generalized domino parity inequalities for the symmetric traveling salesman problem we extend the work of letchford letchford a n 2000 separating a superclass of comb inequalities in planar graphs math oper res 25 443 454 by introducing a new class of valid inequalities for the traveling salesman problem called the generalized domino parity gdp constraints just as letchford s domino parity constraints generalize comb inequalities gdp constraints generalize the most well known multiple handle constraints including clique tree bipartition path and star inequalities furthermore we show that a subset of gdp constraints containing all of the clique tree inequalities can be separated in polynomial time provided that the support graph g is planar and provided that we bound the number of handles by a fixed constant h

output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

a branch and cut approach to the cardinality constrained circuit problem the cardinality constrained circuit problem cccp is the problem of finding a minimum cost circuit in a graph where the circuit is constrained to have at most k edges the cccp is np hard we present classes of facet inducing inequalities for the convex hull of feasible circuits and a branch and cut solution approach using these inequalities

output feedback control of nonlinear systems using direct adaptive fuzzy neural controller in this paper a direct adaptive fuzzy neural output feedback controller dafoc for a class of uncertain nonlinear systems is developed under the constraint that only the system output is available for measurement an output feedback control law and an update law are derived for on line tuning the weighting factors of the dafoc by using strictly positive real lyapunov theory the stability of the closed loop system compensated by the dafoc can be verified moreover the proposed overall control scheme guarantees that all signals involved are bounded and the output of the closed loop system asymptotically tracks the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

solving matching problems with linear programming in this paper we describe an implementation of a cutting plane algorithm for the perfect matching problem which is based on the simplex method the algorithm has the following features it works on very sparse subgraphs ofkn which are determined heuristically global optimality is checked using the reduced cost criterion cutting plane recognition is usually accomplished by heuristics only if these fail the padberg rao procedure is invoked to guarantee finite convergence

a lifting procedure for the asymmetric traveling salesman polytope and a large new class of facets given any family of valid inequalities for the asymmetric traveling salesman polytopep g defined on the complete digraphg we show that all members of are facet defining if the primitive members of usually a small subclass are based on this result we then introduce a general procedure for identifying new classes of facet inducing inequalities forp g by lifting inequalities that are facet inducing forp g whereg is some induced subgraph ofg unlike traditional lifting where the lifted coefficients are calculated one by one and their value depends on the lifting sequence our lifting procedure replaces nodes ofg with cliques ofg and uses closed form expressions for calculating the coefficients of the new arcs which are sequence independent we also introduce a new class of facet inducing inequalities the class of sd source destination inequalities which subsumes as special cases most known families of facet defining inequalities

a fast optimization method based on a hierarchical strategy for the travelling salesman problem abstract an algorithm based on a hierarchical strategy is proposed for solving the travelling salesman problem the tour patterns have been analyzed and compared with those generated from different stages of simulated annealing a set of problems with known solutions has been used to evaluate the new algorithm the hierarchical algorithm is shown to be very fast it finds a path length similar to that obtained using simulated annealing algorithm the path length is quite far from the global minimum but compares favorably to that obtained using simulated annealing

the merchant subtour problem we consider the problem of a travelling merchant who makes money by buying commodities where they are cheap and selling them in other places where he can make a profit the merchant ships commodities of his own choice in a van of fixed capacity given the prices of all the commodities in all of the places and the cost of driving from one place to another the problem the merchant faces each day is to select a subset of the cities that he can visit in a day and to determine the order in which the cities are visited such that the total profit is maximised we call this problem the merchant subtour problem the msp models the pricing problem of a rather complex pickup and delivery problem that was given to us by the dutch logistics company van gend loos we show that a special case of the msp has a totally unimodular constraint matrix this knowledge enables us to develop a tabu search algorithm for finding good feasible solutions to the msp and a branch and price and cut algorithm for solving the msp to optimality the relaxations solved in each node of the branch and bound tree are strengthened by lifted knapsack inequalities lifted cycle inequalities and mod k cuts we present computational results on data sets derived from our main instance of the van gend loos pickup and delivery problem

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

small travelling salesman polytopes we introduce a new class of valid inequalities for the polytope of the symmetric travelling salesman problem we also gave complete characterizations of the polytope for 6 and 7 cities for the latter case the new inequalities are needed these results are related to work of r z norman in the 1950 s

the binested inequalities for the symmetric traveling salesman polytope in this paper we define a family of valid inequalities for the symmetric travelling salesman polytope which are defined on two nested sets of vertices of the graph these inequalities generalize the comb inequalities of chvital grotschel and padberg the clique tree inequalities of grotschel and pulleyblank the path inequalities of cornuejols fonlupt and naddef and the hyperstar inequalities of fleischman this is the largest known family of valid inequalities known so far facet inducing inequalities for the symmetric travelling salesman polytope contained in this class and in no other one are given proving that this is a proper generalization of the previously mentioned families

adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small gain approach this paper considers the adaptive fuzzy robust control problem for a class of single input and single output siso stochastic nonlinear systems in strict feedback form the systems under study possess unstructured uncertainties unknown dead zone uncertain dynamics and unknown gain functions in the controller design fuzzy logic systems are adopted to approximate the unknown functions and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics by combining the backstepping technique with the stochastic small gain approach a novel adaptive fuzzy robust control scheme is developed it is shown that the proposed control approach can guarantee that the closed loop system is input state practically stable isps in probability and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters simulation results are provided to illustrate the effectiveness of the proposed control approach

polynomial time separation of a superclass of simple comb inequalities the comb inequalities are a well known class of facet inducing inequalities for the traveling salesman problem defined in terms of certain vertex sets called the handle and the teeth we say that a comb inequality is simple if the following holds for each tooth either the intersection of the tooth with the handle has cardinality one or the part of the tooth outside the handle has cardinality one or both the simple comb inequalities generalize the classical 2 matching inequalities of edmonds edmonds j 1965 maximum matching and a polyhedron with 0 1 vertices j res nat bur standards69b 125 130 and also the so called chvatal comb inequalities in 1982 padberg and rao padberg m w m r rao 1982 odd minimum cut sets and b matchings math oper res 7 67 80 gave a polynomial time separation algorithm for the 2 matching inequalities i e an algorithm for testing if a given fractional solution to an lp relaxation violates a 2 matching inequality we extend this significantly by giving a polynomial time separation algorithm for a class of valid inequalities which includes all simple comb inequalities

the crown inequalities for the symmetric traveling salesman polytope we define a new family of valid inequalities for the symmetric traveling salesman polytope stspn that is the convex hull of the incidence vectors of all hamiltonian cycles of a complete graph with n nodes the smallest value of n for which the inequalities are defined is 8 we call these inequalities crown inequalities and we prove that they are facet inducing for stspn for n 8 we describe some extensions of the crown inequalities and we prove that they induce facets of stspn as well finally we discuss some issues on the possible applications of these inequalities in a polyhedral cutting plane algorithm

facet identification for the symmetric traveling salesman polytope several procedures for the identification of facet inducing inequalities for the symmetric traveling salesman polytope are given an identification procedure accepts as input the support graph of a point which does not belong to the polytope and returns as output some of the facet inducing inequalities violated by the point a procedure which always accomplishes this task is calledexact otherwise it is calledheuristic we give exact procedures for the subtour elimination and the 2 matching constraints based on the gomory hu and padberg rao algorithms respectively efficient reduction procedures for the input graph are proposed which accelerate these two algorithms substantially exact and heuristic shrinking conditions for the input graph are also given that yield efficient procedures for the identification of simple and general comb inequalities and of some elementary clique tree inequalities these procedures constitute the core of a polytopal cutting plane algorithm that we have devised and programmed to solve a substantial number of large scale problem instances with sizes up to 2392 nodes to optimality

neural network based optimal fuzzy controller design for nonlinear systems a neural learning fuzzy technique is proposed for t s fuzzy model identification of model free physical systems further an algorithm with a defined modelling index is proposed to integrate and to guarantee that the proposed neural based optimal fuzzy controller can stabilize physical systems the modelling index is defined to denote the modelling error evolution and to ensure that the training data for neural learning can describe the physical system behavior very well the algorithm which integrates the neural based fuzzy modelling and optimal fuzzy controlling process can implement off line modelling and on line optimal control for model free physical systems the neural fuzzy inference network is a self organizing inference system to learn fuzzy membership functions and fuzzy subsystems parameters as data feeding in based on the generated t s fuzzy models for the continuous mass spring damper system and chua s chaotic circuit discrete time model car system and articulated vehicle their corresponding fuzzy controllers are formulated from both local concept and global concept fuzzy approach respectively the simulation results demonstrate the performance of the proposed neural based fuzzy modelling technique and of the integrated algorithm of neural based optimal fuzzy control structure

h fuzzy adaptive tracking control design for nonlinear systems with output delays abstract in this study we develop fuzzy adaptive tracking control via two layer fuzzy observers variable structure systems vss and h control algorithm for nonlinear systems with plant uncertainties output delays and external disturbances the takagi sugeno fuzzy dynamic model with adaptation capability is used to approximate the nonlinear system when the system states are not available the states estimated from two layer fuzzy observers combined with vss are used to develop the fuzzy adaptive controller in the first layer the output delays are partitioned into m 1 equal time intervals to construct the same number of fuzzy observers the output delayed states in each time interval are used as the premise variables in the if then rules the second layer of the fuzzy observers uses output delayed error states as its linguistic variables and it is defuzzified from the first layer next we develop a fuzzy adaptive controller to overcome the nonlinearities output delayed states and external disturbances such that h tracking performance is achieved the lyapunov criterion and linear matrix inequalities are used to derive the controller in the present study our previous method is extended to handle a class of uncertain nonlinear systems with output delays and external disturbances which is achieved using robust vss and h control techniques a magnetic levitation system and inverted pendulum system are used as simulation examples to illustrate the validity and confirm the performance of our proposed scheme

odd minimum cut sets and b matchings we show that the determination of a minimum cut set of odd cardinality in a graph with even and odd vertices can be dealt with by a minor modification of the polynomially bounded algorithm of gomory and hu for multi terminal networks we connect this problem to the problem of identifying a matching or blossom constraint that chops off a point which is not contained in the convex hull of matchings or proving that no such inequality exists both the b matching problems without and with upper bounds are considered we discuss how the results of this paper can be used in conjunction with commercial lp packages lo solve b matching problems

an optimality cut for mixed integer linear programs abstract we derive the penalty cut a simple optimality cut of general applicability in pure or mixed linear programs this cut is tested on a number of examples and comparisons with the classical gomory cut are provided

the pickup and delivery problem faces and branch and cut algorithm abstract this paper formulates the pickup and delivery problem also known as the dial a ride problem as an integer program its polyhedral structure is explored and four classes of valid inequalities developed the results of a branch and cut algorithm based on these constraints are presented

a cutting plane algorithm for the general routing problem the general routing problem grp is the problem of finding a minimum cost route for a single vehicle subject to the condition that the vehicle visits certain vertices and edges of a network it contains the rural postman problem chinese postman problem and graphical travelling salesman problem as special cases we describe a cutting plane algorithm for the grp based on facet inducing inequalities and show that it is capable of providing very strong lower bounds and in most cases optimal solutions

identification and control of dynamic systems using recurrent fuzzy neural networks proposes a recurrent fuzzy neural network rfnn structure for identifying and controlling nonlinear dynamic systems the rfnn is inherently a recurrent multilayered connectionist network for realizing fuzzy inference using dynamic fuzzy rules temporal relations are embedded in the network by adding feedback connections in the second layer of the fuzzy neural network fnn the rfnn expands the basic ability of the fnn to cope with temporal problems in addition results for the fnn fuzzy inference engine universal approximation and convergence analysis are extended to the rfnn for the control problem we present the direct and indirect adaptive control approaches using the rfnn based on the lyapunov stability approach rigorous proofs are presented to guarantee the convergence of the rfnn by choosing appropriate learning rates finally the rfnn is applied in several simulations time series prediction identification and control of nonlinear systems the results confirm the effectiveness of the rfnn

implementing an efficient minimum capacity cut algorithm in this paper we present an efficient implementation of theo mn n2 logn time algorithm originally proposed by nagamochi and ibaraki 1992 for computing the minimum capacity cut of an undirected network to enhance computation various ideas are added so that it can contract as many edges as possible in each iteration to evaluate the performance of the resulting implementation we conducted extensive computational experiments and compared the results with that of padberg and rinaldi s algorithm 1990 which is currently known as one of the practically fastest programs for this problem the results indicate that our program is considerably faster than padberg and rinaldi s program and its running time is not significantly affected by the types of the networks being solved

existence of klyachko models for gl n r and gl n c we prove that any irreducible unitary representation of gl n r and gl n c admits an equivariant linear form with respect to one of the subgroups considered by klyachko

differential neuro fuzzy controller for uncertain nonlinear systems in general output based controller design remains an important research area in control theory most of the existing solutions use a state estimation algorithm to reconstruct a plausible approximation of the real state then one can apply a nonlinear controller based on fuzzy logic for example to enforce the system trajectories to a desirable stable equilibrium point nevertheless the aforementioned method may not be suitable for uncertain systems affected by external noises state observers based on the system s structure cannot be applied in those cases however some sort of adaptive estimation may be developed this paper deals with a fuzzy controller that was designed using the state observer solution when the dynamic model of a plant contains uncertainties or it is partially unknown differential neural network dnn approach is applied in this uninformative situation a new learning law containing an adaptive adjustment rate is suggested to enforce the stability condition for the observer s free parameters on the other hand nominal weights are adjusted during the preliminary training process using the least mean square method lyapunov theory is used to obtain the upper bounds for the weight s dynamics the proposed method seems to be a more advanced option to control uncertain systems when the state available information is reduced even when several options exist to control this class of nonlinear systems such as pid the method introduced here uses the knowledge on the system behavior and enforces the reconstruction of the immeasurable states this last issue is an extra advantage because it serves as a general software sensor the well known two link manipulator is used to show the effectiveness of the proposed algorithm a couple of cases are used here the full actuated and the under actuated systems in both situations the controller achieves a better performance than the well known pid controllers and a fuzzy controller using the estimated states produced by a high order sliding mode observer a practical example showing how the fuzzy controller based on the estimated states produced by the differential neural network observer is also presented the system used to test the controller is the anaerobic digestion in this case the benefits of this output based controller are also demonstrated

on the domino parity inequalities for the stsp one method which has been used very successfully for finding optimal and provably good solutions for large instances of the symmetric travelling salesman problem stsp is the branch and cut method this method requires knowledge of classes of useful valid inequalities for the polytope associated with the stsp as well as efficient separation routines for these classes of inequalities recently a new class of valid inequalities called the domino parity inequalites were introduced for the stsp an efficient separation routine is known for these constraints if certain conditions are satisfied by the point to be separated this separation routine has never been implemented or tested we present several performance enhancements for this separation routine and discuss our implementation of this improved algorithm we test our implementation and provide results which we believe demonstrate the practical usefulness of these constraints and the separation routine for the stsp within a branch and cut framework

quelques proprietes des representations spheriques pour les espaces symetriques reductifs let gh be a reductive symmetric space and suppose v is an admissible g k module of finite length possessing a linear functional t vsu which is fixed by h and h k we prove that v can be mapped equivariantly into c gh such that t becomes the pull back of the dirac measure at the origin essential in the proof is the fact that the formal power series of certain matrix coefficients of v satisfy a system of differential equations with regular singularities

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

separating clique trees and bipartition inequalities having a fixed number of handles and teeth in polynomial time many important cutting planes have been discovered for the traveling salesman problem among them are the clique tree inequalities and the more general bipartition inequalities little is known in the way of exact algorithms for separating these inequalities in polynomial time in the size of the fractional point x which is being separated an algorithm is presented here that separates bipartition inequalities of a fixed number of handles and teeth which includes clique tree inequalities of a fixed number of handles and teeth in polynomial time

the graphical relaxation a new framework for the symmetric traveling salesman polytope a present trend in the study of thesymmetric traveling salesman polytope stsp n is to use as a relaxation of the polytope thegraphical relaxation gtsp n rather than the traditionalmonotone relaxation which seems to have attained its limits in this paper we show the very close relationship between stsp n and gtsp n in particular we prove that every non trivial facet of stsp n is the intersection ofn 1 facets of gtsp n n of which are defined by the degree inequalities this fact permits us to define a standard form for the facet defining inequalities for stsp n that we calltight triangular and to devise a proof technique that can be used to show that many known facet defining inequalities for gtsp n define also facets of stsp n in addition we give conditions that permit to obtain facet defining inequalities by composition of facet defining inequalities for stsp n and general lifting theorems to derive facet defining inequalities for stsp n k from inequalities defining facets of stsp n

the precedence constrained asymmetric traveling salesman polytope many applications of the traveling salesman problem require the introduction of additional constraints one of the most frequently occurring classes of such constraints are those requiring that certain cities be visited before others precedence constraints in this paper we study the precedence constrained asymmetric traveling salesman pcats polytope i e the convex hull of incidence vectors of tours in a precedence constrained directed graph we derive several families of valid inequalities and give polynomial time separation algorithms for important subfamilies we then establish the dimension of the pcats polytope and show that under reasonable assumptions the two main classes of inequalities derived are facet inducing

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

on the separation of split cuts and related inequalities the split cuts of cook kannan and schrijver are general purpose valid inequalities for integer programming which include a variety of other well known cuts as special cases to detect violated split cuts one has to solve the associated separation problem the complexity of split cut separation was recently cited as an open problem by cornuejols li cl01 in this paper we settle this question by proving strong completeness of separation for split cuts as a by product we also show completeness of separation for several other classes of inequalities including the mir inequalities of nemhauser and wolsey and some new inequalities which we call balanced split cuts and binary split cuts we also strengthen completeness results of caprara fischetti cf96 for cuts and eisenbrand e99 for chvatal gomory cuts to compensate for this bleak picture we also give a positive result for the symmetric travelling salesman problem we show how to separate in polynomial time over a class of split cuts which includes all comb inequalities with a fixed handle

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

state observer based adaptive fuzzy output feedback control for a class of uncertain nonlinear systems this paper aims to develop state observer based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances an adaptive fuzzy observer is proposed to estimate the system state variables it is shown that the observation errors obtained from the observer are uniformly ultimately bounded applying the estimated system state for design of an output feedback controller the uniformly ultimate boundedness of the tracking errors for the resulting closed loop system can be guaranteed a typical robot arm system is employed in our simulation studies and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances

worst case comparison of valid inequalities for the tsp we consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worst case improvement resulting from their addition to the subtour polyhedron for example we show that the comb inequalities cannot improve the subtour bound by a factor greater than 10 9 the corresponding factor for the class of clique tree inequalities is 8 7 while it is 4 3 for the path configuration inequalities

uniqueness and disjointness of klyachko models we show the uniqueness and disjointness of klyachko models for gln over a non archimedean local field this completes in particular the study of klyachko models on the unitary dual our local results imply a global rigidity property for the discrete automorphic spectrum of gln

separation algorithms for classes of stsp inequalities arising from a new stsp relaxation the problem ofseparating a class of inequalities that are valid for the symmetric traveling salesman problem stsp consists of devising an efficient method that given a fractional pointx for a relaxation of the stsp either finds an inequality in the given class of stsp inequalities that is violated byx or determines that there are no such violated inequalities we can define important classes of stsp inequalities by performing naddef s and rinaldi s 1993 node lifting operation on stsp inequalities defined on small graphs we present efficient methods forexactly separating large classes of stsp inequalities that arise from an stsp relaxation related to node lifting in particular we show how to find efficiently the most violated inequality in the class of stsp inequalities having abackbone set with a constant numberk of vertices and thus separate in polynomial time the class of all stsp inequalities whose backbone set has at mostk vertices

fuzzy basis functions comparisons with other basis functions fuzzy basis functions fbf s which have the capability of combining both numerical data and linguistic information are compared with other basis functions because a fbf network is different from other networks in that it is the only one that can combine numerical and linguistic information comparisons are made when only numerical data is available in particular a fbf network is compared with a radial basis function rbf network from the viewpoint of function approximation their architectural interrelationships are discussed additionally a rbf network which is implemented using a regularization technique is compared with a fbf network from the viewpoint of overcoming ill posed problems a fbf network is also compared with specht s probabilistic neural network and his general regression neural network grnn from an architectural point of view a fbf network is also compared with a gaussian sum approximation in which gaussian functions play a central role finally we summarize the architectural relationships between all the networks discussed in this paper

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

an efficient algorithm for the minimum capacity cut problem given a finite undirected graph with nonnegative edge capacities the minimum capacity cut problem consists of partitioning the graph into two nonempty sets such that the sum of the capacities of edges connecting the two parts is minimum among all possible partitionings the standard algorithm to calculate a minimum capacity cut due to gomory and hu 1961 runs in o n4 time and is difficult to implement we present an alternative algorithm with the same worst case bound which is easier to implement and which was found empirically to be far superior to the standard algorithm we report computational results for graphs with up to 2000 nodes

feedback linearization of discrete time systems abstract we give necessary and sufficient conditions for a nonlinear discrete time system to be locally linearizable by a change of state coordinates and a feedback the conditions are expressed in terms of controllability distributions associated to the system

cohomologically induced distinguished representations and cohomological test vectors let g be a real reductive group and let be a character of a reductive subgroup h of g we construct invariant linear functionals on certain cohomologically induced representations of g and we show that these linear functionals do not vanish on the bottom layers applying this construction we prove two archimedean nonvanishing hypotheses which are vital to the arithmetic study of special values of certain l functions via modular symbols

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

observer based fuzzy adaptive control for multi input multi output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction in this study we present an observer based fuzzy adaptive control scheme for a class of uncertain multi input multi output nonlinear systems with a nonsymmetric control gain matrix unknown control direction and unmeasured states in this scheme fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states the parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors the proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured we prove that all of the signals in the resulting closed loop systems are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

efficient separation routines for the symmetric traveling salesman problem i general tools and comb separation this is the first of a series of two papers dedicated to efficient separation heuristics for violated inequalities in the context of solving to optimality instances of the traveling salesman problem via branch and cut in this paper we give the basic ideas behind these heuristics and design heuristics for comb separation the second paper will deal with more complex inequalities such as clique tree star or path and ladder inequalities and give computational results

a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems abstract an adaptive observer for a class of single input single output siso nonlinear systems is proposed using a generalized dynamic recurrent neural network drnn the neural network nn weights are tuned on line with no off line learning required no exact knowledge of non linearities in the observed system is required furthermore no linearity with respect to unknown system parameters is assumed the drnn observer does not assume that nonlinearities in the system are restricted to the system output only the overall adaptive observer scheme is shown to be uniformly ultimately bounded simulation results have verified the performance of the drnn observer

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

mean based fuzzy identifier and control of uncertain nonlinear systems a mean based adaptive fuzzy control scheme with state estimation performance is proposed for a class of uncertain nonlinear systems in the presence of only output measurement in the control scheme a mean based fuzzy identifier without prior knowledge of membership functions is merged into direct adaptive controller with a linear state estimator the structure of the mean based fuzzy identifier is nonlinear in the adjusted parameters in order to diminish the unfavorable influence of initially designing membership functions on control performance for the nonlinear structure a mean method is used to derive adaptive laws compared with conventional methods the advantage of the mean method is that the computation burden can be effectively alleviated because finding the derivative of fuzzy systems is not required in addition for the linear state estimator the state estimation performance with beforehand given attenuation parameter is established by the design of a compensative controller finally two examples are provided to demonstrate the applicability of the proposed scheme

how to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems this paper focuses on the construction of a fuzzy adaptive output feedback control based on any observer high gain hg observer sliding mode like observer etc for a class of single input single output siso uncertain or ill defined affine nonlinear systems indeed the corrective term of the proposed observer involves a well defined design function which is shown to be satisfied by the commonly used hg based observers namely for the usual hg observers and the sliding mode observers together with their implementable versions the design of the underlying update law as well as the robust control term is based on an appropriate filtering of the output tracking error this particularly allows to overcome the output observation error filtering or the necessity of the famous strictly positive real spr condition

a priori optimization of the probabilistic traveling salesman problem the probabilistic traveling salesman problem ptsp is defined on a graph g v e where v is the vertex set and e is the edge set each vertex vi has a probability pi of being present with each edge vi vj is associated a distance or cost cij in a first stage an a priori hamiltonian tour on g is designed the list of present vertices is then revealed in a second stage the a priori tour is followed by skipping the absent vertices the ptsp consists of determining a first stage solution that minimizes the expected cost of the second stage tour the problem is formulated as an integer linear stochastic program and solved by means of a branch and cut approach which relaxes some of the constraints and uses lower bounding functionals on the objective function problems involving up to 50 vertices are solved to optimality

separating maximally violated comb inequalities in planar graphs the traveling salesman problem tsp is a benchmark problem in combinatorial optimization it was one of the very first problems used for developing and testing approaches to solving large integer programs including cutting plane algorithms and branch and cut algorithms much of the research in this area has been focused on finding new classes of facets for the tsp polytope and much less attention has been paid to algorithms for separating from these classes of facets in this paper we consider the problem of finding violated comb inequalities if there are no violated subtour constraints in a fractional solution of the tsp a comb inequality may not be violated by more than 1 given a fractional solution in the subtour elimination polytope whose graph is planar we either find a violated comb inequality or determine that there are no comb inequalities violated by 1 our algorithm runs in on mcn time where mcn is the time to compute a cactus representation of all minimum cuts of a weighted planar graph on n vertices

clique tree inequalities and the symmetric travelling salesman problem the linear programming cutting plane approach for solving the travelling salesman problem has recently proven to be highly successful cf crowder and padberg crowder h p m w padberg 1980 solving large scale symmetric travelling salesman problems to optimality management sci 26 495 509 grotschel grotschel m 1980a on the symmetric travelling salesman problem solution of a 120 city problem math programming stud 12 61 77 padberg and hong padberg m w s hong 1980 on the symmetric travelling salesman problem a computational study math programming stud 12 78 107 one of the reasons for this success is certainly the fact that instead of ordinary cutting planes gomory cuts etc problem specific cutting planes could be used which define facets of the underlying integer programming polytopes in this paper we shall define a new class of inequalities clique tree inequalities valid for the travelling salesman polytope which properly contains many of the known classes of inequalities like subtour elimination constraints 2 matching constraints comb inequalities and we show that all these new inequalities induce facets of the travelling salesman polytope since the general structure of these new inequalities is quite simple we hope that it will be possible to use the inequalities efficiently in cutting plane procedures for the travelling salesman problem

vecteurs distributions h invariants pour les series principales generalisees d espaces symetriques reductifs et prolongement meromorphe d integrales d eisenstein

relaxed tours and path ejections for the traveling salesman problem abstract we describe an edge based ejection chain method to generate compound neighborhood structures for the traveling salesman problem tsp these neighborhood structures enclose a special substructure which is not necessarily a hamiltonian tour instead the neighborhood components are linked together to compose successive levels of an ejection chain and coordinated by a suitable reference structure to generate compound moves with outstanding proprieties more precisely such a substructure can be viewed as a relaxed tour which allows solution transformations to be obtained without preserving the hamiltonian property at each step furthermore in the ejection chain process the generation of substructures produces a variety of alternating paths for the selection of subsequent ejection moves as well as for the choice of the corresponding trial moves finally we propose two algorithmic variants a preliminary and a full subpath ejection chain method p sec and f sec based on this type of compound neighborhood design both variants are guided by a simple tabu search mechanism computational results on 67 tsplib problems show that both the preliminary and the full methods find optimal and near optimal solutions very quickly frequently outperforming the best heuristic procedures for the tsp in addition the full method generally dominates the best alternative tsp procedures

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

primal separation for 0 1 polytopes the 0 1 primal separation problem is given an extreme point x of a 0 1 polytope p and some point x find an inequality which is tight at x violated by x and valid for p or assert that no such inequality exists it is known that this separation variant can be reduced to the standard separation problem for p

a proof of kirillov s conjecture let g gln k where k is either r or c and let p pn k be the subgroup of matrices in gln k consisting of matrices whose last row is 0 0 0 1 let be an irreducible unitary representation of g gelfand and neumark gel neu proved that if k c and is in the gelfand neumark series of irreducible unitary representations of g then the restriction of to p remains irreducible kirillov kir conjectured that this should be true for all irreducible unitary representations of gln k where k is r or c

the black and white traveling salesman problem the black and white traveling salesman problem bwtsp is defined on a graph g whose vertex set is partitioned into black and white vertices the aim is to design a shortest hamiltonian tour on g subject to cardinality and length constraints both the number of white vertices as well as the length of the tour between two consecutive black vertices are bounded above the bwtsp has applications in airline scheduling and in telecommunications this paper proposes an integer linear formulation for the undirected bwtsp as well as several classes of valid inequalities an exact branch and cut algorithm is then developed extensive tests show that it can solve exactly instances involving up to 100 vertices the algorithm can also be applied directly to solve unit demand vehicle routing problems of similar sizes

a new branch and cut algorithm for the capacitated vehicle routing problem we present a new branch and cut algorithm for the capacitated vehicle routing problem cvrp the algorithm uses a variety of cutting planes including capacity framed capacity generalized capacity strengthened comb multistar partial multistar extended hypotour inequalities and classical gomory mixed integer cuts for each of these classes of inequalities we describe our separation algorithms in detail also we describe the other important ingredients of our branch and cut algorithm such as the branching rules the node selection strategy and the cut pool management computational results for a large number of instances show that the new algorithm is competitive in particular we solve three instances b n50 k8 b n66 k9 and b n78 k10 of augerat to optimality for the first time

meromorphic basis of h invariant distribution vectors for the generalized principal series of reductive symmetrical spaces functional equation abstract let g be the group of real points of a reductive algebraic group defined over r an involution of g and a cartan involution of g commuting with let h be an open subgroup of the group of fixed points for one builds a meromorphic basis for the space of h fixed distributions vectors of induced representations from a stable parabolic subgroup p of g for this we use a method which extends the domain of application of bruhat s thesis in particular to the irreducibility problem for generalized principal series the meromorphy is obtained by means of a functional equation that we establish and which generalizes the equation obtained by e van den ban in the case when p is minimal stable

separating a superclass of comb inequalities in planar graphs many classes of valid and facet inducing inequalities are known for the family of polytopes associated with thesymmetric travelling salesman problem stsp includingsubtour elimination 2 matching andcomb inequalities for a given class of inequalities anexact separation algorithm is a procedure which given an lp relaxation vectorx finds one or more inequalities in the class which are violated byx or proves that none exist such algorithms are at the core of the highly successfulbranch and cut algorithms for the stsp however whereas polynomial time exact separation algorithms are known for subtour elimination and 2 matching inequalities the complexity of comb separation is unknown apartial answer to the comb problem is provided in this paper we define ageneralization of comb inequalities and show that the associated separation problem can be solved efficiently when the subgraph induced by the edges withx e 0 is planar the separation algorithm runs in o n3 time wheren is the number of vertices in the graph

on the design of observer based fuzzy adaptive controller for nonlinear systems with unknown control gain sign in this paper an observer based fuzzy adaptive controller for nonlinear systems with unknown control gain sign is investigated because the system states are not available for measurement a tracking error observer is constructed in this controller the adaptive fuzzy system is used to approximate the unknown nonlinearities and the nussbaum function is incorporated to deal with the unknown control direction i e with the unknown control gain sign the stability of the closed loop system is proven using the strictly positive real spr condition and lyapunov theory finally simulation results are given to verify the feasibility and effectiveness of the proposed controller

the attractive traveling salesman problem in the attractive traveling salesman problem the vertex set is partitioned into facility vertices and customer vertices a maximum profit tour must be constructed on a subset of the facility vertices profit is computed through an attraction function every visited facility vertex attracts a portion of the profit from the customer vertices based on the distance between the facility and customer vertices and the attractiveness of the facility vertex a gravity model is used for computing the profit attraction the problem is formulated as an integer non linear program a linearization is proposed and strengthened through the introduction of valid inequalities and a branch and cut algorithm is developed a tabu search algorithm is also implemented computational results are reported