analysis and design of fuzzy control system abstract a continuous time fuzzy control system which is composed of a fuzzy model and a fuzzy controller is proposed under certain conditions the proposed fuzzy control system can be regarded as a fuzzy pid control system the stability analysis of the fuzzy control system is given a sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of lyapunov s method the results can be applied to the design of a fuzzy pid control system the design procedure can also be applied to the controller design with a non fuzzy model examples are given to illustrate the design of the proposed fuzzy control system

fuzzy stability criterion of a class of nonlinear systems abstract a fuzzy stability criterion of a class of nonlinear systems is discussed in accordance with the definition of stability in the sense of lyapunov first a sufficient condition that guarantees stability of a fuzzy system is given in terms of lyapunov s direct method two concepts for stability of fuzzy systems are defined locally stable and globally table second a construction procedure for lyapunov functions is presented finally the construction procedure is applied to the fuzzy stability criterion of a class of nonlinear systems that can be approximated by fuzzy systems

the c 3 theorem and a d 2 algorithm for large scale stochastic mixed integer programming set convexification this paper considers the two stage stochastic integer programming problem with an emphasis on instances in which integer variables appear in the second stage drawing heavily on the theory of disjunctive programming we characterize convexifications of the second stage problem and develop a decomposition based algorithm for the solution of such problems in particular we verify that problems with fixed recourse are characterized by scenario dependent second stage convexifications that have a great deal in common we refer to this characterization as the c3 common cut coefficients theorem based on the c3 theorem we develop a decomposition algorithm which we refer to as disjunctive decomposition d2 in this new class of algorithms we work with master and subproblems that result from convexifications of two coupled disjunctive programs we show that when the second stage consists of 0 1 milp problems we can obtain accurate second stage objective function estimates after finitely many steps this result implies the convergence of the d2 algorithm

beam search heuristic to solve stochastic integer problems under probabilistic constraints abstract this paper proposes a beam search heuristic strategy to solve stochastic integer programming problems under probabilistic constraints beam search is an adaptation of the classical branch and bound method in which at any level of the search tree only the most promising nodes are kept for further exploration whereas the remaining are pruned out permanently the proposed algorithm has been compared with the branch and bound method the numerical results collected on the probabilistic set covering problem show that the beam search technique is very efficient and appears to be a promising tool to solve difficult stochastic integer problems under probabilistic constraints

an improved input delay approach to stabilization of fuzzy systems under variable sampling in this paper we investigate the problem of stabilization for sampled data fuzzy systems under variable sampling a novel lyapunov krasovskii functional lkf is defined to capture the characteristic of sampled data systems and an improved input delay approach is proposed by the use of an appropriate enlargement scheme new stability and stabilization criteria are obtained in terms of linear matrix inequalities lmis compared with the existing results the newly obtained ones contain less conservatism some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

stochastic programming with integer variables including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design starting from mean risk approaches with different risk measures we identify corresponding two and multi stage stochastic integer programs that are large scale block structured mixed integer linear programs if the underlying probability distributions are discrete we highlight the role of mixed integer value functions for structure and stability of stochastic integer programs when applied to the block structures in stochastic integer programming well known algorithmic principles such as branch and bound lagrangian relaxation or cutting plane methods open up new directions of research we review existing results in the field and indicate departure points for their extension

lagrangian solution techniques and bounds for loosely coupled mixed integer stochastic programs many production problems involve facility setups that lead to integer variables production decisions that are continuous and demands that are likely to be random while these problems can be quite difficult to solve we propose a model and an efficient solution technique for this basic class of stochastic mixed integer programs we use a set of scenarios to reflect uncertainty the resulting mathematical model is solved using lagrangian relaxation we show that the duality gap of our relaxation is bounded above by a constant that depends on the cost function and the number of branching points in the scenario tree we apply our technique to the problem of generating electric power numerical results indicate significant savings when the stochastic model is used instead of a deterministic one

identification of matrix generators of a chevalley group abstract we give a polynomial time algorithm that replaces an arbitrary module of a finite chevalley group by the adjoint module written with respect to a chevalley basis

on solving discrete two stage stochastic programs having mixed integer first and second stage variables in this paper we propose a decomposition based branch and bound dbab algorithm for solving two stage stochastic programs having mixed integer first and second stage variables a modified benders decomposition method is developed where the benders subproblems define lower bounding second stage value functions of the first stage variables that are derived by constructing a certain partial convex hull representation of the two stage solution space this partial convex hull is sequentially generated using a convexification scheme such as the reformulation linearization technique rlt or lift and project process which yields valid inequalities that are reusable in the subsequent subproblems by updating the values of the first stage variables a branch and bound algorithm is designed based on a hyperrectangular partitioning process using the established property that any resulting lower bounding benders master problem defined over a hyperrectangle yields the same objective value as the original stochastic program over that region if the first stage variable solution is an extreme point of the defining hyperrectangle or the second stage solution satisfies the binary restrictions we prove that this algorithm converges to a global optimal solution some numerical examples and computational results are presented to demonstrate the efficacy of this approach

approximating the stochastic knapsack problem the benefit of adaptivity we consider a stochastic variant of the np hard 0 1 knapsack problem in which item values are deterministic and item sizes are independent random variables with known arbitrary distributions items are placed in the knapsack sequentially and the act of placing an item in the knapsack instantiates its size our goal is to compute a solution policy that maximizes the expected value of items successfully placed in the knapsack where the final overflowing item contributes no value we consider both nonadaptive policies that designate a priori a fixed sequence of items to insert and adaptive policies that can make dynamic choices based on the instantiated sizes of items placed in the knapsack thus far an important facet of our work lies in characterizing the benefit of adaptivity for this purpose we advocate the use of a measure called the adaptivity gap the ratio of the expected value obtained by an optimal adaptive policy to that obtained by an optimal nonadaptive policy we bound the adaptivity

computing chevalley bases in small characteristics abstract let l be the lie algebra of a simple algebraic group defined over a field f and let h be a split maximal toral subalgebra of l then l has a chevalley basis with respect to h if char f 2 3 it is known how to find it in this paper we treat the remaining two characteristics to this end we present a few new methods implemented in magma which vary from the computation of centralizers of one root space in another to the computation of a specific part of the lie algebra of derivations of l

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

a new algorithm for factoring polynomials over finite fields in f t there are two standard methods one is due to e berlekamp the other appears to be a folk method both are described by d knuth in 3 pp 381 397 further improvements for special values of q are given by r moenck in 5j see also e berlekamp 1 note that both methods as described in the references apply only when d 1 however straightforward modifications described below allow d 1 both methods use the calculation of resultants or equivalently the solution of linear equations to reduce the problem to finding the roots of a polynomial which has all of its roots in f when p is very small probabilistic methods are used an improvement to the folk method method along with a more explicit calculation of the work required has recently been given by m rabin 6 we present here a new probabilistic method which when combined with the above algorithms avoids the need for both resultants and linear equations it leads to algorithms which are conceptually simpler than previous methods moreover it works equally well for all finite fields f regardless of the magnitude of q when used for factoring a quadratic x2 a it reduces to berlekamp s algorithm other standard algorithms for factoring quadratics are due to d h lehmer 4 and d shanks 7 our algorithm is also suitable for finding solutions of polynomial equations over finite fields

decomposition with branch and cut approaches for two stage stochastic mixed integer programming decomposition has proved to be one of the more effective tools for the solution of large scale problems especially those arising in stochastic programming a decomposition method with wide applicability is benders decomposition which has been applied to both stochastic programming as well as integer programming problems however this method of decomposition relies on convexity of the value function of linear programming subproblems this paper is devoted to a class of problems in which the second stage subproblem s may impose integer restrictions on some variables the value function of such integer subproblem s is not convex and new approaches must be designed in this paper we discuss alternative decomposition methods in which the second stage integer subproblems are solved using branch and cut methods one of the main advantages of our decomposition scheme is that stochastic mixed integer programming smip problems can be solved by dividing a large problem into smaller mip subproblems that can be solved in parallel this paper lays the foundation for such decomposition methods for two stage stochastic mixed integer programs

conditional value at risk in stochastic programs with mixed integer recourse in classical two stage stochastic programming the expected value of the total costs is minimized recently mean risk models studied in mathematical finance for several decades have attracted attention in stochastic programming we consider conditional value at risk as risk measure in the framework of two stage stochastic integer programming the paper addresses structure stability and algorithms for this class of models in particular we study continuity properties of the objective function both with respect to the first stage decisions and the integrating probability measure further we present an explicit mixed integer linear programming formulation of the problem when the probability distribution is discrete and finite finally a solution algorithm based on lagrangean relaxation of nonanticipativity is proposed

lmi based fuzzy chaotic synchronization and communications addresses synthesis approaches for signal synchronization and secure communications of chaotic systems by using fuzzy system design methods based on linear matrix inequalities lmis by introducing a fuzzy modeling methodology many well known continuous and discrete chaotic systems can be exactly represented by takagi sugeno t s fuzzy models with only one premise variable following the general form of fuzzy chaotic models the structure of the response system is first proposed then according to the applications of synchronization to the fuzzy models that have common bias terms or the same premise variable of drive and response systems the driving signals are developed with four different types fuzzy character crisp and predictive driving signals synthesizing from the observer and controller points of view all types of drive response systems achieve asymptotic synchronization for chaotic communications the asymptotical recovering of messages is ensured by the same framework it is found that many well known chaotic systems can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either one type of driving signals or all several numerical simulations are shown with expected satisfactory performance

l shaped decomposition of two stage stochastic programs with integer recourse we consider two stage stochastic programming problems with integer recourse the l shaped method of stochastic linear programming is generalized to these problems by using generalized benders decomposition nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques finite convergence of the method is established when gomory s fractional cutting plane algorithm or a branch and bound algorithm is applied

stochastic set packing problem abstract in this paper a stochastic version of the set packing problem spp is studied via scenario analysis we consider a one stage recourse approach to deal with the uncertainty in the coefficients it consists of maximizing in the stochastic spp a composite function of the expected value minus the weighted risk of obtaining a scenario whose objective function value is worse than a given threshold the splitting variable representation is decomposed by dualizing the nonanticipativity constraints that link the deterministic spp with a 0 1 knapsack problem for each scenario under consideration as a result a structured larger pure 0 1 model is created we present several procedures for obtaining good feasible solutions as well as a preprocessing approach for fixing variables the lagrange multipliers updating is performed by using the volume algorithm computational experience is reported for a broad variety of instances which shows that the new approach usually outperforms a state of the art optimization engine producing a comparable optimality gap with smaller several orders of magnitude computing time

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

scenarios and policy aggregation in optimization under uncertainty a common approach in coping with multiperiod optimization problems under uncertainty where statistical information is not really enough to support a stochastic programming model has been to set up and analyze a number of scenarios the aim then is to identify trends and essential features on which a robust decision policy can be based this paper develops for the first time a rigorous algorithmic procedure for determining such a policy in response to any weighting of the scenarios the scenarios are bundled at various levels to reflect the availability of information and iterative adjustments are made to the decision policy to adapt to this structure and remove the dependence on hindsight

computer construction of split cartan subalgebras abstract we give a polynomial time algorithm that finds a split cartan subalgebra of a finite chevalley lie algebra

bfc a branch and fix coordination algorithmic framework for solving some types of stochastic pure and mixed 0 1 programs we present a framework for solving some types of 0 1 multi stage scheduling planning problems under uncertainty in the objective function coe cients and the right hand side a scenario analysis scheme with full recourse is used the solution o ered for each scenario group at each stage takes into account all scenarios but without subordinating to any of them the constraints are modelled by a splitting variables representation via scenarios so a 0 1 model for each scenario is consid ered plus the non anticipativity constraints that equate the 0 1 variables from the same group of scenarios in each stage the mathematical representation of the model is very amenable for the proposed framework to deal with the 0 1 character of the variables a branch and fix coordi nation approach is introduced for coordinating the selection of the branching nodes and branching variables in the scenario subproblems to be jointly optimized some computational experience is reported for di erent types of problems

the volume algorithm producing primal solutions with a subgradient method we present an extension to the subgradient algorithm to produce primal as well as dual solutions it can be seen as a fast way to carry out an approximation of dantzig wolfe decomposition this gives a fast method for producing approximations for large scale linear programs it is based on a new theorem in linear programming duality we present successful experience with linear programs coming from set partitioning set covering max cut and plant location

two stage stochastic hierarchical multiple risk problems models and algorithms in this paper we consider a class of two stage stochastic risk management problems which may be stated as follows a decision maker determines a set of binary first stage decisions after which a random event from a finite set of possible outcomes is realized depending on the realization of this outcome a set of continuous second stage decisions must then be made that attempt to minimize some risk function we consider a hierarchy of multiple risk levels along with associated penalties for each possible scenario the overall objective function thus depends on the cost of the first stage decisions plus the expected second stage risk penalties we develop a mixed integer 0 1 programming model and adopt an automatic convexification procedure using the reformulation linearization technique to recast the problem into a form that is amenable to applying benders partitioning approach as a principal computational expedient we show how the reformulated higher dimensional benders subproblems can be efficiently solved via certain reduced sized linear programs in the original variable space in addition we explore several key ingredients in our proposed procedure to enhance the tightness of the prescribed benders cuts and the efficiency with which they are generated finally we demonstrate the computational efficacy of our approaches on a set of realistic test problems

dynamic programming and strong bounds for the 0 1 knapsack problem two new algorithms recently proved to outperform all previous methods for the exact solution of the 0 1 knapsack problem this paper presents a combination of such approaches where in additi on valid inequalities are generated and surrogate relaxed and a new initial core problem is adopted the algorithm is able to solve all classical test instances with up to 10 000 variables in less than 0 2 seconds on a hp9000 735 99 computer the c language implementation of the algorithm is available on the internet

enhancing a branch and bound algorithm for two stage stochastic integer network design based models in this paper we present branch and bound b b strategies for two stage stochastic integer network design based models with integrality constraints in the first stage variables these strategies are used within l shaped decomposition based b b framework we propose a valid inequality in order to improve b b performance we use this inequality to implement a multirooted b b tree a selective use of optimality cuts is explored in the b b approach and we also propose a subgradient based technique for branching on 0 1 feasible solutions finally we present computational results for a fixed charge network design problem with random demands

risk aversion via excess probabilities in stochastic programs with mixed integer recourse we consider linear two stage stochastic programs with mixed integer recourse instead of basing the selection of an optimal first stage solution on expected costs alone we include into the objective a risk term reflecting the probability that a preselected cost threshold is exceeded after we have put the resulting mean risk model into perspective with stochastic dominance we study further structural properties of the model and derive some basic stability results in the algorithmic part of the paper we propose a scenario decomposition method and report initial computational experience

new formulations for the uncapacitated multiple allocation hub location problem in this paper we review the integer linear formulations of the uncapacitated multiple allocation hub location problem we study the scope of validity of these formulations and give new ones that generalize the older formulations our formulations allow one or two visits to hubs and include a more general cost structure that needs not satisfy the triangle inequality we prove that the constraints defined by cliques of a related intersection graph are tighter constraints than the classical ones we also discuss a pre processing of the problem which is very useful for reducing its size finally we check the strength of the new formulations and compare them with others in the literature by solving instances of two commonly used data sets the cab civil aeronautics board and ap australian post and also randomly generated instances our computational results clearly show that our formulations outperform all others previously used for small and medium problems

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

a heuristic procedure for stochastic integer programs with complete recourse in this paper we propose a successive approximation heuristic which solves large stochastic mixed integer programming problem with complete fixed recourse we refer to this method as the scenario updating method since it solves the problem by considering only a subset of scenarios which is updated at each iteration only those scenarios which imply a significant change in the objective function are added the algorithm is terminated when no such scenarios are available to enter in the current scenario subtree several rules to select scenarios are discussed bounds on heuristic solutions are computed by relaxing some of the non anticipativity constraints the proposed procedure is tested on a multistage stochastic batch sizing problem