simultaneous column and row generation for large scale linear programs with column dependent rows in this paper we develop a simultaneous column and row generation algorithm that could be applied to a general class of large scale linear programming problems these problems typically arise in the context of linear programming formulations with exponentially many variables the defining property for these formulations is a set of linking constraints which are either too many to be included in the formulation directly or the full set of linking constraints can only be identified if all variables are generated explicitly due to this dependence between columns and rows we refer to this class of linear programs as problems with column dependent rows to solve these problems we need to be able to generate both columns and rows on the fly within an efficient solution approach we emphasize that the generated rows are structural constraints and distinguish our work from the branch and cut and price framework we first characterize the underlying assumptions for the proposed column and row generation algorithm these assumptions are general enough and cover all problems with column dependent rows studied in the literature up until now to the best of our knowledge we then introduce in detail a set of pricing subproblems which are used within the proposed column and row generation algorithm this is followed by a formal discussion on the optimality of the algorithm to illustrate our approach the paper is concluded by applying the proposed framework to the multi stage cutting stock and the quadratic set covering problems

direct adaptive nn control of a class of nonlinear systems in this paper direct adaptive neural network nn control is presented for a class of affine nonlinear systems in the strict feedback form with unknown nonlinearities by utilizing a special property of the affine term the developed scheme avoids the controller singularity problem completely all the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory the control performance of the closed loop system is guaranteed by suitably choosing the design parameters simulation results are presented to show the effectiveness of the approach

modified neural dynamic surface approach to output feedback of mimo nonlinear systems we report an adaptive output feedback dynamic surface control dsc maintaining the prescribed performance for a class of uncertain nonlinear systems with multiinput and multioutput designing neural network observers and modifying the dsc method achieves several control objectives first to achieve output feedback control the finite time echo state networks esn observer with fast convergence is designed to obtain the online system states thus the immeasurable states in traditional state feedback control are estimated and the unknown functions are approximated by esn then a modified dsc approach is developed by introducing a high order sliding mode differentiator to replace the first order filter in each step thus the effect of filter performance on closed loop stability is reduced furthermore the input to state stability guarantees that all signals of the whole closed loop system are semiglobally uniformly ultimately bounded specifically the performance functions make the tracking errors converge to a compact set around equilibrium two numerical examples illustrated the proposed control scheme with satisfactory results

large deflections of a cantilever beam under an inclined end load abstract large deflections of a cantilever beam subjected to a tip concentrated load whose inclination to the deformed axis of the beam is assumed as constant the mathematical formulation yields a non linear two point boundary value problem amenable to numerical integration a relation is obtained between the load and the tip angle of the beam when the tip concentrated load is normal to the deformed axis of the beam many possible loads are found for a specified tip angle for the specified load the tip angle is found to be unique however there is a change in the deformation pattern of the beam having a specified tip angle with the corresponding multiple loads this confirms the uniqueness of the solution for the governing non linear differential equations of a cantilever beam under a tip concentrated load whose inclination is normal to its deformed axis

enhancing an algorithm for set covering problems abstract in this note we present enhancements to a previously published algorithm for the optimal solution of set covering problems these enhancements relate to the use of a langrangean heuristic feasible solution exclusion constraints gomory f cuts and an improved branching strategy computational results for problems involving up to 400 rows and 4000 columns indicate that the enhanced algorithm gives better computational results than the original algorithm

surrogate constraint normalization for the set covering problem the set covering problem scp is central in a wide variety of practical applications for which finding good feasible solutions quickly often in real time is crucial surrogate constraint normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming this framework remains the core of the most effective constructive heuristics for the solution of the scp chiefly represented by the widely used chvatal method this paper introduces a number of normalization rules and demonstrates their superiority to the classical chvatal rule especially when solving large scale and real world instances directions for new advances on the creation of more elaborate normalization rules for surrogate heuristics are also provided

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

extended variational formulations and f e models for nonlinear beams under nonconservative loading abstract for nonconservative mechanical systems classical variational principles do not hold true hence the principle of incremental virtual work is usually taken as a convenient foundation for finite element solution methods 2 8 9 recent results on the so called inverse problem of calculus of variations however lead to extended variational formulations which can be provided even for nonconservative systems in the present paper this approach is used for the particular case of a nonlinear beam subjected to a co planar follower static loading suitable finite element models are deduced from the extended variational principle and their numerical performance is assessed by means of some meaningful examples

on the persistency of excitation in radial basis function network identification of nonlinear systems considers radial basis function rbf network approximation of a multivariate nonlinear mapping as a linear parametric regression problem linear recursive identification algorithms applied to this problem are known to converge provided the regressor vector sequence has the persistency of excitation pe property the main contribution of this paper is formulation and proof of pe conditions on the input variables in the rbf network identification the regressor vector is a nonlinear function of these input variables according to the formulated condition the inputs provide pe if they belong to domains around the network node centers for a two input network with gaussian rbf that have typical width and are centered on a regular mesh these domains cover about 25 of the input domain volume the authors further generalize the proposed solution of the standard rbf network identification problem and study affine rbf network identification that is important for affine nonlinear system control for the affine rbf network the author formulates and proves a pe condition on both the system state parameters and control inputs

an explicit solution of the large deformation of a cantilever beam under point load at the free tip the large deformation of a cantilever beam under point load at the free tip is investigated by an analytic method namely the homotopy analysis method ham the explicit analytic formulas for the rotation angle at the free tip are given which provide a convenient and straightforward approach to calculate the vertical and horizontal displacements of a cantilever beam with large deformation these explicit formulas are valid for most practical problems thus providing a useful reference for engineering applications the corresponding mathematica code is given in the appendix

robust adaptive neural control for a class of perturbed strict feedback nonlinear systems this paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities the unknown nonlinearities comprise two types of nonlinear functions one naturally satisfies the triangularity condition and can be approximated by linearly parameterized neural networks while the other is assumed to be partially known and consists of parametric uncertainties and known bounding functions with the utilization of iterative lyapunov design and neural networks the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied the design method does not require a priori knowledge of the signs of the unknown virtual control coefficients leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural network approximation errors it is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed loop system signals the control performance can be guaranteed by an appropriate choice of the design parameters simulation studies are included to illustrate the effectiveness of the proposed approach

consensus based distributed cooperative learning from closed loop neural control systems in this paper the neural tracking problem is addressed for a group of uncertain nonlinear systems where the system structures are identical but the reference signals are different this paper focuses on studying the learning capability of neural networks nns during the control process first we propose a novel control scheme called distributed cooperative learning dcl control scheme by establishing the communication topology among adaptive laws of nn weights to share their learned knowledge online it is further proved that if the communication topology is undirected and connected all estimated weights of nns can converge to small neighborhoods around their optimal values over a domain consisting of the union of all state orbits second as a corollary it is shown that the conclusion on the deterministic learning still holds in the decentralized adaptive neural control scheme where however the estimated weights of nns just converge to small neighborhoods of the optimal values along their own state orbits thus the learned controllers obtained by dcl scheme have the better generalization capability than ones obtained by decentralized learning method a simulation example is provided to verify the effectiveness and advantages of the control schemes proposed in this paper

a heuristic method for the set covering problem we present a lagrangian based heuristic for the well known set covering problem scp the algorithm was initially designed for solving very large scale scp instances involving up to 5 000 rows an

learning from iss modular adaptive nn control of nonlinear strict feedback systems this paper studies learning from adaptive neural control anc for a class of nonlinear strict feedback systems with unknown affine terms to achieve the purpose of learning a simple input to state stability iss modular anc method is first presented to ensure the boundedness of all the signals in the closed loop system and the convergence of tracking errors in finite time subsequently it is proven that learning with the proposed stable iss modular anc can be achieved the cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods to overcome these difficulties the stable closed loop system in the control process is decomposed into a series of linear time varying ltv perturbed subsystems with the appropriate state transformation using a recursive design the partial persistent excitation condition for the radial basis function neural network nn is established which guarantees exponential stability of ltv perturbed subsystems consequently accurate approximation of the closed loop system dynamics is achieved in a local region along recurrent orbits of closed loop signals and learning is implemented during a closed loop feedback control process the learned knowledge is reused to achieve stability and an improved performance thereby avoiding the tremendous repeated training process of nns simulation studies are given to demonstrate the effectiveness of the proposed method

adaptive neural control of mimo nonlinear state time varying delay systems with unknown dead zones and gain signs in this paper adaptive neural control is proposed for a class of uncertain multi input multi output mimo nonlinear state time varying delay systems in a triangular control structure with unknown nonlinear dead zones and gain signs the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions the unknown time varying delays are compensated for using appropriate lyapunov krasovskii functionals in the design the approach removes the assumption of linear functions outside the deadband as an added contribution by utilizing the integral lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead zone disturbance the closed loop control system is proved to be semi globally uniformly ultimately bounded simulation results demonstrate the effectiveness of the approach

global optimality conditions for discrete and nonconvex optimizationwith applications to lagrangian heuristics and column generation the well known and established global optimality conditions based on the lagrangian formulation of an optimization problem are consistent if and only if the duality gap is zero we develop a set of global optimality conditions that are structurally similar but are consistent for any size of the duality gap this system characterizes a primaldual optimal solution by means of primal and dual feasibility primal lagrangian e optimality and in the presence of inequality constraints a relaxed complementarity condition analogously called complementarity the total size e of those two perturbations equals the size of the duality gap at an optimal solution further the characterization is equivalent to a near saddle point condition which generalizes the classic saddle point characterization of a primaldual optimal solution in convex programming the system developed can be used to explain to a large degree when and why lagrangian heuristics for discrete optimization are successful in reaching near optimal solutions further experiments on a set covering problem illustrate how the new optimality conditions can be utilized as a foundation for the construction of new lagrangian heuristics finally we outline possible uses of the optimality conditions in column generation algorithms and in the construction of core problems

a lagrangian based heuristic for large scale set covering problems we present a new lagrangian based heuristic for solving large scale set covering problems arising from crew scheduling at the italian railways ferrovie dello stato our heuristic obtained impressive results when compared to state of the art codes on a test bed provided by the company which includes instances with sizes ranging from 50 000 variables and 500 constraints to 1 000 000 variables and 5000 constraints 1998 the mathematical programming society inc published by elsevier science b v

stability of nonlinearly elastic rods this paper describes previously unknown stabilities and instabilities of planar equilibrium configurations of a nonlinearly elastic rod that is buckled under the action of a dead load the governing equations are derived from variational principles including ones of isoperimetric type properties of stability are accordingly determined by study of the second variation stabilities to deformations both in the plane and out of the plane are considered among the newly discovered properties are secondary bifurcation from the first buckled mode marked differences between stability to two dimensional and to three dimensional variations and the stabilizing influence of resistance to twist in the isoperimetric examples the analysis makes crucial use of a novel device to account for the dependence of the second variation on constraints

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

an outer approximate subdifferential method for piecewise affine optimization piecewise affine functions arise from lagrangian duals of integer programming problems and optimizing them provides good bounds for use in a branch and bound method methods such as the subgradient method and bundle methods assume only one subgradient is available at each point but in many situations there is more information available we present a new method for optimizing such functions which is related to steepest descent but uses an outer approximation to the subdifferential to avoid some of the numerical problems with the steepest descent approach we provide convergence results for a class of outer approximations and then develop a practical algorithm using such an approximation for the compact dual to the linear programming relaxation of the uncapacitated facility location problem we make a numerical comparison of our outer approximation method with the projection method of conn and cornuejols and the bundle method of schramm and zowe

persistency of excitation in identification using radial basis function approximants in this paper identification algorithms whose convergence and rate of convergence hinge on the regressor vector being persistently exciting are discussed it is then shown that if the regressor vector is constructed out of radial basis function approximants it will be persistently exciting provided a kind of ergodic condition is satisfied in addition bounds on parameters associated with the persistently exciting regressor vector are provided these parameters are connected with both the convergence and rates of convergence of the algorithms involved

stable adaptive tracking of uncertain systems using nonlinearly parametrized on line approximators the design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered the lyapunov synthesis approach is used to develop state feedback adaptive control schemes based on a general class of nonlinearly parametrized on line approximation models the key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher order terms of the on line approximator with respect to the network weights satisfy certain bounding conditions an adaptive bounding design is used to show that the overall neural control system guarantees semi global uniform ultimate boundedness within a neighbourhood of zero tracking error the theoretical results are illustrated through a simulation example

numerical results from large deflection beam and frame problems analysed by means of elliptic integrals numerical evaluations of elliptic integral solutions of some large deflection beam and frame problems are presented the values are given in tabular form with up to six significant figures the numerical technique used for evaluating the elliptic integrals is described

robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors this paper describes the design of the robust adaptive fuzzy controller for uncertain single input single output nonlinear dynamical systems with unknown nonlinearities these unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy if then rules whose parameters are adjusted on line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory the lyapunov synthesis approach is used to develop a state feedback adaptive control algorithm based on the adaptive fuzzy model the key assumption is that the reconstruction errors satisfy certain bounding conditions the control law consists of two terms one is the certainty equivalent control and the other is the bounding control a bounding parameter adaptive law is used to obtain this bounding control the overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded it is also shown that in the special case the tracking error exponentially converges to zero even though the approximation errors exist

output feedback control of uncertain nonlinear systems using a self structuring adaptive fuzzy observer this paper describes the design of an output feedback controller based on an adaptive fuzzy observer for uncertain single input single output nonlinear dynamical systems we have focused on the realization of a minimal dynamic order for the adaptive fuzzy observer for this purpose we adopt an adaptive fuzzy observer in which no strictly positive real spr condition is needed and we combine a self structuring scheme with an on line estimation of fuzzy parameters by using this proposed scheme we can reduce the dynamic order of the adaptive output feedback fuzzy control system the lyapunov synthesis approach is used to guarantee a global uniform ultimate boundedness property of the state estimation error and tracking error as well as all other signals in the closed loop system no a priori knowledge of an upper limits on the uncertainties including optimal parameters and modeling errors is required the theoretical results are illustrated through simulation examples

the probabilistic set covering problem in a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability we analyze the structure of the set of probabilistically efficient points of binary random vectors develop methods for their enumeration and propose specialized branch and bound algorithms for probabilistic set covering problems

integrated design of a linear neuro adaptive controller in the presence of norm bounded uncertainties adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network nn design parameters to performance requirements this study proposes a methodology for the design of an integrated linear adaptive model reference controller that guarantees component wise boundedness of the tracking error within an a priori specified compact domain the approach is based on the design of a robust invariant ellipsoidal set where both the nn reconstruction error and the neuro adaptive control are considered as bounded persistent uncertainties we show that all the performance and control requirements for the closed loop system can be expressed as linear matrix inequality constraints this brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem an advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design param

optimal solution of set covering partitioning problems using dual heuristics we present an algorithm for a mixed set covering partitioning model that includes as special cases the well known set covering problem and set partitioning problem the novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm the heuristics are continuous adaptations of the well known greedy and 3 opt methods that have been applied to a variety of combinatorial optimization problems our algorithm has outperformed the current best set covering algorithm of balas and ho 1980 by about a factor of 3 and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude

on stability of elastic rod planar equilibrium configurations abstract the jacobi test is used to analyze the stability of planar equilibrium configurations for clamped clamped and clamped hinged elastic rods the governing equilibrium equation and jacobi equation are derived from variational principles and their solution is presented in terms of the jacobi elliptical functions the critical equation which determines the stability properties of rod equilibrium is solved numerically the results of the analysis are presented in graphical form as instability regions on bifurcation diagrams

adaptive fuzzy decentralized control for a class of strong interconnected nonlinear systems with unmodeled dynamics the state feedback decentralized stabilization problem is considered for interconnected nonlinear systems in the presence of unmodeled dynamics the functional relationship in affine form between the strong interconnected functions and error signals is established which makes backstepping based fuzzy control successfully generalized to strong interconnected nonlinear systems by combining adaptive control with both backstepping design and the approximation property of fuzzy systems an adaptive decentralized control algorithm is developed it is demonstrated by both theoretical analysis and simulation study that the proposed control strategy ensures semiglobally uniformly ultimately bounded of all signals within the closed loop systems

adaptive neural control for a class of nonlinearly parametric time delay systems in this paper an adaptive neural controller for a class of time delay nonlinear systems with unknown nonlinearities is proposed based on a wavelet neural network wnn online approximation model a state feedback adaptive controller is obtained by constructing a novel integral type lyapunov krasovskii functional which also efficiently overcomes the controller singularity problem it is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed loop systems an example is provided to illustrate the application of the approach

algorithms for railway crew management crew management is concerned with building the work schedules of crews needed to cover a planned timetable this is a well known problem in operations research and has been historically associated with airlines and mass transit companies more recently railway applications have also come on the scene especially in europe in practice the overall crew management problem is decomposed into two subproblems called crew scheduling and crew rostering in this paper we give an outline of different ways of modeling the two subproblems and possible solution methods two main solution approaches are illustrated for real world applications in particular we discuss in some detail the solution techniques currently adopted at the italian railway company ferrovie dello stato spa for solving crew scheduling and rostering problems

large deflections of a cantilever beam subjected to a follower force abstract the large deflection problem of a non uniform spring hinged cantilever beam under a tip concentrated follower force is considered the angle of inclination of the force with respect to the deformed axis of the beam remains unchanged during deformation the mathematical formulation of this problem yields a nonlinear two point boundary value problem which is reduced to an initial value problem by change of variables the resulting problem can be solved without iterations it is shown that there exist no critical loads in the euler sense divergence for any flexural stiffness distribution and angle of inclination of the follower force the load displacement characteristics of a uniform cantilever under a follower force normal to the deformed beam axis are presented

a new neuro fds definition for indirect adaptive control of unknown nonlinear systems using a method of parameter hopping the indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper the method is based on a new neuro fuzzy dynamical system neuro fds definition which uses the concept of adaptive fuzzy systems afss operating in conjunction with high order neural network functions fhonnfs since the plant is considered unknown we first propose its approximation by a special form of an fds and then the fuzzy rules are approximated by appropriate honnfs thus the identification scheme leads up to a recurrent high order neural network rhonn which however takes into account the fuzzy output partitions of the initial fds the proposed scheme does not require a priori experts information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions once the system is identified around an operation point it is regulated to zero adaptively weight updating laws for the involved honnfs are provided which guarantee that both the identification error and the system states reach zero exponentially fast while keeping all signals in the closed loop bounded the existence of the control signal is always assured by introducing a novel method of parameter hopping which is incorporated in the weight updating law simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given also the applicability of the method is tested on a direct current dc motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation

adaptive tracking control for stochastic uncertain non linear systems satisfying short and long term cost criteria the tracking control problem for a class of stochastic and uncertain non linear systems is addressed the proposed controller uses suitable radial basis function neural network designs for the approximation of the unknown non linearities while it is arbitrarily regulated in order to effectively penalize the tracking error this regulation is implemented through a risk sensitivity parameter a stability analysis based on lyapunov functions obtained by the backstepping technique proves that all the error variables are bounded in probability simultaneously for any given risk sensitivity parameter the system performance is regulated with respect to both a desired small average tracking error and low long term average cost in accordance to a risk sensitive cost criterion moreover the larger this parameter is the mean square tracking error becomes semiglobally uniformly ultimately bounded in a smaller area while a lower level of a long term average cost is achieved the effectiveness of the design approac

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

a 3 flip neighborhood local search for the set covering problem the set covering problem scp calls for a minimum cost family of subsets from n given subsets which together covers the entire ground set in this paper we propose a local search algorithm for scp which has the following three characteristics 1 the use of 3 flip neighborhood which is the set of solutions obtainable from the current solution by exchanging at most three subsets as the size of 3 flip neighborhood is o n3 the neighborhood search becomes expensive if implemented naively to overcome this we propose an efficient implementation that reduces the number of candidates in the neighborhood without sacrificing the solution quality 2 we allow the search to visit the infeasible region and incorporate the strategic oscillation technique realized by adaptive control of penalty weights 3 the size reduction of the problem by using the information from the lagrangian relaxation is incorporated which is indispensable for solving very large instances according to computational comparisons on benchmark instances with other existing heuristic algorithms for scp our algorithm performs quite effectively for various types of problems especially for very large scale instances

learning from neural control of nonlinear systems in normal form a deterministic learning theory was recently proposed which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of simple nonlinear systems in this paper we investigate deterministic learning from adaptive neural control anc of a class of nonlinear systems in normal form with unknown affine terms the existence of the unknown affine terms makes it difficult to achieve learning by using previous methods to overcome the difficulties firstly an extension of a recent result is presented on stability analysis of linear time varying ltv systems then with a state transformation the closed loop control system is transformed into a ltv form for which exponential stability can be guaranteed when a partial persistent excitation pe condition is satisfied accurate approximation of the closed loop control system dynamics is achieved in a local region along a recurrent orbit of closed loop signals consequently learning of control system dynamics i e closed loop identification from adaptive neural control of nonlinear systems with unknown affine terms is implemented

lagrangian relaxation via ballstep subgradient methods we exhibit useful properties of ballstep subgradient methods for convex optimization using level controls for estimating the optimal value augmented with simple averaging schemes they asymptotically find objective and constraint subgradients involved in optimality conditions when applied to lagrangian relaxation of convex programs they find both primal and dual solutions and have practicable stopping criteria up until now similar results have only been known for proximal bundle methods and for subgradient methods with divergent series stepsizes whose convergence can be slow encouraging numerical results are presented for large scale nonlinear multicommodity network flow problems

an linear programming based lower bound for the simple assembly line balancing problem the simple assembly line balancing problem is a classical integer programming problem in operations research a set of tasks each one being an indivisible amount of work requiring a number of time units must be assigned to workstations without exceeding the cycle time we present a new lower bound namely the lp relaxation of an integer programming formulation based on dantzig wolfe decomposition we propose a column generation algorithm to solve the formulation therefore we develop a branch and bound algorithm to exactly solve the pricing problem we assess the quality of the lower bound by comparing it with other lower bounds and the best known solution of the various instances from the literature computational results show that the lower bound is equal to the best known objective function value for the majority of the instances moreover the new lp based lower bound is able to prove optimality for an open problem c 2004 elsevier b v all rights reserved

an algorithm for set covering problem in this paper we present an algorithm for the set covering problem that combines problem reduction tests with dual ascent subgradient optimisation and linear programming computational results are presented for problems involving up to 400 rows and 4000 columns

a dynamic subgradient based branch and bound procedure for set covering we discuss a branch and bound algorithm for set covering whose centerpiece is a new integrated upper bounding lower bounding procedure called dynamic subgradient optimization dynsgrad this new procedure applied to a lagrangean dual at every node of the search tree combines the standard subgradient method with primal and dual heuristics that interact to change the lagrange multipliers and tighten the upper and lower bounds fix variables and periodically restate the lagrangean itself extensive computational testing is reported as a stand alone heuristic dynsgrad performs significantly better than other procedures in terms of the quality of solutions obtainable with a certain computational effort when incorporated into a branch and bound algorithm dynsgrad considerably advances the state of the art in solving set covering problems

learning from adaptive neural dynamic surface control of strict feedback systems learning plays an essential role in autonomous control systems however how to achieve learning in the nonstationary environment for nonlinear systems is a challenging problem in this paper we present learning method for a class of n th order strict feedback systems by adaptive dynamic surface control dsc technology which achieves the human like ability of learning by doing and doing with learned knowledge to achieve the learning this paper first proposes stable adaptive dsc with auxiliary first order filters which ensures the boundedness of all the signals in the closed loop system and the convergence of tracking errors in a finite time with the help of dsc the derivative of the filter output variable is used as the neural network nn input instead of traditional intermediate variables as a result the proposed adaptive dsc method reduces greatly the dimension of nn inputs especially for high order systems after the stable dsc design we decompose the stable closed loop system into a series of linear time varying perturbed subsystems using a recursive design the recurrent property of nn input variables is easily verified since the complexity is overcome using dsc subsequently the partial persistent excitation condition of the radial basis function nn is satisfied by combining a state transformation accurate approximations of the closed loop system dynamics are recursively achieved in a local region along recurrent orbits then the learning control method using the learned knowledge is proposed to achieve the closed loop stability and the improved control performance simulation studies are performed to demonstrate the proposed scheme can not only reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error but also greatly alleviate the computational burden because of reducing the number and complexity of nn input variables

an efficient local search heuristic with row weighting for the unicost set covering problem abstract the set covering problem scp is np hard we propose a new row weighting local search rwls algorithm for solving the unicost variant of the scp i e uscps where the costs of all sets are identical rwls is a heuristic algorithm that has three major components united in its local search framework 1 a weighting scheme which updates the weights of uncovered elements to prevent convergence to local optima 2 tabu strategies to avoid possible cycles during the search and 3 a timestamp method to break ties when prioritizing sets rwls has been evaluated on a large number of problem instances from the or library and compared with other approaches it is able to find all the best known solutions bks and improve 14 of them although requiring a higher computational effort on several instances rwls is especially effective on the combinatorial or library instances and can improve the best known solution to the hardest instance cyc11 considerably rwls is conceptually simple and has no instance dependent parameters which makes it a practical and easy to use uscp solver

an effective and simple heuristic for the set covering problem abstract this paper investigates the development of an effective heuristic to solve the set covering problem scp by applying the meta heuristic meta raps meta heuristic for randomized priority search in meta raps a feasible solution is generated by introducing random factors into a construction method then the feasible solutions can be improved by an improvement heuristic in addition to applying the basic meta raps the heuristic developed herein integrates the elements of randomizing the selection of priority rules penalizing the worst columns when the searching space is highly condensed and defining the core problem to speedup the algorithm this heuristic has been tested on 80 scp instances from the or library the sizes of the problems are up to 1000 rows 10 000 columns for non unicost scp and 28 160 rows 11 264 columns for the unicost scp this heuristic is only one of two known scp heuristics to find all optimal best known solutions for those non unicost instances in addition this heuristic is the best for unicost problems among the heuristics in terms of solution quality furthermore evolving from a simple greedy heuristic it is simple and easy to code this heuristic enriches the options of practitioners in the optimization area

analytical treatment of equilibrium configurations of cantilever under terminal loads using jacobi elliptical functions abstract the paper provides an exact analytical solution for the equilibrium configurations of a cantilever rod subject to inclined force and tip moment acting on its free end the solution is given in terms of jacobi s elliptical functions and illustrated by several numerical examples and several graphical presentations of shapes of deformed cantilevers possible forms of the underlying elastica of a cantilever are discussed in detail and various simple formulas are given for calculating the characteristic dimensions of the elastica for the case when a cantilever is subject only to applied force three load conditions are discussed the follower load problem the load determination problem and the conservative load problem for all cases either a formula or an effective procedure for determining the solution is provided in particular a new efficient procedure is given to determine all possible equilibrium shapes in the case of the conservative load problem