multidimensional gains for stochastic approximation this paper deals with iterative jacobian based recursion technique for the root finding problem of the vector valued function whose evaluations are contaminated by noise instead of a scalar step size we use an iterate dependent matrix gain to effectively weigh the different elements associated with the noisy observations the analytical development of the matrix gain is built on an iterative dependent linear function interfered by additive zero mean white noise where the dimension of the function is m ge 1 and the dimension of the unknown variable is n ge 1 necessary and sufficient conditions for m ge n algorithms are presented pertaining to algorithm stability and convergence of the estimate error covariance matrix two algorithms are proposed one for the case where m ge n and the second one for the antithesis the two algorithms assume full knowledge of the jacobian the recursive algorithms are proposed for generating the optimal iterative dependent matrix gain the proposed algorithms here aim for per iteration minimization of the mean square estimate error we show that the proposed algorithm satisfies the presented conditions for stability and convergence of the covariance in addition the convergence rate of the estimation error covariance is shown to be inversely proportional to the number of iterations for the antithesis m contraction of the error covariance is guaranteed this underdetermined system of equations can be helpful in training neural networks numerical examples are presented to illustrate the performance capabilities of the proposed multidimensional gain while considering nonlinear functions

branching in branch and price a generic scheme developing a branching scheme that is compatible with the column generation procedure can be challenging application specific and generic schemes have been proposed in the literature but they have their drawbacks one generic scheme is to implement standard branching in the space of the compact formulation to which the dantzig wolfe reformulation was applied however in the presence of multiple identical subsystems the mapping to the original variable space typically induces symmetries an alternative in an application specific context can be to expand the compact formulation to offer a wider choice of branching variables other existing generic schemes for use in branch and price imply modifications to the pricing problem this is a concern because the pricing oracle on which the method relies might become obsolete beyond the root node this paper presents a generic branching scheme in which the pricing oracle of the root node remains of use after branching assuming that the pricing oracle can handle bounds on the subproblem variables the scheme does not require the use of an extended formulation of the original problem it proceeds by recursively partitioning the subproblem solution set branching constraints are enforced in the pricing problem instead of being dualized via lagrangian relaxation and the pricing problem is solved by a limited number of calls to the pricing oracle this generic scheme builds on previously proposed approaches and unifies them we illustrate its use on the cutting stock and bin packing problems this is the first branch and price algorithm capable of solving such problems to integrality without modifying the subproblem or expanding its variable space

output feedback control based on a high order sliding manifold approach in this note we address the problem of output feedback control of multiple input multiple output plants the proposed approach is based on a high order sliding manifold strategy the resulting controller exhibits strong robustness properties similar to high gain control laws but avoids peaking phenomena thanks to the adoption of a time varying sliding surface moreover the dynamic control law is continuous and differentiable thus avoiding chattering problems

a survey on iterative learning control for nonlinear systems in this article we review the recent advances in iterative learning control ilc for nonlinear dynamic systems in the research field of ilc two categories of system nonlinearities are considered namely the global lipschitz continuous glc functions and local lipschitz continuous llc functions ilc for glc systems is widely studied and analysed using contraction mapping approach and the focus of recent exploration moves to application problems though a number of theoretical issues remain open ilc for llc systems is currently a hot area and the recent research focuses on ilc design and analysis by means of lyapunov approach the objectives of this article are to introduce recent development and advances in nonlinear ilc schemes highlight their effectiveness and limitations as well as discuss the directions for further exploration of nonlinear ilc

adaptive iterative learning control for linear systems with binary valued observations this brief presents a novel adaptive iterative learning control ilc algorithm for a class of single parameter systems with binary valued observations using the certainty equivalence principle the adaptive ilc algorithm is designed by employing a projection identification algorithm along the iteration axis it is shown that even though the available system information is very limited and the desired trajectory is iteration varying the proposed adaptive ilc algorithm can guarantee the convergence of parameter estimation over a finite time interval along the iterative axis meanwhile the tracking error is pointwise convergence asymptotically two examples are given to validate the effectiveness of the algorithm

classification of dantzig wolfe reformulations for binary mixed integer programming problems abstract in this note we provide a classification of dantzig wolfe reformulations for binary mixed integer programming problems we specifically focus on modeling the binary conditions in the convexification approach to the dantzig wolfe decomposition for a general binary mixed integer programming problem an extreme point of the overall problem does not necessarily correspond to an extreme point of the subproblem therefore the binary conditions cannot in general be imposed on the new master problem variables but must be imposed on the original binary variables in some cases however it is possible to impose the binary restrictions directly on the new master problem variables the issue of imposing binary conditions on the original variables versus the master problem variables has not been discussed systematically for mip problems in general in the literature and most of the research has been focused on the pure binary case the classification indicates in which cases you can and cannot impose binary conditions on the new master problem variables

design of a fuzzy controller with fuzzy sliding surface abstract fuzzy logic controllers have succeeded in many control problems that the conventional control theories have difficulties to deal with however the design of the fuzzy logic controllers depends to a large extent on the expert s knowledge or on trial and error moreover due to the linguistic expression of the fuzzy controller it has not been easy to guarantee the stability and robustness of the fuzzy control systems to overcome these drawbacks we propose to design a fuzzy controller with the fuzzy sliding surface the fuzzy rules are defined based on this fuzzy sliding surface and the output of the fuzzy controller is inferred by the proper compositional rule of inference then we show the stability of this fuzzy control system and the boundedness of the tracking error by using the lyapunov theory finally we apply this fuzzy controller to control a nonlinear time varying system and confirm the validity of the controller

iterative learning control based on extremum seeking this paper proposes a non model based approach to iterative learning control ilc via extremum seeking single input single output discrete time nonlinear systems are considered where the objective is to recursively construct an input such that the corresponding system output tracks a prescribed reference trajectory as closely as possible on finite horizon the problem is formulated in terms of extremum seeking control which is amenable to a range of local and global optimisation methods contrary to the existing ilc literature the formulation allows the initial condition of each iteration to be incorporated as an optimisation variable to improve tracking sufficient conditions for convergence to the reference trajectory are provided the main feature of this approach is that it does not rely on knowledge about the system s model to perform iterative learning control in contrast to most results in the literature

convergence analysis of saturated iterative learning control systems with locally lipschitz nonlinearities in this article the robust trajectory tracking problem of iterative learning control ilc for uncertain nonlinear systems is considered and the effects from locally lipschitz nonlinearities input saturations and nonzero system relative degrees are treated a saturated ilc algorithm is given with the convergence analysis exploited using a composite energy function based approach it is shown that the tracking error can be guaranteed to converge both pointwisely and uniformly furthermore the input updating signal can be ensured to eventually satisfy the input saturation requirements with increasing iterations two examples are given to demonstrate the validity of saturated ilc for systems with the relative degree of one input saturation and locally lipschitz nonlinearity

selected topics in column generation dantzig wolfe decomposition and column generation devised for linear programs is a success story in large scale integer programming we outline and relate the approaches and survey mainly recent contributions not yet found in textbooks we emphasize the growing understanding of the dual point of view which has brought considerable progress to the column generation theory and practice it stimulated careful initializations sophisticated solution techniques for the restricted master problem and subproblem as well as better overall performance thus the dual perspective is an ever recurring concept in our selected topics

a column generation approach to the multiple depot vehicle scheduling problem we give a new formulation to the multiple depot vehicle scheduling problem as a set partitioning problem with side constraints whose continuous relaxation is amenable to be solved by column generation we show that the continuous relaxation of the set partitioning formulation provides a much tighter lower bound than the additive bound procedure previously applied to this problem we also establish that the additive bound technique cannot provide tighter bounds than those obtained by lagrangian decomposition in the framework in which it has been used so far computational results that illustrate the robustness of the combined set partitioning column generation approach are reported for problems four to five times larger than the largest problems that have been exactly solved in the literature finally we show that the gap associated with the additive bound based on the assignment and shortest path relaxations can be arbitrarily bad in the general case and as bad as 50 in the symmetric case

a barbalat like lemma with its application to learning control this paper presents the convergence property for a sequence of functions over a finite interval of time which square integral has a zero limit it is proven that if such a sequence of functions is equicontinuous the sequence itself will converge uniformly to zero over the entire interval for illustration purposes this result is applied and its usefulness shown in learning control systems analysis

computational study of a column generation algorithm for bin packing and cutting stock problems this paper reports on our attempt to design an efficient exact algorithm based on column generation for the cutting stock problem the main focus of the research is to study the extend to which standard branch and bound enhancement features such as variable fixing the tightening of the formulation with cutting planes early branching and rounding heuristics can be usefully incorporated in a branch and price algorithm we review and compare lower bounds for the cutting stock problem we propose a pseudo polynomial heuristic we discuss the implementation of the important features of the integer programming column generation algorithm and in particular the implementation of the branching scheme our computational results demonstrate the efficiency of the resulting algorithm for various classes of bin packing and cutting stock problems

adaptive boundary iterative learning control for an euler bernoulli beam system with input constraint this paper addresses the vibration control and the input constraint for an euler bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint a restrained adaptive boundary iterative learning control abilc law is proposed based on a time weighted lyapunov krasovskii like composite energy function in order to deal with the uncertainty of a system parameter and reject the external disturbances three adaptive laws are designed and learned in the iteration domain all the system states of the closed loop system are proved to be bounded in each iteration along the iteration axis the displacements asymptotically converge toward zero simulation results are provided to illustrate the effectiveness of the proposed abilc scheme

exponential stability of nonlinear differential repetitive processes with applications to iterative learning control abstract this paper studies exponential stability properties of a class of two dimensional 2d systems called differential repetitive processes drps since a distinguishing feature of drps is that the problem domain is bounded in the time direction the notion of stability to be evaluated does not require the nonlinear system defining a drp to be stable in the typical sense in particular we study a notion of exponential stability along the discrete iteration dimension of the 2d dynamics which requires the boundary data for the differential pass dynamics to converge to zero as the iterations evolve our main contribution is to show under standard regularity assumptions that exponential stability of a drp is equivalent to that of its linearized dynamics in turn exponential stability of this linearization can be readily verified by a spectral radius condition the application of this result to iterative learning control ilc is discussed theoretical findings are supported by a numerical simulation of an ilc algorithm

robust cooperative learning control for directed networks with nonlinear dynamics this paper studies a class of robust cooperative learning control problems for directed networks of agents a with nonidentical nonlinear dynamics that do not satisfy a global lipschitz condition and b in the presence of switching topologies initial state shifts and external disturbances all uncertainties are not only time varying but also iteration varying it is shown that the relative formation of nonlinear agents achieved via cooperative learning can be guaranteed to converge to the desired formation exponentially fast as the number of iterations increases a necessary and sufficient condition for exponential convergence of the cooperative learning process is that at each time step the network topology graph of nonlinear agents can be rendered quasi strongly connected through switching along the iteration axis simulation tests illustrate the effectiveness of our proposed cooperative learning results in refining arbitrary high precision relative formation of nonlinear agents

a unified adaptive iterative learning control framework for uncertain nonlinear systems in this note we propose a unified framework for adaptive iterative learning control design for uncertain nonlinear systems it is shown that if a lyapunov based adaptive control law is available for the system under consideration and the lyapunov function satisfies certain conditions it is straightforward to extend the adaptive controller to handle repetitive systems operating over a finite time interval according to the value of a certain parameter the parametric adaptation law can be a pure time domain adaptation a pure iteration domain adaptation or a combination of both a pure iteration domain adaptation is described by a difference equation a pure time domain adaptation is described by a differential equation and a combination of both is described by a differential difference equation the advantages and disadvantages of the three possible adaptation types are discussed and some illustrative examples are given

high order fuzzy sliding manifold control the design of high order sliding fuzzy control strategies is addressed and carried out by using rigorous mathematical tools of the singular perturbation theory the resulting fuzzy controller implements an output feedback to solve output tracking problems and has the double benefit to be robust and low order namely the controller order is the plant relative degree simulations are presented to show the effectiveness of the proposed strategy

robust fuzzy control of mechanical systems this paper considers the problem of controlling a mechanical system described by euler lagrange equations to follow a desired trajectory in the presence of uncertainties a fuzzy logic system fls is used to approximate the unknown dynamics of the system based on the a priori information the premise part of the fls as well as a nominal weight matrix are designed first and are fixed a compensation signal to the weight matrix error is designed based on lyapunov analysis to further reduce the tracking error due to the function reconstruction error a second compensation signal is also synthesized by running two estimators online for weight matrix error bound and function reconstruction error bound the implementation of the proposed controller needs no a priori information on these bounds exponential tracking to a desired trajectory up to a uniformly ultimately bounded error is achieved with the proposed control the effectiveness of this control is demonstrated through simulation and experiment results these results also show that by incorporating a priori informations about the system the fuzzy logic control can result good tracking behavior using a few fuzzy if then rules

new formulation for representing higher order tsk fuzzy systems this paper introduces a recursive relation between an existing takagi sugeno kang tsk fuzzy system of order n and systems of order n 1 and 0 the presented method helps to realize higher order tsk fuzzy systems using first and zero order tsk fuzzy system models which are available in simulation software e g matlab and its toolboxes this method has two major benefits 1 easier and faster simulation of higher order tsk systems using available software and 2 possibility of tuning high order tsk systems by methods like anfis which can only tune first and zero order tsk systems the final section of this paper includes a comparison of simulation speed if the proposed method is used or not and nonlinear function estimation by applying anfis on high order tsk system using the proposed method simulation results prove the superiority and usefulness of the proposed method

neural ailc for error tracking against arbitrary initial shifts this paper concerns with the adaptive iterative learning control using neural networks for systems performing repetitive tasks over a finite time interval two standing issues of such iterative learning control processes are addressed one is the initial condition problem and the other is that related to the approximation error instead of the state tracking an error tracking approach is proposed to tackle the problem arising from arbitrary initial shifts the desired error trajectory is prespecified at the design stage suitable to different tracking tasks the initial value of the desired error trajectory for each cycle is required to be the same as that of the actual error trajectory it is just a requirement for the initial value of the desired error trajectory but does not pose any requirement for the initial value of the actual error trajectory it is shown that the actual error trajectory is adjustable and is able to converge to a prespecified neighborhood of the origin while all variables of the closed loop system are of uniform boundedness the robustness improvement in case of nonzero approximation error is made possible due to the use of a deadzone modified lyapunov functional the resultant estimation for the bound of the approximation error avoids deterioration in tracking performance the effectiveness of the designed learning controller is validated through an illustrative example

min cut clustering we describe a decomposition framework and a column generation scheme for solving a min cut clustering problem the subproblem to generate additional columns is itself an np hard mixed integer programming problem we discuss strong valid inequalities for the subproblem and describe some efficient solution strategies computational results on compiler construction problems are reported

realization of pid controls by fuzzy control methods abstract this paper shows that pid controllers can be realized by fuzzy control methods of product sum gravity method and simplified fuzzy reasoning method pid controllers however cannot be constructed by min max gravity method known as mamdani s fuzzy reasoning method furthermore extrapolative reasoning can be executed by the product sum gravity method and simplified fuzzy reasoning method by extending membership functions of antecedent parts of fuzzy rules

output tracking control of mimo fuzzy nonlinear systems using variable structure control approach the output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied our approach is based on the takagi sugeno t s fuzzy modeling method and a variable structure control vsc technique therefore the systems considered are not and need not be in the triangular and parametric strict feedback form which are prevalent among adaptive model following control for nonlinear systems or in the normal form which pervades almost all existing results in neuro fuzzy model following control approach we first study the problem of stabilization of t s fuzzy systems by using a vsc technique a method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed then the method is extended to design controllers for output tracking of t s fuzzy nonlinear systems in two cases i e systems which possess the so called strong passive subsystems and strong stable zero dynamics respectively finally illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers simulation results show that the goal of output tracking can be achieved by the proposed controllers

a new sliding mode control with fuzzy boundary layer this study develops a sliding mode controller based on fuzzy variable boundary layer with a control gain and boundary layer thickness as design parameters the control gain is an important factor affecting the control performance of variable structure system vss sliding mode controllers based on a variable boundary layer are superior to the fixed layer method for tracking in order to regulate the design parameters and increase operating efficiency the proposed methodologies make use of fuzzy inference which reduces the number of fuzzy inputs by using fuzzy algorithms in choosing a control gain and boundary layer we propose methods which have better tracking performance than the conventional method finally the results of simulation are given to demonstrate the validity of this algorithm

a composite energy function based learning control approach for nonlinear systems with time varying parametric uncertainties a new learning control approach is developed in this note to address a class of nonlinear systems with time varying parametric uncertainties the concept of composite energy function cef which provides the system information along both time and learning repetition horizons is introduced in the analysis of learning control cef consists of two parts the first part is a standard lyapunov function which is used to access system behavior along time horizon during each learning cycle the second part is an l sup 2 norm of parametric learning errors which reflects the variation of the system status when the control system is updated on the basis of learning cycles the proposed learning control algorithm achieves asymptotical convergence along a learning repetition horizon at the same time the boundedness and pointwise convergence of the tracking error along time horizon is guaranteed the proposed learning control strategy is applicable to quite general classes of nonlinear systems without requiring the global lipschitz continuity condition and zero relative degree condition

robust fuzzy logic control of mechanical systems an approach for the design of fuzzy control laws for tracking control of a large class of mechanical systems is proposed the approach employs the framework of lyapunov s stability theory to formulate a class of control laws that guarantee convergence of the tracking errors to within specification limits in presence of bounded parameter uncertainties and input disturbances the proposed control laws possess a large number of parameters and functional relationships to be chosen by the designer according to a methodology developed in the paper the large number of design degrees of freedom makes the approach suitable for fuzzy logic implementation a number of fuzzy implementations of the proposed control methodology are provided all implementations guarantee tracking error convergence to within prespecified performance limits an extensive simulation study using a model of a two degree of freedom robot manipulator was conducted fuzzy and non fuzzy implementations of the proposed methodology were compared to control laws designed using other design methods simulation study results indicate a superiority of the proposed control methodology compared to other approaches the study also demonstrates better performance of the fuzzy control implementation compared to its non fuzzy counterpart

a comparison of heuristics and relaxations for the capacitated plant location problem abstract approaches proposed in the literature for the capacitated plant location problem are compared the comparison is based on new theoretical and computational results the main emphasis is on relaxations in particular dominance relations among the various relaxations found in the literature are identified in the computational study the relaxations are compared as a function of various characteristics of the test problems several of these relaxations can be used to generate heuristic feasible solutions that are better than the classical greedy or interchange heuristics both in computing time and in the quality of the solutions found