the balanced linear programming problem abstract the balanced linear programming problem blpp arises in situations which require equitable distribution of a scarce resource the blpp can be transformed to the standard form of the linear programming problem by introducing 2 n 2 additional variables and 2 n additional constraints this transformation is not desirable from the computational point of view for larger values of n as it increases the problem size substantially it is also undesirable from a theoretical perspective as it might affect the special structure of the constraint matrix in this paper we develop an algorithm for the blpp which does not require problem enlargement the algorithm is based on the relationship between the blpp and the minimax linear programming problem and solving the latter problem parametrically our algorithm in essence performs steps that are similar to those performed in the parametric simplex method with parametric right hand side we then adapt our algorithm for the network flow problem and this specialized algorithm can be applied on the network directly without maintaining the simplex tableau

an exact decomposition algorithm for the generalized knapsack sharing problem abstract this paper presents an exact algorithm for solving the knapsack sharing problem with common items in literature this problem is also denominated the generalized knapsack sharing problem gksp the gksp is np hard because it lays on the 0 1 knapsack problem and the knapsack sharing problem the proposed exact method is based on a rigorous decomposition technique which leads to an intense simplification of the solution procedure for the gksp furthermore in order to accelerate the procedure for finding the optimum solution an upper bound and several reduction strategies are considered computational results on two sets of benchmark instances from literature show that the proposed method outperforms the other approaches in most instances

bounded knapsack sharing a bounded knapsack sharing problem is a maximin or minimax mathematical programming problem with one or more linear inequality constraints an objective function composed of single variable continuous functions called tradeoff functions and lower and upper bounds on the variables a single constraint problem which can have negative or positive constraint coefficients and any type of continuous tradeoff functions including multi modal multiple valued and staircase functions is considered first limiting conditions where the optimal value of a variable may be plus or minus infinity are explicitly considered a preprocessor procedure to transform any single constraint problem to a finite form problem an optimal feasible solution exists with finite variable values is developed optimality conditions and three algorithms are then developed for the finite form problem for piecewise linear tradeoff functions the preprocessor and algorithms are polynomially bounded the preprocessor is then modified to handle bounded knapsack sharing problems with multiple constraints an optimality condition and algorithm is developed for the multiple constraint finite form problem for multiple constraints the time needed for the multiple constraint finite form algorithm is the time needed to solve a single constraint finite form problem multiplied by the number of constraints some multiple constraint problems cannot be transformed to multiple constraint finite form problems

a min max sum resource allocation problem and its applications in this paper we consider a class of discrete resource allocation problems with a min max sum objective function we first provide several examples of practical applications of this problem we then develop a branch and bound procedure for solving the general case of this computationally intractable problem the proposed solution procedure employs a surrogate relaxation technique to obtain lower and upper bounds on the optimal objective function value of the problem to obtain the multipliers of the surrogate relaxation two alternative approaches are discussed we also discuss a simple approximation algorithm with a tight bound our computational results support the effectiveness of the branch and bound procedure for fairly large size problems

some exact algorithms for the knapsack sharing problem abstract the knapsack sharing problem ksp is formulated as an extension to the ordinary knapsack problem the ksp is n p hard we present a branch and bound algorithm and a binary search algorithm to solve this problem to optimality these algorithms are implemented and computational experiments are carried out to analyse the behavior of the developed algorithms as a result we find that the binary search algorithm solves ksps with up to 20 000 variables in less than a minute in our computing environment

on solving linear programs with the ordered weighted averaging objective abstract the problem of aggregating multiple criteria to form overall objective functions is of considerable importance in many disciplines the most commonly used aggregation is based on the weighted sum the ordered weighted averaging owa aggregation introduced by yager uses the weights assigned to the ordered values i e to the worst value the second worst and so on rather than to the specific criteria this allows to model various aggregation preferences preserving simultaneously the impartiality neutrality with respect to the individual criteria in this paper we analyze solution procedures for linear programs with the owa objective functions two alternative linear programming formulations are introduced and their computational efficiency is analyzed

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

a graphical method to solve a family of allocation problems abstract this paper discusses the classical resource allocation problem by very elementary arguments on lagrangian duality it is shown that this problem can be reduced to a single one dimensional maximization of a differentiable concave function moreover a simple graphical method is developed and applied to a family of well known problems from the literature

technical note integer allocation problems of min max type with quasiconvex separable functions the paper treats the problem of integer resource allocations using the min max criterion the objective function is assumed to be strictly quasiconvex in the integer sense and separable the optimality conditions are used to obtain a solution algorithm which may be simplified in the case of strict monotonicity

equitable aggregations and multiple criteria analysis abstract in the past decade increasing interest in equity issues resulted in new methodologies in the area of operations research this paper deals with the concept of equitably efficient solutions to multiple criteria optimization problems multiple criteria optimization usually starts with an assumption that the criteria are incomparable however many applications arise from situations which present equitable criteria moreover some aggregations of criteria are often applied to select efficient solutions in multiple criteria analysis the latter enforces comparability of criteria possibly rescaled this paper presents aggregations which can be used to derive equitably efficient solutions to both linear and nonlinear multiple optimization problems an example with equitable solutions to a capital budgeting problem is analyzed in detail an equitable form of the reference point method is introduced and analyzed

new multi objective method to solve reentrant hybrid flow shop scheduling problem this paper focuses on the multi objective resolution of a reentrant hybrid flow shop scheduling problem rhfs in our case the two objectives are the maximization of the utilization rate of the bottleneck and the minimization of the maximum completion time this problem is solved with a new multi objective genetic algorithm called l nsga which uses the lorenz dominance relationship the results of l nsga are compared with nsga2 spea2 and an exact method a stochastic model of the system is proposed and used with a discrete event simulation module a test protocol is applied to compare the four methods on various configurations of the problem the comparison is established using two standard multi objective metrics the lorenz dominance relationship provides a stronger selection than the pareto dominance and gives better results than the latter the computational tests show that l nsga provides better solutions than nsga2 and spea2 moreover its solutions are closer to the optimal front the efficiency of our method is verified in an industrial field experiment

a common framework for complete and incomplete attitude synchronization in networks with switching topology in this paper we study attitude synchronization for elements in the unit sphere in mathbb r scriptscriptstyle scriptscriptstyle 3 and for elements in the three dimensional 3 d rotation group for a network with switching topology the agents angular velocities are assumed to be the control inputs and a switching control law for each agent is devised that guarantees synchronization provided that all elements are initially contained in a region which we identify later in the paper the control law is decentralized and it does not require a common orientation frame among all agents we refer to synchronization of unit vectors in mathbb r scriptscriptstyle 3 as incomplete synchronization and of 3 d rotation matrices as complete synchronization our main contribution lies in showing that these two problems can be analyzed under a common framework where all agents dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension

algorithms for separable nonlinear resource allocation problems we consider a simple resource allocation problem with a single resource constraint the objective function is composed of separable convex performance functions one for each activity likewise the constraint has separable convex resource usage functions one for each activity the objective is to minimize the sum of the performance functions subject to satisfying the resource constraint and nonnegativity constraints this problem extends the well studied problem in which the resource constraint is linear we present several algorithms to solve the problem these algorithms extend approaches developed for the linearly constrained problem they can readily solve large problems and find the optimal solution in a number of iterations that does not exceed the number of variables we provide several examples for illustration purposes present computational results and highlight the similarities and differences among the algorithms

interleaved lattice based minimax distance designs summarywe propose a new method to construct maximin distance designs with arbitrary numbers of dimensions and points the proposed designs hold interleaved layer structures and are by far the best maximin distance designs in four or more dimensions applicable to distance measures with equal or unequal weights our method is useful for emulating computer experiments when a relatively accurate a priori guess on variable importance is available

representation of general and polyhedral subsemilattices and sublattices of product spaces abstract it is shown that each element of the lattice of meet resp join sublattices of a product s of n chains has a representation as the intersection of n subsets of s the i th of which is decreasing resp increasing for each fixed value of the i th coordinate for each i this result is applied to show that an arbitrary element of the lattice of sublattices of s has a representation as the intersection of n 2 subsets the ij th of which is decreasing for each fixed value of the i th and increasing for each fixed value of the j th coordinate for each i j irreducible representations are given in each case providing an alternative proof of an instance of hashimoto s 1952 representation of sublattices of a distributive lattice moreover irreducible representations are given for the polyhedral members of the lattice of closed convex subsets of n dimensional euclidean space that are at once subsemilattices or sublattices it is alsoshown that the polyhedral subsemilattices and sublattices can be represented as duals respectively of pre leontief substitution systems and generalized network flow problems finally the problems of checking whether a polyhedral set is a subsemilattice or sublattice are reduced to that of solving a system of linear inequalities thereby showing that these recognition problems can be solved in polynomial time

combining equity and utilitarianism in a mathematical programming model we discuss the problem of combining the conflicting objectives of equity and utilitarianism for social policy making in a single mathematical programming model the definition of equity we use is the rawlsian one of maximizing the minimum utility over individuals or classes of individuals however when the disparity of utility becomes too great the objective becomes progressively utilitarian such a model is particularly applicable not only to health provision but to other areas as well building a mixed integer linear programming milp formulation of the problem raises technical issues because the objective function is nonconvex and the hypograph is not milp representable in its initial form we present a succinct formulation and show that it is sharp in the sense that its linear programming relaxation describes the convex hull of the feasible set before extra resource allocation or policy constraints are added we apply the formulation to a healthcare planning problem and show that instances of realistic size are easily solved by standard milp software this paper was accepted by dimitris bertsimas optimization

a branch and bound algorithm for the mini max spanning forest problem the mini max spanning forest problem requires to find a spanning forest of an undirected graph that minimizes the maximum of the costs of constituent trees in a previous work we proved this problem np hard in the current paper we present three lower bounds for this problem and develop a branch and bound algorithm to solve the problem exactly the algorithm is implemented and numerical experiments are conducted on a series of test problems the experiments compare the performances of the proposed bounds and search strategies in the algorithm as well as investigate the effects of instance characteristics on the behavior of the algorithm also extension of the problem to the case of more than two root vertices as well as to the problem of determining the root locations are discussed

on equitable resource allocation problems a lexicographic minimax approach in this expository paper we review a variety of resource allocation problems in which it is desirable to allocate limited resources equitably among competing activities applications for such problems are found in diverse areas including distribution planning production planning and scheduling and emergency services location each activity is associated with a performance function representing for example the weighted shortfall of the selected activity level from a specified target a resource allocation solution is called equitable if no performance function value can be improved without either violating a constraint or degrading an already equal or worse off i e larger performance function value that is associated with a different activity a lexicographic minimax solution determines this equitable solution that is it determines the lexicographically smallest vector whose elements the performance function values are sorted in nonincreasing order the problems reviewed include large scale allocation problems with multiple knapsack resource constraints multiperiod allocation problems for storable resources and problems with substitutable resources the solution of large scale problems necessitates the design of efficient algorithms that take advantage of special mathematical structures indeed efficient algorithms for many models will be described we expect that this paper will help practitioners to formulate and solve diverse resource allocation problems and motivate researchers to explore new models and algorithmic approaches

solving knapsack sharing problems with general tradeoff functions a knapsack sharing problem is a maximin or minimax mathematical programming problem with one or more knapsack constraints an inequality constraint with all non negative coefficients all knapsack sharing algorithms to date have assumed that the objective function is composed of single variable functions called tradeoff functions which are strictly increasing continuous functions this paper develops optimality conditions and algorithms for knapsack sharing problems with any type of continuous tradeoff function including multiple valued and staircase functions which can be increasing decreasing unimodal bimodal or even multi modal to do this optimality conditions are developed for a special type of multiple valued nondecreasing tradeoff function called an ascending function the optimal solution to any knapsack sharing problem can then be found by solving an equivalent problem where all the tradeoff functions have been transformed to ascending functions polynomial algorithms are developed for piecewise linear tradeoff functions with a fixed number of breakpoints the techniques needed to construct efficient algorithms for any type of tradeoff function are discussed

chimeralike states in two distinct groups of identical populations of coupled stuart landau oscillators we show the existence of chimeralike states in two distinct groups of identical populations of globally coupled stuart landau oscillators the existence of chimeralike states occurs only for a small range of frequency difference between the two populations and these states disappear for an increase of mismatch between the frequencies here the chimeralike states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population we also find that such states observed in two distinct groups of identical populations of nonlocally coupled oscillators are different from the above case in which coexisting domains of synchronized and desynchronized oscillations are observed in one population and the second population exhibits synchronized oscillations for spatially prepared initial conditions perturbation from such spatially prepared initial condition leads to the existence of imperfectly synchronized states an imperfectly synchronized state represents the existence of solitary oscillators which escape from the synchronized group in population i and synchronized oscillations in population ii also the existence of chimera state is independent of the increase of frequency mismatch between the populations we also find the coexistence of different dynamical states with respect to different initial conditions which causes multistability in the globally coupled system in the case of nonlocal coupling the system does not show multistability except in the cluster state region

passivity based pose synchronization in three dimensions this paper addresses passivity based pose synchronization in the special euclidean group se 3 we first develop a passivity based distributed velocity input law to achieve pose synchronization we next show that the pose synchronizes exponentially fast under an assumption on the initial states of the bodies with an exponential convergence rate given by algebraic connectivity of interconnection graphs we also prove pose synchronization in the presence of communication delays and topology switches we moreover give further extensions of the present law where desirable velocities and collision avoidance are taken into account finally the effectiveness of the present inputs is demonstrated through numerical simulations and experiments on a planar 2d test bed

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

inverse optimal design of input to state stabilizing nonlinear controllers we show that input to state stabilizability as defined by sontag 1989 1995 is both necessary and sufficient for the solvability of a hamilton jacobi isaacs equation associated with a meaningful differential game problem similar to but more general than the nonlinear h sub spl infin problem the significance of the result stems from the fact that constructive solutions to the input to state stabilization problem are available presented in the paper and that as shown here inverse optimal controllers possess margins on input to state stability against a certain class of input unmodeled dynamics rather than completion of squares the main tools in our analysis are legendre fenchel transformations and the general form of young s inequality

globally clustered chimera states in delay coupled populations we have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically and aperiodically and become unstable depending upon the value of coupling delay we also find that the coupling delay induces frequency suppression in the desynchronized group we provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena

pinning control for cluster synchronisation of complex dynamical networks with semi markovian jump topology in this paper a pinning controller is designed for cluster synchronisation of complex dynamical networks with semi markovian jump topology which covers the concept of the conventional markovian jump as a special case to decide on the pinned node for the cluster synchronisation a novel procedure is proposed based on a topological structure in addition criteria for the synchronisation are separately derived for the controller with the mode independent and mode dependent pinned node respectively a practical example is given to illustrate the effectiveness of the proposed methods

optimisation and adaptation of synchronisation controllers for networked second order infinite dimensional systems abstractthe adaptation and optimisation of synchronisation control for networked second order distributed parameter systems are considered the objective is to design output feedback controllers guaranteeing agreement between the states of the n systems that individually track a reference model the controller structure involves feedback terms consisting of the pairwise difference of the measurements of the second order systems as well as coupling terms that enforce consensus placing the closed loop networked systems in aggregate form allows for further optimisation of the synchronisation gains using the aggregate systems closed loop energy as a suitable optimisation measure the search for the synchronisation gains reduces to the minimisation of the optimisation index which eventually is described by the trace of the solution to a parameterised lyapunov operator equation considering the adaptation of the synchronisation gains offers an alternative to optimisation the adaptation is based on lyapuno

intermittency transition to generalized synchronization in coupled time delay systems we report the nature of the transition to generalized synchronization gs in a system of two coupled scalar piecewise linear time delay systems using the auxiliary system approach we demonstrate that the transition to gs occurs via an on off intermittency route and that it also exhibits characteristically distinct behaviors for different coupling configurations in particular the intermittency transition occurs in a rather broad range of coupling strength for the error feedback coupling configuration and in a narrow range of coupling strength for the direct feedback coupling configuration it is also shown that the intermittent dynamics displays periodic bursts of periods equal to the delay time of the response system in the former case while they occur in random time intervals of finite duration in the latter case the robustness of these transitions with system parameters and delay times has also been studied for both linear and nonlinear coupling configurations the results are corroborated analytically by suitable stability conditions for asymptotically stable synchronized states and numerically by the probability of synchronization and by the transition of sub lyapunov exponents of the coupled time delay systems we have also indicated the reason behind these distinct transitions by referring to the unstable periodic orbit theory of intermittency synchronization in low dimensional systems

lexicographic optimality in the multiple objective linear programming the nucleolar solution abstract in this paper we study the problem of multiple objective linear programming molp we introduce a new solution concept which is related to that of the nucleolus of n person cooperative game theory we prove that a general molp problem always has a solution in the new sense the points in the nucleolus are efficient in the classic way we prove existence and at the same time we introduce a constructing algorithm for computing it

synchronization of networks of nonidentical euler lagrange systems with uncertain parameters and communication delays this paper addresses the problem of synchronizing networks of nonidentical nonlinear dynamical systems described by euler lagrange equations which are assumed fully actuated with their states available for measurement but with unknown parameters the only assumption made on the communication graph is that it is connected moreover the communication is subject to constant time delays which are also unknown the main result of the paper is the construction of an adaptive controller that achieves global full state synchronization i e the difference between the agents positions and velocities asymptotically converges to zero if a desired trajectory for all systems is given a slight modification to the proposed scheme achieves also full state synchronization simulations using a ten robot manipulator network are used to illustrate the performance of the proposed schemes

technical note on min max integer allocation problems this note treats a bottleneck integer allocation problem the results obtained supercede those in this journal due to zeitlin zeitlin z 1981 integer allocation problems of min max type with quasiconvex separable functions opns res 29 207 211 who has considered a similar allocation problem with a strictly quasiconvex objective function

phase synchronization control of complex networks of lagrangian systems on adaptive digraphs this paper presents a formation control and synchronization method that utilizes adaptive network topologies for a class of complex dynamical networks comprised of a large number of highly nonlinear euler lagrange el systems a time varying and switching network topology constructed by the adaptive graph laplacian matrix relaxes the standard requirement of consensus stability even permitting exponential synchronization on an unbalanced digraph or a weakly connected digraph that can sporadically lose connectivity the time varying graph laplacian matrix is adapted by an adaptive control scheme based on relative positions and errors of synchronization and tracking the adaptive graph laplacian is integrated with a phase synchronization controller that synchronizes the relative motions of el systems moving in elliptical orbits thereby yielding a smaller synchronization error than an uncoupled tracking control law in the presence of bounded disturbances and modeling errors an example of reconfiguring hundreds of spacecraft in low earth orbit shows the effectiveness of the proposed phase synchronization controller for a large number of complex el systems moving in periodic elliptical orbits

proportional equity flow problem for terminal arcs the proportional equity flow problem extends a class of problems referred to as equity flow problems whose objective is to equitably distribute flow among the arcs in a flow circulation network the proportionally bounded flow circulation problem places lower and upper bounds on each arc flow that are nondecreasing continuous functions of the flow through one special arc and the objective is to maximize the flow through the special arc the proportional equity flow problem for terminal arcs problem ta is then defined as a special case where all the proportional arcs enter a sink vertex applications of both the general problem and problem ta are given two optimality conditions for problem ta are developed as well as an algorithm that is polynomially bounded for many types of nondecreasing continuous proportional bounding functions specifically the algorithm is shown to be polynomially bounded if the largest root of an equation can be found in polynomial time

global synchronization criteria of linearly coupled neural network systems with time varying coupling in this paper global synchronization of linearly coupled neural network nn systems with time varying coupling is investigated the dynamical behavior of the uncoupled system at each node is general which can be chaotic or others the coupling configuration is time varying i e the coupling matrix is not a constant matrix based on lyapunov function method and the specific property of householder transform some criteria for the global synchronization are obtained by these criteria one can verify whether the coupled system with time varying coupling is globally synchronized which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration finally two simulations are given to demonstrate the effectiveness of the theoretical results

integral control on lie groups in this paper we extend the popular integral control technique to systems evolving on lie groups more explicitly we provide an alternative definition of integral action for proportional derivative controlled systems whose configuration evolves on a nonlinear space where configuration errors cannot be simply added up to compute a definite integral we then prove that the proposed integral control allows to cancel the drift induced by a constant bias in both first order velocity and second order torque control inputs for fully actuated systems evolving on abstract lie groups we illustrate the approach by 3 dimensional motion control applications

a graphical method to solve a maximin allocation problem abstract this note extends a simple graphical method of a solving resource allocation problem the objective function being the sum of returns developed by vidal to the case where the objective function is of a maximin type

on the rendezvous problem for multiple nonholonomic agents in this note a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced the proposed nonholonomic control law is discontinuous and time invariant and using tools from nonsmooth lyapunov theory and graph theory the stability of the overall system is examined similarly to the linear case the convergence of the multi agent system relies on the connectivity of the communication graph that represents the inter agent communication topology the control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph moreover the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework

a max min allocation problem its solutions and applications this paper describes a max min allocation problem that has m constraints and n nonnegative integer variables by exploring the structure of the optimal solution to this max min allocation problem we develop a nonsimplex based algorithm that finds an optimal solution within omn2 operations in addition we show that a space allocation problem for a flexible component insertion machine can be formulated as a special case of this max min allocation problem with one constraint furthermore we present some manufacturing and production problems that can he formulated as max min allocation problems and hence can be solved efficiently

passivity as a design tool for group coordination we pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set to stabilize this set we study a class of feedback rules that are implementable with local information available to each member when the information flow between neighboring members is bidirectional we show that the closed loop system exhibits a special interconnection structure which inherits the passivity properties of its components by exploiting this structure we develop a passivity based design framework which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature the passivity approach offers additional design flexibility compared to these special cases and systematically constructs a lurie type lyapunov function for the closed loop system we further study the robustness of these feedback laws in the presence of a time varying communication topology and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense

delay enhanced coherent chaotic oscillations in networks with large disorders we study the effect of coupling delay in a regular network with a ring topology and in a more complex network with an all to all global topology in the presence of impurities disorder we find that the coupling delay is capable of inducing phase coherent chaotic oscillations in both types of networks thereby enhancing the spatiotemporal complexity even in the presence of 50 of symmetric disorders of both fixed and random types furthermore the coupling delay increases the robustness of the networks up to 70 of disorders thereby preventing the network from acquiring periodic oscillations to foster disorder induced spatiotemporal order we also confirm the enhancement of coherent chaotic oscillations using snapshots of the phases and values of the associated kuramoto order parameter we also explain a possible mechanism for the phenomenon of delay induced coherent chaotic oscillations despite the presence of large disorders and discuss its applications

stable flocking of multiple inertial agents on balanced graphs in this note we consider the flocking of multiple agents which have significant inertias and evolve on a balanced information graph here by flocking we mean that all the agents move with a common velocity while keeping a certain desired internal group shape we first show that flocking algorithms that neglect agents inertial effect can cause unstable group behavior to incorporate this inertial effect we use the passive decomposition which decomposes the closed loop group dynamics into two decoupled systems a shape system representing the internal group shape and a locked system describing the motion of the center of mass then analyzing the locked and shape systems separately with the help of graph theory we propose a provably stable flocking control law which ensures that the internal group shape is exponentially stabilized to a desired one while all the agents velocities converge to the centroid velocity that is also shown to be time invariant this result still holds for slow switching balanced information graphs simulation is performed to validate the theory

minimax resource allocation problems optimization and parametric analysis abstract we consider a linear minimax resource allocation problem with single variable terms in the objective function and multiple knapsack type resource constraints all variables are continuous and nonnegative efficient algorithms for such large scale problems have been developed by luss and smith and by tang this paper describes an enhanced algorithm that provides a more efficient search for the optimal solution further we develop post optimization schemes and parametric analysis that are employed once an optimal solution for the original minimax problem is obtained post optimization provides a perturbed optimal solution under a specified change in the data whereas parametric analysis provides a continuum of optimal solutions when some data elements are changed over a given interval

computing leximin optimal solutions in constraint networks in many real world multiobjective optimization problems one needs to find solutions or alternatives that provide a fair compromise between different conflicting objective functions which could be criteria in a multicriteria context or agent utilities in a multiagent context while being efficient i e informally ensuring the greatest possible overall agents satisfaction this is typically the case in problems implying human agents where fairness and efficiency requirements must be met preference handling resource allocation problems are another examples of the need for balanced compromises between several conflicting objectives a way to characterize good solutions in such problems is to use the leximin preorder to compare the vectors of objective values and to select the solutions which maximize this preorder in this article we describe five algorithms for finding leximin optimal solutions using constraint programming three of these algorithms are original other ones are adapted in constraint programming settings from existing works the algorithms are compared experimentally on three benchmark problems

minimax resource allocation problems with resource substitutions represented by graphs resource allocation problems focus on the allocation of limited resources among competing activities we examine such problems when certain substitutions among resources are possible the substitutional relations can be represented by a graph comprised of multiple components in each component the nodes correspond to resources and the arcs correspond to feasible substitutions the objective is of the minimax form where each term is a continuous strictly decreasing function of a single activity level the objective is to minimize the largest term subject to a limited supply of multiple resources potential applications to such problems are found for example in the manufacture of high tech products we develop an efficient algorithm to solve such problems at each iteration a relaxed minimax problem is solved a max flow algorithm is then applied to determine whether the solution of the relaxed problem is feasible for the original problem if the solution is infeasible a tighter relaxed problem is f

inverse optimal adaptive control for attitude tracking of spacecraft the attitude tracking control problem of a rigid spacecraft with external disturbances and an uncertain inertia matrix is addressed using the adaptive control method the adaptive control laws proposed in this paper are optimal with respect to a family of cost functionals this is achieved by the inverse optimality approach without solving the associated hamilton jacobi isaacs partial differential hjipd equation directly the design of the optimal adaptive controllers is separated into two stages by means of integrator backstepping and a control lyapunov argument is constructed to show that the inverse optimal adaptive controllers achieve h sub spl infin disturbance attenuation with respect to external disturbances and global asymptotic convergence of tracking errors to zero for disturbances with bounded energy the convergence of adaptive parameters is also analyzed in terms of invariant manifold numerical simulations illustrate the performance of the proposed control algorithms

on the max min 0 1 knapsack problem with robust optimization applications given a set of items a set of scenarios and a knapsack of fixed capacity a nonnegative weight is associated with each item and a value is associated with each item under each scenario the max min knapsack mnk problem is defined as filling the knapsack with a selected set of items so that the minimum total value gained under all scenarios is maximized the mnk problem is a generalization of the conventional knapsack problem to situations with multiple scenarios this extension significantly enlarges its scope of applications especially in the application of recent robust optimization developments in this paper the mnk problem is shown to be strongly np hard for an unbounded number of scenarios and pseudopolynomially solvable for a bounded number of scenarios effective lower and upper bounds are generated by surrogate relaxation the ratio of these two bounds is shown to be bounded by a constant for situations where the data range is limited to be within a fixed percentage from its mean this result leads to an approximation algorithm for mnk in the special case a branch and bound algorithm has been implemented to efficiently solve the mnk problem to optimality extensive computational results are presented

an exact algorithm for the knapsack sharing problem with common items we are concerned with a variation of the knapsack problem as well as of the knapsack sharing problem where we are given a set of n items and a knapsack of a fixed capacity as usual each item is associated with its profit and weight and the problem is to determine the subset of items to be packed into the knapsack however in the problem there are s players and the items are divided into s 1 disjoint groups nk k 0 1 s the player k is concerned only with the items in n0 nk where n0 is the set of common items while nk represents the set of his own items the problem is to maximize the minimum of the profits of all the players an algorithm is developed to solve this problem to optimality and through a series of computational experiments we evaluate the performance of the developed algorithm 2004 elsevier b v all rights reserved

chimeras with multiple coherent regions we study chimeric states in a coupled phase oscillator system with piecewise linear nonlocal coupling by modifying the details of the coupling it is possible to obtain multiple chimeric states with a specified number of coherent regions and with specified phase relationships the case of a two component chimera is illustrated and the generalization to arbitrary chimeric configurations is discussed the phase relations between the two clusters of phase oscillators is described in some detail

a cooperative local search based algorithm for the multiple scenario max min knapsack problem the purpose of this article is to present a novel method to approximately solve the multiple scenario max min knapsack problem msm2kp this problem models many real world situations e g when for many scenarios noted pi in mathcal p 1 ldots p the aim is to identify the one offering a better alternative in term of maximizing the worst possible outcome herein is presented a cooperative approach based on two local search algorithms i a limited area local search applied in the elite neighborhood and which accepts the first solution with some deterioration threshold of the current solution ii a wide range local search is applied to perform a sequence of paths exchange to improve the current solution results have been analyzed by means state of the art methods and via problem instances obtained by a generator code taken from the literature the tests were executed in compeltely comparable scenarios to those of the literature the results are promising and the efficiency of the proposed approach is also shown

connection between cooperative positive systems and integral input to state stability of large scale systems we consider a class of continuous time cooperative systems evolving on the positive orthant r n we show that if the origin is globally attractive then it is also globally stable and furthermore there exists an unbounded invariant manifold where trajectories strictly decay this leads to a small gain type condition which is sufficient for global asymptotic stability gas of the origin we establish the following connection to large scale interconnections of integral input to state stable iss subsystems if the cooperative system is integral iss and arises as a comparison system associated with a large scale interconnection of i iss systems then the composite nominal system is also i iss we provide a criterion in terms of a lyapunov function for integral input to state stability of the comparison system furthermore we show that if a small gain condition holds then the classes of systems participating in the large scale interconnection are restricted in the sense that certain iiss systems cannot occur moreover this small gain condition is essentially the same as the one obtained previously by dashkovskiy ruffer and wirth 2007 in press for large scale interconnections of iss systems

a lexicographic minimax algorithm for multiperiod resource allocation resource allocation problems are typically formulated as mathematical programs with some special structure that facilitates the development of efficient algorithms we consider a multiperiod problem in which excess resources in one period can be used in subsequent periods the objective minimizes lexicographically the nonincreasingly sorted vector of weighted deviations of cumulative activity levels from cumulative demands to this end we first develop a new minimax algorithm that minimizes the largest weighted deviation among all cumulative activity levels the minimax algorithm handles resource constraints ordering constraints and lower and upper bounds at each iteration it fixes certain variables at their lower bounds and sets groups of other variables equal to each other as long as no lower bounds are violated the algorithm takes advantage of the problem s special structure e g each term in the objective is a linear decreasing function of only one variable this algorithm solves large problems very fast orders of magnitude faster than well known linear programming packages the latter are of course not designed to solve such minimax problems efficiently the lexicographic procedure repeatedly employs the minimax algorithm described above to solve problems each of the same format but with smaller dimension

input to state stability of networked control systems a new class of lyapunov uniformly globally asymptotically stable ugas protocols in networked control systems ncs is considered it is shown that if the controller is designed without taking into account the network so that it yields input to state stability iss with respect to external disturbances not necessarily with respect to the error that will come from the network implementation then the same controller will achieve semi global practical iss for the ncs when implemented via the network with a lyapunov ugas protocol moreover the iss gain is preserved the adjustable parameter with respect to which semi global practical iss is achieved is the maximal allowable transfer interval mati between transmission times

minimax resource allocation with tree structured substitutable resources we examine an allocation problem in which limited resources are allocated among competing activities certain substitutions among resources are possible the substitutional relations are formulated using tree structures where a node resource can substitute for all its descendants potential applications with such resources are found for example in the manufacturing of high technology products the objective is to minimize the maximum weighted relative deviation of the activity levels from given demands our formulation of this problem involves a large number of possible resource constraints we develop an efficient minimax algorithm that is based on an iterative solution of relaxed problems where each such problem considers at most one aggregated constraint from each tree the algorithm is extended to minimize lexicographically the nonincreasingly sorted vector of all terms in the objective each of which represents an activity s deviation computational results show that the algorithm solves large problems using relatively small computation time

target assignment in robotic networks distance optimality guarantees and hierarchical strategies we study the problem of multi robot target assignment to minimize the total distance traveled by the robots until they all reach an equal number of static targets in the first half of the paper we present a necessary and sufficient condition under which true distance optimality can be achieved for robots with limited communication and target sensing ranges moreover we provide an explicit non asymptotic formula for computing the number of robots needed to achieve distance optimality in terms of the robots communication and target sensing ranges with arbitrary guaranteed probabilities the same bounds are also shown to be asymptotically tight in the second half of the paper we present suboptimal strategies for use when the number of robots cannot be chosen freely assuming first that all targets are known to all robots we employ a hierarchical communication model in which robots communicate only with other robots in the same partitioned region this hierarchical communication model leads to constant approximations of true distance optimal solutions under mild assumptions we then revisit the limited communication and sensing models by combining simple rendezvous based strategies with a hierarchical communication model we obtain decentralized hierarchical strategies that achieve constant approximation ratios with respect to true distance optimality results of simulation show that the approximation ratio is as low as 1 4

continuous maximin knapsack problems with glb constraints this paper introduces the continuous minimax knapsack problem with generalized lower bound constraints and describes an algorithm that solves this problem in o n logn time we also discuss the related problem with generalized upper bound constraints

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

synchronization of time delayed systems in this paper we study synchronization in linearly coupled time delayed systems we first consider coupled nonidentical ikeda systems with a square wave coupling rate using the theory of the time delayed equation we derive less restrictive synchronization conditions than those resulting from the krasovskii lyapunov theory yang kuang delay differential equations academic press new york 1993 then we consider a wide class of nonlinear nonidentical time delayed systems we also propose less restrictive synchronization conditions in an approximative sense even if the coefficients in the linear time delayed equation on the synchronization error are time dependent theoretical analysis and numerical simulations fully verify our main results

an algorithm for solving linearly constrained minimax problems abstract in this study we propose an algorithm for solving a minimax problem over a polyhedral set defined in terms of a system of linear inequalities at each iteration a direction is found by solving a quadratic programming problem and then a suitable step size along that direction is taken through an extension of armijo s approximate line search technique we show that each accumulation point is a kuhn tucker solution and give a condition that guarantees convergence of the whole sequence of iterations through the use of an exact penalty function the algorithm can be used for solving constrained nonlinear programming in this case our algorithm resembles that of han but differs from it both in the direction finding and the line search steps

the bipartite rationing problem in the bipartite rationing problem a set of agents share a single resource available in different types each agent has a claim over only a subset of the resource types and these claims overlap in arbitrary fashion the goal is to divide fairly the various types of resources between the claimants when resources are in short supply with a single type of resource this is the standard rationing problem o neill b 1982 a problem of rights arbitration from the talmud math soc sci 2 4 345 371 of which the three benchmark solutions are the proportional uniform gains and uniform losses methods we extend these methods to the bipartite context imposing the familiar consistency requirement the division is unchanged if we remove an agent respectively a resource and take away at the same time his share of the various resources respectively reduce the claims of the relevant agents the uniform gains and uniform losses methods have infinitely many consistent extensions but the proportional me

relaxation based algorithms for minimax optimization problems with resource allocation applications we consider minimax optimization problems where each term in the objective function is a continuous strictly decreasing function of a single variable and the constraints are linear we develop relaxation based algorithms to solve such problems at each iteration a relaxed minimax problem is solved providing either an optimal solution or a better lower bound we develop a general methodology for such relaxation schemes for the minimax optimization problem the feasibility tests and formulation of subsequent relaxed problems can be done by using phase i of the simplex method and the farkas multipliers provided by the final simplex tableau when the corresponding problem is infeasible such relaxation based algorithms are particularly attractive when the minimax optimization problem exhibits additional structure we explore special structures for which the relaxed problem is formulated as a minimax problem with knapsack type constraints efficient algorithms exist to solve such problems the relaxation schemes are also adapted to solve certain resource allocation problems with substitutable resources there instead of phase i of the simplex method a max flow algorithm is used to test feasibility and formulate new relaxed problems

new upper bounds and exact methods for the knapsack sharing problem a new upper bound is proposed for the knapsack sharing problem a new dichotomous search based exact algorithm is proposed the new algorithm outperforms a most recent exact algorithm of the literature and the cplex solver v 12 in this paper we study the knapsack sharing problem ksp which is a variant of the well known np hard knapsack problem we investigate the use of a dichotomous search based exact method for solving the ksp such a method is based on decomposing the original problem into a series of minimizing and maximizing knapsack problems where each of them is embedded into a dichotomous search bounded by both lower and upper bounds throughout the interval search we introduce new upper bounds and incremental valid lower bounds one of these upper bounds can be viewed as an extended of dantzig upper bound whereas a series of valid lower bounds are obtained when solving a subset of knapsack problems finally the proposed algorithm is evaluated on a set of problem instances of the literature and other new harder ones the provided results are compared to those reached by the cplex solver and a more recent exact algorithm of the literature the computational part shows the dominance of the new exact method

distributed geodesic control laws for flocking of nonholonomic agents we study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions by analyzing the velocity vectors of agents on a circle for planar motion or sphere for 3 d motion we develop a geodesic control law that minimizes a misalignment potential and results in velocity alignment and flocking the proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected we further show that flocking is possible even when the topology of the proximity graph changes over time so long as a weaker notion of joint connectivity is preserved

a sufficiently smooth projection operator in this note we introduce a new parameter projection operator for adaptation laws the projection operator replaces the common lipschitz continuity property with the stronger property of arbitrarily many times continuous differentiability the proposed projection is useful for backstepping based robust adaptive controllers which require multiple differentiations of the adaptation law

contraction analysis of time delayed communications and group cooperation we study stability of interacting nonlinear systems with time delayed communications using contraction theory and a simplified wave variable design inspired by robotic teleoperation we show that contraction is preserved through specific time delayed feedback communications and that this property is independent of the values of the delays the approach is then applied to group cooperation with linear protocols where it is shown that synchronization can be made robust to arbitrary time delays

the linear sharing problem the linear sharing problem is defined as a linear programming problem with a maximin objective function comprised of nondecreasing continuous tradeoff functions this paper develops some properties including optimality conditions for this problem it also develops an efficient algorithm that alternately calculates a new global upper bound on the objective function and then determines if a feasible solution exists that meets the new objective function global upper bound the process continues until the algorithm finds a feasible and thus an optimal solution the algorithm also determines if the problem contains no feasible solution or if the objective function is unbounded a technique to handle problems with unbounded tradeoff variables is developed and computational experience is given

observer design for stochastic nonlinear systems via contraction based incremental stability this paper presents a new design approach to nonlinear observers for ito stochastic nonlinear systems with guaranteed stability a stochastic contraction lemma is presented which is used to analyze incremental stability of the observer a bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity the observer design is based on a non unique state dependent coefficient sdc form which parametrizes the nonlinearity in an extended linear form the observer gain synthesis algorithm called linear matrix inequality state dependent algebraic riccati equation lmi sdare is presented the lmi sdare uses a convex combination of multiple sdc parametrizations an optimization problem with state dependent linear matrix inequality sdlmi constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances two variations of lmi sdare algorithm are also proposed one of them named convex state dependent riccati equation csdre uses a chosen convex combination of multiple sdc matrices and the other named fixed sdare uses constant sdc matrices that are pre computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre computed by a convex lmi optimization problem a connection between contraction analysis and l 2 gain of the nonlinear system is established in the presence of noise and disturbances results of simulation show superiority of the lmi sdare algorithm to the extended kalman filter ekf and state dependent differential riccati equation sddre filter

disaggregation and resource allocation using convex knapsack problems with bounded variables the allocation of a specific amount of a given resource among competitive alternatives can often be modelled as a knapsack problem this model formulation is extremely efficient because it allows convex cost representation with bounded variables to be solved without great computational efforts practical applications of this problem abound in the fields of operations management finance manpower planning marketing etc in particular knapsack problems emerge in hierarchical planning systems when a first level of decisions need to be further allocated among specific activities which have been previously treated in an aggregate way in this paper we provide a recursive procedure to solve such problems the method differs from classical optimization algorithms of convex programming in that it determines at each iteration the optimal value of at least one variable applications and computational results are presented

the flow circulation sharing problem the flow circulation sharing problem is defined as a network flow circulation problem with a maximin objective function the arcs in the network are partitioned into regular arcs and tradeoff arcs where each tradeoff arc has a non decreasing tradeoff function associated with it all arcs have lower and upper bounds on their flow while the value of the smallest tradeoff function is maximized the model is useful in equitable resource allocation problems over time which is illustrated in a coal strike example and a submarine assignment example some properties including optimality conditions are developed each cut in the network defines a knapsack sharing problem which leads to an optimality condition similar to the max flow min cut theorem an efficient algorithm for both the continuous and integer versions of the flow circulation sharing problem is developed and computational experience given in addition efficient algorithms are developed for problems where some of the arcs have infinite flow upper bounds

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

linear max min programming theoretical aspects of the programming problem of maximizing the minimum value of a set of linear functionals subject to linear constraints are explored solution strategies are discussed and an optimality condition is developed an algorithm is also presented

synchronization and balancing on the n torus in this paper we study the behavior of a network of n agents each evolving on the circle we propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the possibly time varying and unidirectional communication graphs the global convergence analysis on the n torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the euclidean space

a min max resource allocation problem with substitutions abstract in this paper a model for a resource allocation problem with substitution is presented the model extends a previous one proposed by luss and smith for resource allocation without substitutions in general two resources are substitutable if they can be used in place of one another in the allocation process if two resources are substitutable for the same set of activities then they can be combinaed into and treated as a single resource otherwise substitution needs to be dealt with explicitly one application of the resource allocation problem with substitutions arises from the assembly of electronic components onto circuit boards typically several components can be assembled in the same locations of a board they then become substitutes of one another the problem here is to determine how much to produce of the circuit boards and how to efficiently allocate the components so as to minimize the maximum weighted deviation from target demands of the boards it is explained how the proposed model can be solved by a parametric transportation algorithm present some computational results and discuss a nonlinear extension

consensus over ergodic stationary graph processes in this technical note we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are generated by an ergodic and stationary random process we prove that consensus algorithms converge almost surely if and only if the expected graph of the network contains a directed spanning tree our results contain the case of independent and identically distributed graph processes as a special case we also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper