fuzzy goal programming complementary slackness conditions and computational schemes abstract goal programming gp is an important category in linear programming and multiobjective versions which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem in this paper we deal with fuzzy goal programming fgp which is a generalized problem in vague nature where parameters relations and goals are given as fuzzy quantities with respect to imprecise data recently inuiguchi et al m inuiguchi j ramik t tanio m vlach satisficing solutions and duality in interval and fuzzy linear programming fuzzy sets and systems 135 2003 151 177 have proved some important dual theorems on fgp which are very close to the same crisp versions in continuation to their works based on fuzzy extensions of relations we get complementary slackness conditions for fgp which have an essential role in many optimization techniques moreover we obtain the most optimistic and pessimistic satisficing solutions employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty our practical schemes implement an efficient interior point algorithm as sub procedure so they are polynomial time algorithms

output regulation of linear systems with bounded continuous feedback this paper studies the classical problem of output regulation for linear systems subject to control constraint the asymptotically regulatable region the set of all initial conditions of the plant and the exosystem for which output regulation is possible is characterized in terms of the null controllable region of the antistable subsystem of the plant continuous output regulation laws of both state feedback type and error feedback type are constructed from a given stabilizing state feedback law it is shown that a stabilizing feedback law that achieves a larger domain of attraction leads to a feedback law that achieves output regulation on a larger subset of the asymptotically regulatable region a feedback law that achieves global stabilization on the asymptotically null controllable region leads to a feedback law that achieves output regulation on the entire asymptotically regulatable region

cores of nonatomic linear production games cores of games of the form f where is a vector of nonatomic measures and fz max xa z x 0 or equivalently fz min are described in terms of and the data defining f along the way we give a general condition on a game which implies that each measure in its core is a linear combination of a fixed finite set of nonatomic measures

brief an analysis and design method for linear systems subject to actuator saturation and disturbance we present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant this condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis this condition is then extended to determine the invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements the effectiveness of the developed methods is illustrated with examples

output regulation of nonlinear systems with nonhyperbolic zero dynamics previous solvability conditions for the output relation of nonlinear systems are applicable only to those with hyperbolic zero dynamics it is shown in this note that output regulation of nonlinear systems with nonhyperbolic zero dynamics is also possible by a reduction of the plant dynamics and an augmentation of the exosystem

output feedback control of saturated discrete time linear systems using parameter dependent lyapunov functions in this paper we present a new output feedback control approach for discrete time linear systems subject to actuator saturations using parameter dependent lyapunov functions the saturation level indicator serves as a scheduling parameter the resulting nonlinear controller is expressed in a quasi lpv linear parameter varying form and the stabilization and disturbance attenuation problems are formulated and solved as finite dimensional linear matrix inequality lmi optimization problems our approach is less conservative than a single quadratic lyapunov function method specifically the proposed output feedback control law asymptotically stabilizes the open loop system with a larger domain of attraction and achieves better disturbance attenuation under energy and magnitude bounded disturbances

on the concavity of delivery games abstract delivery games introduced by hamers borm van de leensel and tijs in 1994 are combinatorial optimization games that arise from delivery problems closely related to the chinese postman problem cpp they showed that delivery games are not necessarily balanced for delivery problems corresponding to the class of bridge connected euler graphs they showed that the related games are balanced this paper focuses on the concavity property for delivery games a delivery game arising from a delivery model corresponding to a bridge connected euler graph need not be concave the main result will be that for delivery problems corresponding to the class of bridge connected cyclic graphs which is a subclass of the class of bridge connected euler graphs the related delivery games are concave further we discuss some extreme points of the core and the value for this class of concave delivery games

totally balanced combinatorial optimization games combinatorial optimization games deal with cooperative games for which the value of every subset of players is obtained by solving a combinatorial optimization problem on the resources collectively owned by this subset a solution of the game is in the core if no subset of players is able to gain advantage by breaking away from this collective decision of all players the game is totally balanced if and only if the core is non empty for every induced subgame of it we study the total balancedness of several combinatorial optimization games in this paper for a class of the partition game 5 we have a complete characterization for the total balancedness for the packing and covering games 3 we completely clarify the relationship between the related primal dual linear programs for the corresponding games to be totally balanced our work opens up the question of fully characterizing the combinatorial structures of totally balanced packing and covering games for which we present some interesting examples the totally balanced matching vertex cover and minimum coloring games

an application of the aumann shapley prices for cost allocation in transportation problems the aumann shapley a s prices are axiomatically determined on certain classes of piecewise continuously differentiable cost functions one of these classes consists of all cost functions derived from the transportation problems and some of their generalizations these prices are used here to allocate costs among destinations in a way that each destination will pay its real part in the total transportation costs an economic transportation model is presented in which the a s prices are compatible with consumer demands finally an algorithm is provided to calculate both the optimal solution and the associated a s prices for transportation problems

generalized network problems yielding totally balanced games a class of multiperson mathematical optimization problems is considered and is shown to generate cooperative games with nonempty cores the class includes but is not restricted to numerous versions of network flow problems it was shown by owen that for games generated by linear programming optimization problems optimal dual solutions correspond to points in the core we identify a special class of network flow problems for which the converse is true i e every point in the core corresponds to an optimal dual solution

a general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

nonlinear day to day traffic dynamics with driver experience delay modeling stability and bifurcation analysis abstract in day to day traffic assignment problems travelers past experiences have important impact on their cost prediction which influences their route choice and consequently the arising flow patterns in the network many travelers execute the same trip in every few days not daily which leads to time delays in the system in this paper we propose a nonlinear discrete time model with driver experience delay the linear stability of the stochastic user equilibrium is analyzed by studying the eigenvalues of the jacobian matrix of the system while the nonlinear oscillations arising at the bifurcations are investigated by normal form calculations numerical continuation and simulation the methods are demonstrated on a two route example by applying rigorous analysis we show that the linearly unstable parameter domain as well as the period of arising oscillations increase with the delay moreover delays and nonlinearities result in an extended domain of bistability where the stochastic user equilibrium coexists with stable and unstable oscillations this study explains the influence of initial conditions on the dynamics of transportation networks and may provide guidance for network design and management

on a nonlinear multivariable servomechanism problem abstract multivariable nonlinear plants with both measured and unmeasured vector disturbance signals are considered output feedback dynamic control laws are designed for the problem of tracking a constant or slowly varying reference input while rejecting constant or slowly varying disturbances

fuzzy cooperative games arising from linear production programming problems with fuzzy parameters abstract in the present study we consider a production model in which multiple decision makers pool resources to produce finished goods such a production model which is assumed to be linear can be formulated as mathematical programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process it is shown that a cooperative game with values of coalitions represented by fuzzy numbers arises from the linear production programming problem with fuzzy parameters and such a game is referred to as a fuzzy linear production programming game the values of coalitions of the game can be obtained by employing a parametric approach to solving the linear production programming problem with fuzzy parameters it is proven that the core of the game is not empty and an interval in the core is computed by using the ideas of sensitivity analysis and the duality theory of linear programming problems

solutions based on fuzzy goals in fuzzy linear programming games abstract in this paper we deal with linear programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process and consider fuzzy linear programming games arising from the linear programming problems constructing fuzzy goals of coalitions with respect to payoff in order to suitably reflect fuzzy environments in which the linear programming games are formulated we define solutions maximizing minimal fuzzy goal and solutions maximizing the sum of fuzzy goals and develop computational methods for obtaining the solutions finally we give a numerical example to illustrate construction of a fuzzy linear programming game and derivation of the solutions

semiglobal stabilization and output regulation of singular linear systems with input saturation the semi global stabilization problem and output regulation problem of singular linear systems subject to input saturation are addressed a reduced order normal system is obtained by a standard coordinate transformation it is further shown that the controller that solves the stabilization output regulation problem of the reduced order normal systems also solves the stabilization output regulation problem of the original singular systems

on computational methods for solutions of multiobjective linear production programming games abstract in this paper we consider a production model in which multiple decision makers pool resources to produce finished goods such a production model which is assumed to be linear can be formulated as a multiobjective linear programming problem it is shown that a multi commodity game arises from the multiobjective linear production programming problem with multiple decision makers and such a game is referred to as a multiobjective linear production programming game the characteristic sets in the game can be obtained by finding the set of all the pareto extreme points of the multiobjective programming problem it is proven that the core of the game is not empty and points in the core are computed by using the duality theory of multiobjective linear programming problems moreover the least core and the nucleolus of the game are examined finally we consider a situation that decision makers first optimize their multiobjective linear production programming problem and then they examine allocation of profits and or costs computational methods are developed and illustrative numerical examples are given

cost allocation for a tree network with heterogeneous customers we analyze a cost allocation problem which could naturally arise from a situation wherein a tree networkt n 0 e serving heterogeneous customers has to be constructed the customers located atn require some service from a central supplier located at vertex 0 the customers have heterogeneous preferences for the level or quality of service received from the central supplier we formulate the above cost allocation problem as a cooperative game referred to as anextended tree game the extended tree game is a proper extension of megiddo s 1978 tree game wherein all the customers have identical preferences regarding the level of service received we prove that an extended tree game is convex and we show that its shapley value can be computed in p n time wherep is the number of distinct preference levels we further provide a complete facial description of the core polytope of an extended tree game and demonstrate that even when there are only two classes of customers the number of nonredundant core constraints could be exponential in n nevertheless we are able to construct an p n algorithm to check the core membership of an arbitrary cost allocation which can be used to construct an p n 3 combinatorial algorithm to compute the nucleolus of an extended tree game finally we show that the complements of the facet defining coalitions for the core are all connected in an auxiliary tree graph with node setn

multi criteria minimum cost spanning tree games abstract the minimum cost spanning tree game mcst game is a well known model within operations research games that has been widely studied in the literature in this paper we introduce the multi criteria version of the mcst game as a set valued tu game we prove that the extension of bird s cost allocation rule provides dominance core elements in this game we also give a family of core solutions that are different from the previous one these solutions are based on proportional allocations obtained using scalar solutions of the multi criteria spanning tree problem besides we prove necessary and sufficient conditions ensuring that the preference core of this game is not empty

an interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters abstract a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed in general two types of fuzziness of human judgements should be incorporated in multiobjective programming problems one is the experts ambiguous understanding of the nature of the parameters in the problem formulation process and the other is the fuzzy goals of the decision maker for each of the objective functions in order to cope with both types of fuzziness multiobjective linear programming problems with fuzzy parameters which reflect the experts ambiguous understanding in the problem formulation are formulated and the concept of generalized multiobjective linear programming and m pareto optimality is introduced in our interactive fuzzy satisficing method the satisficing solution of the decision maker is derived efficiently from among m pareto optimal solutions on the basis of the proposed method an interactive computer program is written to implement man machine interactive procedures finally an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs

an algebraic approach to bounded controllability of linear systems in this paper we present an algebraic approach to the proof that a linear system with matrices a b is null controllable using bounded inputs if and only if it is null controllable with unbounde

on the core and dual set of linear programming games we study the relation between the core of a given lp game and the set of payoff vectors generated by optimal dual solutions to the corresponding linear program it is well known that the set of dual payoffs is contained in the core and that cores of games in which players are replicated converge to the set of dual payoffs when the number of replications tends to infinity we give a necessary and sufficient condition for finite convergence as corollaries we strengthen a sufficient condition due to owen and obtain new conditions as well we also study conditions in which the core and the set of dual payoffs coincide even without replication we give a necessary and sufficient condition for this phenomenon and present two classes of lp games with this property which properly subsumes all examples of this type discussed in the literature

on the core and f nucleolus of flow games using the ellipsoid method both deng et al deng x q fang x sun 2006 finding nucleolus of flow game proc 17th acm siam sympos discrete algorithms acm press new york 124 131 and potters et al potters j h reijnierse a biswas 2006 the nucleolus of balanced simple flow networks games econom behav 54 205 225 show that the nucleolus of simple flow games where all edge capacities are equal to one can be computed in polynomial time our main result is a combinatorial method based on eliminating redundant s t path constraints such that only a polynomial number of constraints remains this leads to efficient algorithms for computing the core nucleolus and nucleon of simple flow games deng et al also prove that computing the nucleolus for general flow games is np hard we generalize this by proving that computing the f nucleolus of flow games is np hard for all priority functions f that satisfy f a 0 for all coalitions a with worth v a 0 so including the priority functions corresponding to the nucleolus nucleon and per capita nucleolus

on the core of network synthesis games we use polynomial formulations to show that several rational and discrete network synthesis games including the minimum cost spanning tree game satisfy the assumptions of owen s linear production game model we also discuss computational issues related to finding and recognizing core points for these classes of games

a generalized linear production model a unifying model we introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producerss is not restricted to be the vector sum of the resources held by the members ofs we provide sufficient conditions for the non emptiness of the core of the associated generalized linear production game and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem our generalized linear production model is a proper generalization of the linear production model introduced by owen and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework we use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non empty core we further employ our model to prove the non emptiness of the core of two other classes of cooperative games which were not previously studied in the literature and we also use our generalized model to provide an alternative proof for the non emptiness of the core of the class of minimum cost spanning tree games thus it appears that the generalized linear production model is a unifying model which can be used to explain the non emptiness of the core of cooperative games generated by various seemingly different optimization models

pairwise solutions and the core of transportation situations the main aim of this paper is to study the relationship between the so called pairwise solutions and the core of transportation situations or games with this objective in mind we show that every core element of a transportation situation is contained in a pairwise solution with a specific weight system therefore every core element is in fact a particular pairwise distribution furthermore given a core element we outline a procedure in three steps to obtain the corresponding pairwise distribution with weight system

totally balanced games arising from controlled programming problems a cooperative game in characteristic function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a generally nonlinear mathematical programming problem either directly or through committee voting conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced this assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers in the linear case the core is closely related to the solutions of the dual problem applications are made to a variety of economic models including the transferable utility trading economies of shapley and shubik and a multishipper one commodity transshipment model with convex cost functions and concave revenue functions dropping the assumption of transferable utility leads to a class of controlled multiobjective or pareto programming problems which again yield totally balanced games

semi global exponential stabilization of linear systems subject to input saturation via linear feedbacks abstract it is known that a linear time invariant system subject to input saturation can be globally asymptotically stabilized if it has no eigenvalues with positive real parts it is also shown by fuller 1997 and sussmann and yang 1991 that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws in this paper we show the existence of linear state feedback and or output feedback control laws for semi global exponential stabilization rather than global asymptotic stabilization of such systems we explicitly construct linear static state feedback laws and or linear dynamic output feedback laws that semi globally exponentially stabilize the given system our results complement the negative result of fuller 1977 and sussmann and yang 1991

global internal stabilizability does not imply global external stabilizability for small sensor disturbances it was shown by sontag ibid vol 34 no 4 p 435 43 1989 that for control affine nonlinear systems global asymptotic stabilizability via continuous state feedback implies global input to state stabilizability with respect to actuator disturbances we show that the analogous result for sensor disturbances does not hold we construct a second order system which admits a continuous memoryless globally asymptotically stabilizing state feedback controller but for which no such controller can prevent finite escape times from every initial condition in the presence of small sensor disturbances

on the output regulation for linear systems in the presence of input saturation some results on the problem of achieving output regulation in the presence of sinusoidal constant exogenous signals for linear systems subject to input saturation are presented in particular the issue of enlarging the set of initial conditions for which the problem has solutions is addressed

output regulation for linear systems subject to input saturation the purpose of this paper is to examine the problem of controlling a linear time invariant system subject to input saturation in order to have its output track or reject a family of reference or disturbance signals produced by some external generator it is shown that a semiglobal framework for this problem is a natural one within this framework a set of solvability conditions are given and feedback laws that solve the problem are constructed the theory developed in this paper incorporates earlier results established for linear systems without input saturation

totally balanced games and games of flow a class of characteristic function games arising from maximum flow problems is introduced and is shown to coincide with the class of totally balanced games the proof relies on the max flow min cut theorem of ford and fulkerson and on the observation that the class of totally balanced games is the span of the additive games with the minimum operation

on some network flow games we analyze three subclasses of cooperative games arising from network optimization problems in which the resources such as arcs or nodes in the network are controlled by individuals who have conflicting objectives the first subclass of cooperative games is induced by network optimization problems over directed augmented trees we show that for this subclass of games the kernel coincides with the nucleolus and that the nucleolus can be characterized as the unique revenue allocation vector in which every pair of arc owners who are adjacent in the tree are located symmetrically with respect to their bargaining range we further give a linear characterization of the core of this subclass of games which is then used to provide a more explicit representation of the nucleolus and to construct a strongly polynomial algorithm for generating it the second subclass of cooperative games is induced by maximum flow problems in simple undirected networks we provide a useful parametric representation of the core of this subclass of games which is used to characterize the nucleolus and the intersection of the core and the kernel explicitly we show that the intersection of the core and the kernel consists of all revenue allocations in the core which assign equal payoffs to any pair of unseparated arc owners we further demonstrate that among the core vectors the nucleolus is the unique revenue allocation vector in which the smallest allocations are maximized in a lexicographical sense the third cooperative game that we study is the assignment game introduced by shapley and shubik 1972 this game is induced by the assignment problem which can be cast as a network optimization problem we investigate the relationship between the kernel and the core of the assignment game and provide a necessary and sufficient condition for the core to be contained in the kernel we further show that in general the intersection of the kernel and the core is not a convex set we also exhibit that under certain conditions the nucleolus has a simple characterization as the unique vector in the core in which the smallest revenue allocations are maximized in a lexicographical sense finally we consider the horse market example of bohm bawerk 1923 for which it is shown that the core is contained in the kernel and that the nucleolus is the midpoint of the core

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

analysis and design of singular linear systems under actuator saturation and l2 l disturbances abstract this paper carries out an analysis of the l 2 gain and l performance for singular linear systems under actuator saturation the notion of bounded state stability bss with respect to the influence of l 2 or l disturbances is introduced and conditions under which a system is bounded state stable are established in terms of linear matrix inequalities lmis the disturbance tolerance capability of the system is then measured as the bound on the l 2 or l norm of the disturbances under which the system remains bounded state stable and the disturbance rejection capability is measured by the restricted l 2 gain from the disturbance to the system output or l norm of the system output based on the bss conditions assessment of the disturbance tolerance and rejection capabilities of the system under a given state feedback law is formulated and solved as lmi constrained optimization problems by viewing the feedback gain as an additional variable these optimization problems can be readily adapted for control design our analysis and design reduce to the existing results for regular linear systems in the degenerate case where the singular linear system reduces to a regular system and to the existing results for singular systems in the absence of actuator saturation or when the disturbance is weak enough to not cause saturation

output feedback control for switched linear systems subject to actuator saturation this article is devoted to the output feedback control problem for switched linear systems subject to actuator saturation we consider both continuous and discrete time switched systems using the minimal switching rule nonlinear output feedbacks expressed in the form of quasi linear parameter varying system are designed to satisfy a pre specified disturbance attenuation level defined by the regional 2 l2 gains over a class of energy bounded disturbances the conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation a spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach

subcritical hopf bifurcations in a car following model with reaction time delay a nonlinear car following model of highway traffic is considered which includes the reaction time delay of drivers linear stability analysis shows that the uniform flow equilibrium of the system loses its stability via hopf bifurcations and thus oscillations can appear the stability and amplitudes of the oscillations are determined with the help of normal form calculations of the hopf bifurcation that also handles the essential translational symmetry of the system we show that the subcritical case of the hopf bifurcation occurs robustly which indicates the possibility of bistability we also show how these oscillations lead to spatial wave formation as can be observed in real world traffic flows

dynamic linear programming games with risk averse players motivated by situations in which independent agents wish to cooperate in some uncertain endeavor over time we study dynamic linear programming games which generalize classical linear production games to multi period settings under uncertainty we specifically consider that players may have risk averse attitudes towards uncertainty and model this risk aversion using coherent conditional risk measures for this setting we study the strong sequential core a natural extension of the core to dynamic settings we characterize the strong sequential core as the set of allocations that satisfy a particular finite set of inequalities that depend on an auxiliary optimization model and then leverage this characterization to establish sufficient conditions for emptiness and non emptiness qualitatively whereas the strong sequential core is always non empty when players are risk neutral our results indicate that cooperation in the presence of risk aversion is much more difficult we illustrate this with an application to cooperative newsvendor games where we find that cooperation is possible when it least benefits players and may be impossible when it offers more benefit

day to day dynamic network disequilibria and idealized traveler information systems in this paper we present tatonnement models for calculating static wardropian user equilibria on congested networks with fully general demand and cost structures we present both a qualitative analysis of stability and numerical studies which show that such an approach provides a reliable means for determining static user equilibria we also describe circumstances for which these models depict day to day adjustments from one realizable disequilibrium state to another and how these adjustment processes differ depending on the quality of the information being provided by abstract traveler information systems specifically we demonstrate that such dynamic adjustment processes settle down to equilibria both when information is complete and when it is incomplete

an explicit description of null controllable regions of linear systems with saturating actuators we give simple exact descriptions of the null controllable regions for general linear systems with saturating actuators the description is in terms of a set of extremal trajectories of the anti stable subsystem for lower order systems or systems with only real eigenvalues this description is further simplified to result in explicit formulae for the boundaries of the null controllable regions

nonlinear gain scheduling output feedback control for polynomial nonlinear systems subject to actuator saturation this paper investigates nonlinear gain scheduling control approaches for a class of polynomial nonlinear systems containing an output dependent vector field with input saturation using the polytopic differential inclusion and norm bounded differential inclusion ndi of saturation and dead zone functions the nonlinear plants are transformed into systems with measurable parameters for the polytopic differential inclusion description a quasi linear parameter varying quasi lpv output feedback controller will be sought for saturation control on the other hand the ndi model leads to a nonlinear fractional transformation nft output feedback controller for saturated nonlinear systems the quasi lpv and nft output feedback control synthesis conditions are derived in the forms of output dependent matrix inequalities they can be reformulated as sum of squares sos optimisations and solved efficiently using sos programming the proposed nonlinear gain scheduling saturation control approaches will be dem

stabilization of exponentially unstable linear systems with saturating actuators we study the problem of stabilizing exponentially unstable linear systems with saturating actuators the study begins with planar systems with both poles exponentially unstable for such a system we show that the boundary of the domain of attraction under a saturated stabilizing linear state feedback is the unique stable limit cycle of its time reversed system a saturated linear state feedback is designed that results in a closed loop system having a domain of attraction that is arbitrarily close to the null controllable region this design is then utilized to construct state feedback laws for higher order systems with two exponentially unstable poles

on market prices in linear production games consider a game in which resources may be combined to produce products of known values for linear production processes the game may be characterized by a family of linear programs it is shown that appropriately defined market prices for the resources coincide with the set of optimal dual solutions to one of these linear programs this result generalizes and unifies the known cases in game theory in which the core of a game coincides with the set of dual optimal solutions to a corresponding master linear programming problem

efficient algorithms for game theoretic betweenness centrality betweenness centrality measures the ability of different nodes to control the flow of information in a network in this article we extend the standard definition of betweenness centrality using semivalues a family of solution concepts from cooperative game theory that includes among others the shapley value and the banzhaf power index any semivalue based betweenness centrality measure such as for example the shapley value based betweenness centrality measure has the advantage of evaluating the importance of individual nodes by considering the roles they each play in different groups of nodes our key result is the development of a general polynomial time algorithm to compute the semivalue based betweenness centrality measure and an even faster algorithm to compute the shapley value based betweenness centrality measure both for weighted and unweighted networks interestingly for the unweighted case our algorithm for computing the shapley value based centrality has the same complexity as the best known algorithm for computing the standard betweenness centrality due to brandes 15 we empirically evaluate our measures in a simulated scenario where nodes fail simultaneously we show that compared to the standard measure the ranking obtained by our measures reflects more accurately the influence that different nodes have on the functionality of the network we propose a betweenness centrality based on the shapley value and semivalue we develop polynomial algorithms for our game theoretic metrics we evaluate our measures in scenarios where simultaneous node failures occur our measures obtain better results than standard betweenness centrality we provide an empirical evaluation of algorithms on real life and random graphs

flow control using the theory of zero sum markov games considers the problem of dynamic flow control of arriving packets into an infinite buffer the service rate may depend on the state of the system may change in time and is unknown to the controller the goal of the controller is to design an efficient policy which guarantees the best performance under the worst service conditions the cost is composed of a holding cost a cost of rejecting customers packets and a cost that depends on the quality of the service the problem is studied in the framework of zero sum markov games and a value iteration algorithm is used to solve it it is shown that there exists an optimal stationary policy such that the decisions depend only on the actual number of customers in the queue it is of a threshold type and it uses randomization in at most one state

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided