be solved by linear matrix inequality lmi optimizations simulation studies are included to illustrate the effectiveness of the proposed approach index terms switching control average dwell time controller state reset full order and reduced order controllers lmi

optimality inequalities for average cost markov decision processes and the stochastic cash balance problem for general state and action space markov decision processes we present sufficient conditions for the existence of solutions of the average cost optimality inequalities these conditions also imply the convergence of both the optimal discounted cost value function and policies to the corresponding objects for the average costs per unit time case inventory models are natural applications of our results we describe structural properties of average cost optimal policies for the cash balance problem an inventory control problem where the demand may be negative and the decision maker can produce or scrap inventory we also show the convergence of optimal thresholds in the finite horizon case to those under the expected discounted cost criterion and those under the expected discounted costs to those under the average costs per unit time criterion

modeling ternary mixtures by mean field theory of polyelectrolytes coupled ginzburg landau and swift hohenberg equations abstract the purpose of this work is to model ternary mixtures using the theory of pattern formation and of polyelectrolytes with mean field approximations the model has two local non conserved order parameters in the free energy short range and long range nonlocal interactions between elements of the mixture are considered the spatiotemporal dynamics of the system is described by coupling the time dependent ginzburg landau equation and the swift hohenberg equation these non linear partial differential equations are solved with numerical methods to study the emergent spatially stable configurations the model shows a large diversity of patterns which permit an interpretation of the behavior of some biological systems and presents different growth lengths within its spatial structures

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

the total domination and total bondage numbers of extended de bruijn and kautz digraphs in this paper we consider the total domination number and the total bondage number for digraphs the total bondage number defined as the minimum number of edges whose removal enlarges the total domination number measures to some extent the robustness of a network where a minimum total dominating set is required we determine the total domination number and total bondage number of the extended de burijn digraph and the extended kautz digraph proposed by shibata and gonda in 1995 which generalize the classical de bruijn digraph and the kautz digraph

berge s theorem for noncompact image sets abstract for an upper semi continuous set valued mapping from one topological space to another and for a lower semi continuous function defined on the product of these spaces berge s theorem states lower semi continuity of the minimum of this function taken over the image sets it assumes that the image sets are compact for hausdorff topological spaces this paper extends berge s theorem to set valued mappings with possible noncompact image sets and studies relevant properties of minima

economic lot sizing an o n log n algorithm that runs in linear time in the wagner whitin case we consider the n period economic lot sizing problem where the cost coefficients are not restricted in sign in their seminal paper h m wagner and t m whitin proposed an o n2 algorithm for the special case of this problem where the marginal production costs are equal in all periods and the unit holding costs are nonnegative it is well known that their approach can also be used to solve the general problem without affecting the complexity of the algorithm in this paper we present an algorithm to solve the economic lot sizing problem in o n log n time and we show how the wagner whitin case can even be solved in linear time our algorithm can easily be explained by a geometrical interpretation and the time bounds are obtained without the use of any complicated data structure furthermore we show how wagner and whitin s and our algorithm are related to algorithms that solve the dual of the simple plant location formulation of the economic lot sizing problem

the price of anarchy under nonlinear and asymmetric costs in this paper we characterize the price of anarchy i e the inefficiency between user and system optimal solutions when costs are nonseparable asymmetric and nonlinear generalizing earlier work that has addressed the price of anarchy under separable costs the results in this paper apply primarily to nonatomic games such as the traffic equilibrium problem but also in competitive multiperiod pricing and competitive supply chain settings the bounds established in this paper are tight and explicitly account for the degree of asymmetry and nonlinearity of the cost function we first provide a proof method for problems with a positive definite jacobian matrix subsequently we use ideas from semidefinite optimization in order to account for problems with a positive semidefinite jacobian matrix where the first approach does not apply this latter connection also provides a different application of semidefinite optimization

on condensed forms for partially commuting matrices abstract two complex n n matrices a and b are said to be partially commuting if a and b have a common eigenvector we propose a condensed form for such matrices that can be obtained from a and b by a finite rational computation the condensed form is a pair of block triangular matrices with the sizes of the blocks being uniquely defined by the original matrices we then show how to obtain additional zeros inside the diagonal blocks of a condensed form by using the generalized lanczos procedure as given by elsner and ikramov this procedure can also be considered as a finite rational process we point out several applications of the constructions above it turns out that for laffey pairs of matrices i e for matrices a b such that rank a b 1 the condensed form is a pair of 2 2 block triangular matrices using this fact we show an economical way to find a spanning set for the matrix algebra generated by laffey matrices a and b another application concerns so called k self adjoint matrices we examine such matrices in the unitary space as well as in a krein space of defect 1 as an appendix we give a new description of the shemesh subspace of matrices a and b this is the maximal common invariant subspace of a and b on which these matrices commute

on quadratic lyapunov functions a topological structure as a subset of 0 2 spl pi sup l spl times spl ropf sub sup n 1 is proposed for the set of quadratic lyapunov functions qlfs of a given stable linear system a necessary and sufficient condition for the existence of a common qlf of a finite set of stable matrices is obtained as the positivity of a certain integral the structure and the conditions are considerably simplified for planar systems it is also proved that a set of block upper triangular matrices share a common qlf if each set of diagonal blocks share a common qlf

single and multi period optimal inventory control models with risk averse constraints this paper presents some convex stochastic programming models for single and multi period inventory control problems where the market demand is random and order quantities need to be decided before demand is realized both models minimize the expected losses subject to risk aversion constraints expressed through value at risk var and conditional value at risk cvar as risk measures a sample average approximation method is proposed for solving the models and convergence analysis of optimal solutions of the sample average approximation problem is presented finally some numerical examples are given to illustrate the convergence of the algorithm

topological properties of star graphs abstract our purpose in the present paper is to investigate different topological properties of the recently introduced star graphs which are being viewed as attractive alternatives to n cubes or hypercubes these properties are interesting by themselves from a graph theory point of view as well as they have direct in generating vertex disjoint paths and minimal paths in a star graph they can also be readily utilized to design routing algorithms and to compute contention and traffic congestion in networks that use star graphs as the underlying topology

fault diameter of interconnection networks abstract we introduce the concept of fault diameter of interconnection networks the motivation is to estimate the degradation of performance under maximally fault conditions we derive fault diameter of specific classes of commonly used interconnection networks and various types of product graphs

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

a note on a production control model for a facility with limited storage capacity in a random environment abstract this note presents an extension of our earlier paper on a production inventory system with limited storage capacity in a multi state random environment i e e mohebbi a production inventory model with randomly changing environmental conditions eur j res 174 2006 539 552 more specifically it assumes that the production rate as well as the occurrence rate and batch sizes of a compound poisson demand stream are influenced by the state of a continuous time homogeneous markov chain representing the random environment we present an adaptation of the system point method of level crossings which yields the limiting distribution of inventory level stock on hand for a two parameter production control policy when stockouts are lost

coordinating inventory control and pricing strategies with random demand and fixed ordering cost the infinite horizon case we analyze an infinite horizon single product periodic review model in which pricing and production inventory decisions are made simultaneously demands in different periods are identically distributed random variables that are independent of each other and their distributions depend on the product price pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered the objective is to maximize expected discounted or expected average profit over the infinite planning horizon we show that a stationary s s p policy is optimal for both the discounted and average profit models with general demand functions in such a policy the period inventory is managed based on the classical s s policy and price is determined based on the inventory position at the beginning of each period

a production inventory model with randomly changing environmental conditions we consider a limited capacity production inventory system with linear production rate and compound poisson demand in which both production and demand processes are subject to independently and randomly changing environmental conditions assuming that these conditions are represented by two continuous time homogeneous markov chains and shortages are lost we derive the limiting distribution of the inventory level and present some numerical results in terms of the ensuing performance measures

stability of simultaneously block triangularisable switched systems with partial state reset abstractwe study the stability of a certain class of switched systems where discontinuous jumps resets on some of the state components are allowed at the switching instants it is known that if all components of the state are available for reset the system can be stabilisable by an adequate choice of resets however this question may have negative answer if there are forbidden state components for reset we give a sufficient condition for the stabilisability of a switched system under arbitrary switching by partial state reset in terms of a block simultaneous triangularisability condition based on this sufficient condition we show that the particular class of systems with partially commuting stable system matrices is stabilisable by partial state reset we also provide an algorithm that allows testing whether a switched system belongs to this particular class of systems

extension of de bruijn graph and kautz graph abstract we introduce a method of division of vectors to extend the definitions of de bruijn graphs and kautz graphs basic properties of extended de bruijn graphs and extended kautz graphs are given and finally several new results on isomorphic factorization of those graphs are given

switching lpv control designs using multiple parameter dependent lyapunov functions in this paper we study the switching control of linear parameter varying lpv systems using multiple parameter dependent lyapunov functions to improve performance and enhance control design flexibility a family of lpv controllers is designed each suitable for a specific parameter subregion they are switched so that the closed loop system remains stable and its performance is optimized two switching logics hysteresis switching and switching with average dwell time are examined the control synthesis conditions for both switching logics are formulated as matrix optimization problems which are generally non convex but can be convexified under some simplifying assumptions the hysteresis switching lpv control scheme is then applied to an active magnetic bearing problem

dwell time based stabilisation of switched delay systems using free weighting matrices abstractin this paper we present a quasi convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems piecewise lyapunov krasovskii functionals are introduced and the upper bound for the derivative of lyapunov functionals is estimated by free weighting matrices method to investigate non switching stability of each candidate subsystems then a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system once these conditions are represented by a set of linear matrix inequalities dwell time optimisation problem can be formulated as a standard quasi convex optimisation problem numerical examples are given to illustrate the improvements over previously obtained dwell time bounds using the results obtained in the stability case we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers the algorithm solves the problem with successive linearisation of nonlin

stability of switched systems a lie algebraic condition we present a sucient condition for asymptotic stability of a switched linear system in terms of the lie algebra generated by the individual matrices namely if this lie algebra is solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of linear systems satisfying this condition possesses a quadratic common lyapunov function we also discuss the implications of this result for switched nonlinear systems c 1999 elsevier science b v all rights reserved

robust solutions to uncertain semidefinite programs in this paper we consider semidefinite programs sdps whose data depend on some unknown but bounded perturbation parameters we seek robust solutions to such programs that is solutions which minimize the worst case objective while satisfying the constraints for every possible value of parameters within the given bounds assuming the data matrices are rational functions of the perturbation parameters we show how to formulate sufficient conditions for a robust solution to exist as sdps when the perturbation is full our conditions are necessary and sufficient in this case we provide sufficient conditions which guarantee that the robust solution is unique and continuous holder stable with respect to the unperturbed problem s data the approach can thus be used to regularize ill conditioned sdps we illustrate our results with examples taken from linear programming maximum norm minimization polynomial interpolation and integer programming

a class of nonlinear nonseparable continuous knapsack and multiple choice knapsack problems this paper considers a general class of continuous nonlinear and nonseparable knapsack problems special cases of which arise in numerous operations and financial contexts we develop important properties of optimal solutions for this problem class based on the properties of a closely related class of linear programs using these properties we provide a solution method that runs in polynomial time in the number of decision variables while also depending on the time required to solve a particular one dimensional optimization problem thus for the many applications in which this one dimensional function is reasonably well behaved e g unimodal the resulting algorithm runs in polynomial time we next develop a related solution approach to a class of continuous nonlinear and nonseparable multiple choice knapsack problems this algorithm runs in polynomial time in both the number of variables and the number of variants per item while again dependent on the complexity of the same one dimensional optimization problem as for the knapsack problem computational testing demonstrates the power of the proposed algorithms over a commercial global optimization software package

the lyapunov direct method for the stabilisation of the ball on the actuated beam this article deals with the stabilisation of a ball on an actuated beam independently of whether or not the force acts on the non actuated coordinate the feedback control law is deduced via application of the traditional lyapunov stability method the balancing strategy consists of shaping a convenient energy function that allows us to derive the required asymptotic stabilising controller to this end we introduce an auxiliary control input variable in order to algebraically obtain the kinetic metric and the potential energy of the entire system the formed positive energy function along with the proposed feedback controller assures that the overall system is a dissipative one

stability of switched systems with partial state reset in this note we consider switched systems and switched systems with state reset in particular we focus on the case of partial reset i e where only some state components may undergo the action of a reset first we consider switched systems with pre specified partial reset and investigate under which conditions such systems are stable in a second stage we consider the problem of stabilization by partial reset which consists in finding a suitable partial reset for a given switched system that makes this system stable under arbitrary switching

on diagnosability of large fault sets in regular topology based computer systems the classical diagnosability approach has its limitation when dealing with large fault sets in large multiprocessor systems this is due to limited diagnosability of large multiprocessor systems connected using regular interconnection structures we propose an alternative approach to system diagnosis by allowing a few upper bounded number of units to be diagnosed incorrectly this measure is called t k diagnosability using this new measure it is possible to increase the degree of diagnosability of large system considerably the t k diagnosis guarantees that all the faulty units processors in a system are detected provided the number of faulty units does not exceed t while at most k units are incorrectly diagnosed we provide necessary and sufficient conditions for t k diagnosability and discuss their implication to demonstrate the power of this approach we analyze the diagnosability of large systems connected as hypercube star graph and meshes it is shown that a substantial increase in the degree of diagnosability of these structures is achieved compared with the degree of diagnosability achieved using the classic diagnosability approach at the cost of a comparably small number of incorrectly diagnosed units

a simple forward algorithm to solve general dynamic lot sizing models with n periods in 0n log n or 0n time this paper is concerned with the general dynamic lot size model or generalized wagner whitin model let n denote the number of periods into which the planning horizon is divided we describe a simple forward algorithm which solves the general model in 0n log n time and 0n space as opposed to the well known shortest path algorithm advocated over the last 30 years with 0n2 time a linear i e 0n time and space algorithm is obtained for two important special cases a models without speculative motives for carrying stock i e where in each interval of time the per unit order cost increases by less than the cost of carrying a unit in stock b models with nondecreasing setup costs we also derive conditions for the existence of monotone optimal policies and relate these to known planning horizon and other results from the literature

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

from cost sharing mechanisms to online selection problems we consider a general class of online optimization problems called online selection problems where customers arrive sequentially and one has to decide upon arrival whether to accept or reject each customer if a customer is rejected then a rejection cost is incurred the accepted customers are served with minimum possible cost either online or after all customers have arrived the goal is to minimize the total production costs for the accepted customers plus the rejection costs for the rejected customers these selection problems are related to online variants of offline prize collecting combinatorial optimization problems that have been widely studied in the computer science literature in this paper we provide a general framework to develop online algorithms for this class of selection problems in essence the algorithmic framework leverages any cost sharing mechanism with certain properties into a poly logarithmic competitive online algorithm for the respective problem the competitive ratios ar

brief paper stability properties of reset systems stability properties for a class of reset systems such as systems containing a clegg integrator are investigated we present lyapunov based results for verifying l 2 and exponential stability of reset systems our results generalize the available results in the literature and can be easily modified to cover l p stability for arbitrary email protected 1 several examples illustrate that introducing resets in a linear system may reduce the l 2 gain if the reset controller parameters are carefully tuned

the bondage numbers of extended de bruijn and kautz digraphs in this paper we consider the bondage number b g for a digraph g which is defined as the minimum number of edges whose removal results in a new digraph with larger domination number this parameter measures to some extent the robustness of an interconnection network with respect to link failures by constructing a family of minimum dominating sets we compute the bondage numbers of the extended de bruijn digraph and the extended kautz digraph as special cases we obtain for the de bruijn digraph b d n and the kautz digraph k d n that b b d n d if n is odd and d b b d n 2d if n is even and b k d n d 1

on the fault tolerant embedding of complete binary trees in the pancake graph interconnection network abstract this paper studies the problem of embedding complete binary trees cbt s into an n dimensional pancake graph p n with fault tolerant capability first a new embedding scheme is developed for mapping a source cbt with height m 2 n log m and dilation 2 onto the p n this scheme not only embeds a cbt whose height is very close to the largest possible one but also saves a lot of unused generators and generator products furthermore these unused generators and generator products are used to recover faulty nodes and embed multiple cbt s maximally near 2 3 nodes of the source cbt are allowed to be faulty at the same time and can be recovered by our scheme with dilation 4 alternatively a scheme which can embed a cbt with height m 2 n log m 1 is also given in this case if all nodes in the cbt are faulty they can be recovered in the smallest number of recovery steps and only with dilation 4

average optimality in dynamic programming on borel spaces unbounded costs and controls abstract we show the existence of average cost optimal stationary policies in a class of discrete time markov control processes with borel state space unbounded costs and non compact control sets

average optimality in dynamic programming with general state space a markovian decision model with general state space compact action space and the average cost as criterion is considered the existence of an optimal policy is shown via an optimality inequality in terms of the minimal average cost g and a relative value function w the existence of some w is usually shown via relative compactness in a space of real valued functions on the state space here it shall be shown that one can instead do with pointwise relative compactness in the set of real numbers if one makes use of a generalized lower limit of functions an application to an inventory model is given

average cost markov decision processes with weakly continuous transition probabilities this paper presents sufficient conditions for the existence of stationary optimal policies for average cost markov decision processes with borel state and action sets and weakly continuous transition probabilities the one step cost functions may be unbounded and the action sets may be noncompact the main contributions of this paper are i general sufficient conditions for the existence of stationary discount optimal and average cost optimal policies and descriptions of properties of value functions and sets of optimal actions ii a sufficient condition for the average cost optimality of a stationary policy in the form of optimality inequalities and iii approximations of average cost optimal actions by discount optimal actions

optimal fault tolerant routing algorithm and fault tolerant diameter in directed double loop networks this paper addresses the reliability of directed double loop networks g n r s and studies the problems about optimal fault tolerant routing fault tolerant diameter etc in g n r s firstly we study the shapes of the l shaped tiles which are the minimum distance diagram of directed double loop networks we divide them into four types there are different parameters for each type according to the solutions to the congruence equation then we study the distributions of the optimal equivalent nodes for different destination nodes and present an optimal fault tolerant routing algorithm and a formula computing the fault tolerant diameter finally we prove that there is a lower bound for fault tolerant diameter and show that there may be lots of double optimal directed double loop networks in some infinite clusters of g n r s according to the proposed fault tolerant routing algorithm the reliability and transmission performance will be optimal when some faults occur in g n r s

a counterexample on the optimality equation in markov decision chains with the average cost criterion abstract we consider markov decision processes with denumerable state space and finite control sets the performance index of a control policy is a long run expected average cost criterion and the cost function is bounded below for these models the existence of average optimal stationary policies was recently established in 11 under very general assumptions such a result was obtained via an optimality inequality here we use a simple example to prove that the conditions in 11 do not imply the existence of a solution to the average cost optimality equation

optimizing algebraic connectivity by edge rewiring robustness in complex networks is an ongoing research effort that seeks to improve the connectivity of networks against attacks and failures among other measures algebraic connectivity has been used to characterize processes such as damped oscillation of liquids in connected pipes similar characterizations include the number of edges necessary to disconnect a network the larger the algebraic connectivity the larger the number of edges required to disconnect a network and hence the more robust a network in this paper we answer the question which edge can we rewire to have the largest increase in algebraic connectivity furthermore we extend the rewiring of a single edge to rewiring multiple edges to realize the maximal increase in algebraic connectivity the answer to this question above can provide insights to decision makers within various domains such as communication and transportation networks who seek an efficient solution to optimize the connectivity and thus increase the robustness of their networks most importantly our analytical and numerical results not only provide insights to the number of edges to rewire but also the location in the network where these edges would effectuate the maximal increase in algebraic connectivity and therefore enable a maximal increase in robustness

asymptotic optimality and rates of convergence of quantized stationary policies in stochastic control we consider the discrete approximation of stationary policies for a discrete time markov decision process with polish state and action spaces under total discounted and average cost criteria deterministic stationary quantizer policies are introduced and shown to be able to approximate optimal deterministic stationary policies with arbitrary precision under mild technical conditions thus demonstrating that one can search for varepsilon optimal policies within the class of quantized control policies we also derive explicit bounds on the approximation error in terms of the quantization rate

on the vanishing discount factor approach for markov decision processes with weakly continuous transition probabilities abstract this note deals with average cost markov decision processes with borel state and control spaces possibly unbounded costs and non compact action subsets under the assumption of weak continuity of the transition law it provides an elementary proof of the existence of average cost optimal stationary policies using the vanishing discount factor approach

robust ranking and portfolio optimization the portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out of sample performance due to estimation errors in the expected returns a practical method for portfolio construction is to use assets ordering information expressed in the form of preferences over the stocks instead of the exact expected returns due to the fact that the ranking itself is often described with uncertainty we introduce a generic robust ranking model and apply it to portfolio optimization in this problem there are n objects whose ranking is in a discrete uncertainty set we want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking this robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general to solve this robust ranking problem we apply the constraint generation method where constraints are efficiently generated by solving a network flow problem for empirical tests we use post earnings announcement drifts to obtain ranking uncertainty sets for the stocks in the djia index we demonstrate that our robust portfolios produce smaller risk compared to their non robust counterparts

a unified formulation of kautz network and generalized hypercube hypercube and kautz network each possess certain desirable properties however some of the attractive features of one network are not found in the other a novel class of network topologies proposed in this paper has the generalized hypercube and the kautz network as its two extremes the proposed network inherits the topological properties of both the kautz network and the generalized hypercube to a varying degree this allows us to trade off cost and performance effectively and construct networks which are most suitable for a particular purpose in the present paper we investigate the connectivity wide diameter fault tolerance hamiltonicity

competitive multi period pricing for perishable products a robust optimization approach we study a multi period oligopolistic market for a single perishable product with fixed inventory our goal is to address the competitive aspect of the problem together with demand uncertainty using ideas from robust optimization and variational inequalities the demand function for each seller has some associated uncertainty and we assume that the sellers would like to adopt a policy that is robust to adverse uncertain circumstances we believe this is the first paper that uses robust optimization for dynamic pricing under competition in particular starting with a given fixed inventory each seller competes over a multi period time horizon in the market by setting prices and protection levels for each period at the beginning of the time horizon any unsold inventory at the end of the horizon is worthless the sellers do not have the option of periodically reviewing and replenishing their inventory we study non cooperative nash equilibrium policies for sellers under such a model this kind of a setup can be used to model pricing of air fares hotel reservations bandwidth in communication networks etc in this paper we demonstrate our results through some numerical examples

asynchronous switching output feedback control of discrete time switched linear systems in this paper the problem of dynamic output feedback control synthesis is addressed for discrete time switched linear systems under asynchronous switching the proposed hybrid controller consists of a standard dynamic output feedback switching control law and an impulsive reset law induced by controller state jumps using the average dwell time technique incorporating with multiple quadratic lyapunov functions the switching control synthesis conditions for asymptotic stability with guaranteed weighted l2 gain performance are derived as a set of linear matrix inequalities lmis the proposed hybrid synthesis scheme advances existing design methods for output feedback asynchronous switching control of switched linear systems in two important aspects lmi formulation of the synthesis problem and arbitrary order of the controller state a numerical example is used to illustrate the effectiveness and advantages of the proposed design technique

design to minimize diameter on building block network this paper proposes a simple algorithm for the graph design of small diameter networks for given nodes n and degree d this algorithm can be used to construct a directed graph with diameter logd n which is at most one larger than the lower bound logd n d 1 1 1 its average distance is also close to the lower bound the algorithm can be used to construct a directed graph with smaller diameter compared with any other conventional methods when n is larger

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

integrated market selection and production planning complexity and solution approaches emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance operations models that account for supply costs and constraints as well as a supplier s ability to influence demand characteristics can lead to an improved match between supply and demand this paper presents a class of optimization models that allow a supplier to select from a set of potential markets those markets that provide maximum profit when production procurement economies of scale exist in the supply process the resulting optimization problem we study possesses an interesting structure and we show that although the general problem is mathcal np complete a number of relevant and practical special cases can be solved in polynomial time we also provide a computationally very efficient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances

connectivity of regular directed graphs with small diameters this paper clarifies the relation between the diameter k and the edge or node connectivity ce or c of digraphs the following two inequalities are derived where n is the number of nodes d is the maximum degree and d is the minimum degree

selected topics in robust convex optimization robust optimization is a rapidly developing methodology for handling optimization problems affected by non stochastic uncertain but bounded data perturbations in this paper we overview several selected topics in this popular area specifically 1 recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data 2 tractability of robust counterparts 3 links between ro and traditional chance constrained settings of problems with stochastic data and 4 a novel generic application of the ro methodology in robust linear control

distributed fault tolerant ring embedding and reconfiguration in hypercubes to embed a ring in a hypercube is to find a hamiltonian cycle through every node of the hypercube it is obvious that no 2 sup n node hamiltonian cycle exists in an n dimensional faulty hypercube which has at least one faulty node however if a hypercube has faulty links only and the number of faulty links is at most n 2 at least one 2 sup n node hamiltonian cycle can be found in this paper we propose a distributed ring embedding algorithm that can find a hamiltonian cycle in a fault free or faulty n dimensional hypercube q and the complexity is o n parallel steps the algorithm is based on the recursion property of the hypercube and the free link dimension concept in some cases even when the number of faulty links is larger than n 2 hamiltonian cycles may still exist we show that the largest possible number of faulty links that can be tolerated is 2 sup n 1 1 the performance and the constraints of the fault tolerant algorithm is also analyzed in detail in this paper furthermore a dynamic reconfiguration algorithm for an embedded ring is proposed and discussed due to the distributed nature of the algorithms they are useful for the simulation of ring based multiprocessors on mimd hypercube multiprocessors

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

fundamental properties of reset control systems reset controllers are linear controllers that reset some of their states to zero when their input is zero we are interested in their feedback connection with linear plants and in this paper we establish fundamental closed loop properties including stability and asymptotic tracking this paper considers more general reset structures than previously considered allowing for higher order controllers and partial state resetting it gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded input bounded state stability and steady state performance unlike previous related research which includes the study of impulsive differential equations our stability results require no assumptions on the evolution of reset times

turing patterns with pentagonal symmetry we explore numerically the formation of turing patterns in a confined circular domain with small aspect ratio our results show that stable fivefold patterns are formed over a well defined range of disk sizes offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids using this pattern as a seed more complex biological structures can be mimicked such as the pigmentation pattern of sea urchins and the plate arrangements of the calyxes of primitive camerate crinoids

partially observable total cost markov decision processes with weakly continuous transition probabilities this paper describes sufficient conditions for the existence of optimal policies for partially observable markov decision processes pomdps with borel state observation and action sets when the goal is to minimize the expected total costs over finite or infinite horizons for infinite horizon problems one step costs are either discounted or assumed to be nonnegative action sets may be noncompact and one step cost functions may be unbounded the introduced conditions are also sufficient for the validity of optimality equations semicontinuity of value functions and convergence of value iterations to optimal values since pomdps can be reduced to completely observable markov decision processes comdps whose states are posterior state distributions this paper focuses on the validity of the above mentioned optimality properties for comdps the central question is whether the transition probabilities for the comdp are weakly continuous we introduce sufficient conditions for this and show that the tr