cut generation through binarization for a mixed integer linear program where all integer variables are bounded we study a reformulation introduced by roy that maps general integer variables to a collection of binary variables we study theoretical properties and empirical strength of rank 2 simple split cuts of the reformulation we show that for a pure integer problem with two integer variables these cuts are sufficient to obtain the integer hull of the problem but that this does not generalize to problems in higher dimensions we also give an algorithm to compute an approximation of the rank 2 simple split cut closure we report empirical results on 22 benchmark instances showing that the bounds obtained compare favorably with those obtained with other approximate methods to compute the split closure or lattice free cut closure it gives a better bound than the split closure on 6 instances while it is weaker on 9 instances for an average gap closed 3 8 smaller than the one for the split closure

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

binary extended formulations of polyhedral mixed integer sets we analyze different ways of constructing binary extended formulations of polyhedral mixed integer sets with bounded integer variables and compare their relative strength with respect to split cuts we show that among all binary extended formulations where each bounded integer variable is represented by a distinct collection of binary variables what we call unimodular extended formulations are the strongest we also compare the strength of some binary extended formulations from the literature finally we study the behavior of branch and bound on such extended formulations and show that branching on the new binary variables leads to significantly smaller enumeration trees in some cases

a new class of integrable systems we present a family of dynamical systems associated with the motion of a particle in two space dimensions these systems possess a second integral of motion quadratic in velocities apart from the hamiltonian and are thus completely integrable they were found through the derivation and subsequent resolution of the integrability condition in the form of a partial differential equation pde for the potential a most important point is that the same pde was derived through considerations on the analytic structure of the singularities of the solutions weak painleve property

on the value of binary expansions for general mixed integer linear programs we study the use of binary variables in reformulating general mixed integer linear programs we show that binary reformulations result in problems for which almost all the binary variables replacing a general integer variable need to be explored during branching we also give computational results on the performance of such reformulations in solving the mixed integer programs which support our theoretical results

contact symmetries and integrable non linear dynamical systems the authors present a systematic method of classifying and constructing invariants for lagrangians containing arbitrary polynomial non linear potentials it is based on the assumption that these lagrangians are invariant under contact groups of transformations for a finite number of degrees of freedom they can prove integrability for a large class of polynomial potentials the method can be extended in several directions

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

a disjunctive cutting plane procedure for general mixed integer linear programs in this paper we develop a cutting plane algorithm for solving mixed integer linear programs with general integer variables a novel feature of the algorithm is that it generates inequalities at all optimal vertices of the lp relaxation at each iteration the cutting planes generated in the procedure are found by considering a natural generalization of the 0 1 disjunction used by balas ceria and cornuejols in the context of solving binary mixed integer linear programs 3 4

stable adaptive fuzzy control for mimo nonlinear systems in this paper an indirect adaptive fuzzy control scheme is presented for a class of multi input and multi output mimo nonlinear systems whose dynamics are poorly understood within this scheme fuzzy systems are employed to approximate the plant s unknown dynamics in order to overcome the controller singularity problem the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices a robustifying control term is used to compensate for the lumped errors and all parameter adaptive laws and robustifying control term are derived based on lyapunov stability analysis the proposed scheme guarantees that all the signals in the resulting closed loop system are uniformly ultimately bounded uub moreover the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large a simulation example is used to demonstrate the effectiveness of the proposed control scheme

symmetries separability and volume forms in order to clarify certain misconceptions in the literature we discuss the details of the way determining equations for general symmetries of a lagrangian system differ from determining equations for noether symmetries and establish the minimal set of extra conditions which have to be imposed in practical situations for the former to reduce to the latter we further derive properties by which in situations where the system is integrable through quadratic integrals in involution the components of the corresponding noether symmetries themselves can be used to compute the separation variables if they exist for the hamilton jacobi equation

explicit integrability for hamiltonian systems and the painleve conjecture we analyze a class of hamiltonian systems in two dimensions for which we proved that a second constant of motion exists it is shown that using the two first integrals the equations of motion can be written in a form which allows their integration by quadratures an analysis of the equations of motion in this reduced form establishes the behavior of the solutions in the complex time plane it is shown explicitly that the systems belonging to this class possess the weak painleve property i e their solutions in complex time can present singularities of a specific algebraic type

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

on the facets of the mixed integer knapsack polyhedron we study the mixed integer knapsack polyhedron that is the convex hull of the mixed integer set defined by an arbitrary linear inequality and the bounds on the variables we describe facet defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable these inequalities strengthen and or generalize known inequalities for several special cases we report computational results on using the inequalities as cutting planes for mixed integer programming

direct integration of generalized lie or dynamical symmetries of three degrees of freedom nonlinear hamiltonian systems integrability and separability it is shown that by directly integrating the characteristic equation of the infinitesimals of the generalized lie or dynamical symmetries associated with three degrees of freedom hamiltonians one can almost by inspection obtain the required involutive integrals of motion whenever they exist the method is illustrated for the coupled quartic and cubic oscillators considered earlier further all the separable coordinates can be obtained by integrating a subset of the characteristic equation associated with the coordinate variables alone

adjoint symmetries separability and volume forms two results of a preceding paper are generalized the first is about characterizing to what extent preservation of the energy function of a lagrangian of mechanical type turns dynamical symmetries into noether symmetries the generalization here is twofold polynomial integrals of arbitrary degree are considered and the kinetic energy can have an arbitrary metric the second result here again for arbitrary metrics is about the way separation variables for the hamilton jacobi equation when they are ensured to exist by eisenhart s theorem can be computed in principle from a factorization property of a certain volume form the main novelty in the way the generalizations are discussed is that the emphasis is shifted from symmetries to the dual concept of adjoint symmetries

generalised symmetries of some nonlinear finite dimensional systems an approach based on the theorem that every variational symmetry of a variational problem is also a symmetry of the euler lagrange equation has been applied to find the generalised symmetries for the generalised henon heiles system a system possessing non polynomial type potential and a super integrable system the constants of motion of these systems have also been found

the probability monopoly probability is a very special case of fuzziness it always faces two limits first it works with bivalent sets a second probability measures need small infinities a probability measure maps the sets in a sigma algebra to the unit interval spl lsqb o 1 spl rsqb fuzzy theory challenges the probability monopoly probabilists have attacked it with gusto to keep their monopoly status to have the only uncertainty theory in the unit interval spl lsqb o 1 spl rsqb but the fuzzy math is sound its world view of shades of gray has a deep intuitive ring and the new fuzzy products have come into their own in the marketplace

lie symmetries and invariants of the lotka volterra system in this paper we use the lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3d lotka volterra system

adaptive fuzzy control of a class of mimo nonlinear systems this paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous time multi input multi output nonlinear dynamic systems within these schemes fuzzy systems are employed to approximate the plant s unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors by using a regularized matrix inverse a stable well defined adaptive controller is firstly investigated then in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values a second adaptive controller is proposed all parameter adaptive laws and robustifying control terms are derived based on lyapunov stability analysis so that under appropriate assumptions semi global stability and asymptotic convergence to zero of tracking errors can be guaranteed simulations performed on a two link robot manipulator illustrate the approach and exhibit its performance

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

direct integration of generalized lie symmetries of nonlinear hamiltonian systems with two degrees of freedom integrability and separability many of the integrable coupled nonlinear oscillator systems are associated with generalized lie symmetries involving velocity dependent terms for a class of systems with two degrees of freedom the authors show that by integrating the characteristic equation associated with the generalized symmetries the required involutive integrals of motion can be obtained explicitly in a straightforward manner almost by inspection and without recourse to noether s theorem further all the separable coordinates can be obtained by integrating a subset of the characteristic equation associated with the coordinate variables alone the explicit examples include the two coupled generalized henon heiles quartic sextic and other polynomial oscillator systems as well as the perturbed kepler system

gait detection based stable locomotion control system for biped robots it is a challenge to maintain a steady and stable locomotion when a biped robot navigates an uneven surface or a step firstly it needs to detect the gait of the robot and related environmental objectives and then to perform appropriate controls of stable locomotion in this paper a new type of sensing module with flexible force is designed to be mounted under the robotic sole to measure the foot pressure map which is essential for the analysis of zero moment point zmp to assist the biped robot to detect the gait conditions in addition a neuro fuzzy control scheme is also proposed to control the zmp trajectories and relative balancing by integrating the data of a 3 axis gyroscope to adaptive posture the experimental results show that the designed control system has improved the biped robot adaptive ability to overcome landform changes and the stability of locomotion while standing or walking on uneven terrain

the complete whittaker theorem for two dimensional integrable systems and its application the authors prove for a particle moving in a plane under the influence of a conservative force that when the motion is constrained by a second invariant quadratic in the velocities then the potential allows separability of the hamilton jacobi equation in rectangular polar elliptical cylinder or parabolic cylinder coordinates this link shows the intimate connection between quadratic invariants and the two dimensional hamilton jacobi equation they give examples of the utility of parabolic cylinder coordinates in cases of recent study

invariance and integrability henon heiles and two coupled quartic anharmonic oscillator systems it is shown that the henon heiles and two coupled quartic anharmonic oscillator systems possess non trivial generalised lie symmetries for specific sets of parametric values for which second integrals of motion can also be constructed directly using noether s theorem thereby establishing their complete integrability

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

split rank of triangle and quadrilateral inequalities a simple relaxation consisting of two rows of a simplex tableau is a mixed integer set with two equations two free integer variables and nonnegative continuous variables recently andersen et al and cornuejols and margot showed that the facet defining inequalities of this set are either split cuts or intersection cuts obtained from lattice free triangles and quadrilaterals from an example given by cook et al it is known that one particular class of facet defining triangle inequality does not have finite split rank in this paper we show that all other facet defining triangle and quadrilateral inequalities have finite split rank

fuzzy adaptive control of multivariable nonlinear systems abstract the robust fuzzy adaptive control scheme is developed for a class of unknown nonlinear mimo systems two types of uncertainties are considered i e the matched uncertainty and the unmatched uncertainties in the control procedure fuzzy logic systems are implemented to estimate the unknown functions and robust compensators are designed in h sense for attenuating the unmatched uncertainties it is shown that the proposed control is continuous guarantees global stability and the h performance index extensive simulations on the tracking control of a two link rigid robotics manipulator verify the effectiveness of the proposed algorithms

chva tal closures for mixed integer programming problems chvatal introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality this viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems the basic ingredient in these cutting plane proofs is that for a polyhedronp and integral vectorw if max wx x p wx integer t thenwx t is valid for all integral vectors inp we consider the variant of this step where the requirement thatwx be integer may be replaced by the requirement that bar wx be integer for some other integral vector bar w the cutting plane proofs thus obtained may be seen either as an abstraction of gomory s mixed integer cutting plane technique or as a proof version of a simple class of the disjunctive cutting planes studied by balas and jeroslow our main result is that for a given polyhedronp the set of vectors that satisfy every cutting plane forp with respect to a specified subset of integer variables is again a polyhedron this allows us to obtain a finite recursive procedure for generating the mixed integer hull of a polyhedron analogous to the process of repeatedly taking chvatal closures in the integer programming case these results are illustrated with a number of examples from combinatorial optimization our work can be seen as a continuation of that of nemhauser and wolsey on mixed integer cutting planes

mir closures of polyhedral sets we study the mixed integer rounding mir closures of polyhedral sets the mir closure of a polyhedral set is equal to its split closure and the associated separation problem is np hard we describe a mixed integer programming mip model with linear constraints and a non linear objective for separating an arbitrary point from the mir closure of a given mixed integer set we linearize the objective using additional variables to produce a linear mip model that solves the separation problem exactly using a subset of these additional variables yields an mip model which solves the separation problem approximately with an accuracy that depends on the number of additional variables used our analysis yields an alternative proof of the result of cook et al 1990 that the split closure of a polyhedral set is again a polyhedron we also discuss a heuristic to obtain mir cuts based on our approximate separation model and present some computational results

solving mixed integer bilinear problems using milp formulations in this paper we examine a mixed integer linear programming reformulation for mixed integer bilinear problems where each bilinearterm involves the product of a nonnegative integer variable and a nonnegative continuous variable this reformulation is obtained by first replacing a general integer variable with its binary expansion and then using mccormick envelopes to linearize the resulting product of continuous and binary variables we present the convex hull of the underlying mixed integer linear set the effectiveness of this reformulation and associated facet defining inequalities are computationally evaluated on five classes of instances

hybrid adaptive fuzzy identification and control of nonlinear systems we present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller and adaptive fuzzy identification model parameters first using adaptive fuzzy building blocks with a common set of parameters we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of uncertain structure nonlinear dynamic systems we then propose a hybrid adaptive ha law for adjusting the parameters the ha law utilizes two types of errors in the adaptive system the tracking error and the modeling error performance analysis using a lyapunov synthesis approach proves the superiority of the ha law over the direct adaptive da method in terms of faster and improved tracking and parameter convergence furthermore this is achieved at negligible increased implementation cost or computational complexity we prove a theorem that shows the properties of this hybrid adaptive fuzzy control system i e bounds for the integral of the squared errors and the conditions under which these errors converge asymptotically to zero are obtained finally we apply the hybrid adaptive fuzzy controller to control a chaotic system and the inverted pendulum system

generalizations of noether s theorem in classical mechanics in this paper a review is presented of various approaches to the generalization of the version of noether s theorem which is presented in most textbooks on classical mechanics its motivation is the controversy still persisting around the possible scope of a noether type theorem allowing for velocity dependent transformations our analysis is centered around the one factor common to all known treatments namely the structure of the related first integral we first discuss the most general framework in which a function of the above mentioned structure constitutes a first integral of a given lagrangian system and show that one cannot really talk about an interrelationship between symmetries and first integrals there we then compare different proposed generalizations of noether s theorem by describing the nature of the restrictions which characterize them when they are situated within the broadest framework we prove a seemingly new equivalence result between the two main approaches that of invaria

fuzzy incremental control algorithm of loop heat pipe cooling system for spacecraft applications reliable and high precision thermal control technologies are essential for the safe flight of advanced spacecraft a fuzzy incremental control strategy is proposed for control of an lhp space cooling system comprising a loop heat pipe and a variable emittance radiator with mems louver the generating and performing algorithm of the fuzzy control rules is provided with an analytical form based on the understanding of dynamics and control mechanisms of the space cooling system this paper also presents a novel integrated mathematical model for the dynamic analysis of the lhp space cooling system and a numerical evaluation of the investigated control schemes numerical simulation results on the closed loop control effects suggest that the proposed control strategy takes advantage of no steady error small overshoots and short settling times thus benefiting safe highly accurate and reliable operation of the entire space cooling system the overshoots of the most important operating parameters t o b q r and p under the proposed fuzzy incremental control have been reduced to 16 3 17 6 and 18 6 of the compared pid control s while the respective settling times have been shortened to 33 9 42 3 and 30 5 of the reference values

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

adaptive fuzzy control for mimo nonlinear systems with nonsymmetric control gain matrix and unknown control direction in this paper an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi input multi output nonlinear systems with nonsymmetric control gain matrix and unknown control direction the nonsymmetric control gain matrix is expressed as the sum of a symmetric matrix and a skew symmetric matrix and the symmetric matrix as well as the skew symmetric matrix is approximated by fuzzy systems by using the symmetric matrix decomposition technique the estimated symmetric matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes based on the decomposition results the adaptive fuzzy controller is developed to avoid the possible singularity problem and the parameter initialization problem a robust control term is employed to compensate for the lumped errors and a nussbaum type function is incorporated in the robust control term to deal with the unknown control direction the proposed scheme guarantees that all the signals in the resulting closed loop system are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

generalized lie symmetries and complete integrability of certain nonlinear hamiltonian systems with three degrees of freedom a systematic method for investigating the existence of nontrivial generalized lie symmetries is presented and the associated integrals of motion for nonlinear oscillator systems with three degrees of freedom defined in terms of the lagrangian by l 1 2 x2 y2 z2 v x y z are constructed then the method is applied to study the integrability properties of quartically and cubically coupled nonlinear oscillators with three degrees of freedom compatibility with the painleve property is also investigated

lie symmetries and infinite dimensional lie algebras of certain nonlinear dissipative systems we point out that the dissipative force free duffing oscillator and holmes rand nonlinear oscillator admit infinite dimensional symmetry algebras for certain parametric choices for which the systems become integrable from the nature of the symmetry vector fields one can also write down the integrals of motion for the above systems in addition we point out that the other dissipative systems discussed in the literature also admit infinite dimensional lie algebras

on convergence in mixed integer programming let p subseteq mathbb r m n be a rational polyhedron and let pi be the convex hull of p cap mathbb z m times mathbb r n we define the integral lattice free closure of p as the set obtained from p by adding all inequalities obtained from disjunctions associated with integral lattice free polyhedra in mathbb r m we show that the integral lattice free closure of p is again a polyhedron and that repeatedly taking the integral lattice free closure of p gives pi after a finite number of iterations such results can be seen as a mixed integer analogue of theorems by chvatal and schrijver for the pure integer case one ingredient of our proof is an extension of a result by owen and mehrotra in fact we prove that for each rational polyhedron p the split closures of p yield in the limit the set pi

cutting planes from extended lp formulations given a mixed integer set defined by linear inequalities and integrality requirements on some of the variables we consider extended formulations of its continuous lp relaxation and study the effect of adding cutting planes in the extended space in terms of optimization extended lp formulations do not lead to better bounds as their projection onto the original space is precisely the original lp relaxation however adding cutting planes in the extended space can lead to stronger bounds in this paper we show that for every 0 1 mixed integer set with n integer and k continuous variables there is an extended lp formulation with 2n k 1 2n k 1 variables whose elementary split closure is integral the proof is constructive but it requires an inner description of the lp relaxation we then extend this idea to general mixed integer sets and construct the best extended lp formulation for such sets with respect to lattice free cuts we also present computational results on the two row continuous group relaxation showing the strength of cutting planes derived from extended lp formulations