connected graph representations of the quantum propagator and semiclassical expansions the time evolution operator u t s of a spinless nonrelativistic n body quantum system in euclidean space with real analytic time dependent scalar interaction v x t is studied a complete formal asymptotic expansion involving simple connected graphs is derived for the full coordinate and mixed coordinate momentum representation propagators the derivation is based on dyson s series for u t s and the combinatorics involved in the cluster expansion of the classical grand partition function these results provide an efficient means of generating nonperturbative propagator expansions in the physical variables mass m planck s constant h time displacement t s the structural bridge between the wkb and wigner kirkwood expansions is sketched for mixed representations of u t s in the heat equation context the graphical expansions are found for mixed representations of the density operator e beta h finally an explicit differential formula is obtained for wigner s distribution function f x p beta

nonsmooth nonnegative matrix factorization nsnmf we propose a novel nonnegative matrix factorization model that aims at finding localized part based representations of nonnegative multivariate data items unlike the classical nonnegative matrix factorization nmf technique this new model denoted nonsmooth nonnegative matrix factorization nsnmf corresponds to the optimization of an unambiguous cost function designed to explicitly represent sparseness in the form of nonsmoothness which is controlled by a single parameter in general this method produces a set of basis and encoding vectors that are not only capable of representing the original data but they also extract highly focalized patterns which generally lend themselves to improved interpretability the properties of this new method are illustrated with several data sets comparisons to previously published methods show that the new nsnmf method has some advantages in keeping faithfulness to the data in the achieving a high degree of sparseness for both the estimated basis and the encoding vectors and in better interpretability of the factors

sliding mode control of linear systems with mismatched uncertainties abstract it is well known that sliding mode control is robust to matched uncertainties that lie in the range space of the input matrix however many systems are affected by mismatched uncertainties and yet do not enjoy the matching conditions it is the purpose of this paper to present a new dynamical approach of sliding variable formulation which when the system is in sliding mode can explicitly deal with mismatched uncertainties our first step is to treat certain states as inputs to a reduced order system and use adaptive techniques to design fictitious controllers for these inputs which can then tackle the mismatched uncertainties the second step is to use sliding control to realize the adaptive fictitious controllers the design is systematic modular and intuitively simple

nonlinear non negative component analysis algorithms in this paper general solutions for nonlinear non negative component analysis for data representation and recognition are proposed motivated by a combination of the non negative matrix factorization nmf algorithm and kernel theory which has lead to a recently proposed nmf algorithm in a polynomial feature space we propose a general framework where one can build a nonlinear non negative component analysis method using kernels the so called projected gradient kernel non negative matrix factorization pgknmf in the proposed approach arbitrary positive definite kernels can be adopted while at the same time it is ensured that the limit point of the procedure is a stationary point of the optimization problem moreover we propose fixed point algorithms for the special case of gaussian radial basis function rbf kernels we demonstrate the power of the proposed methods in face and facial expression recognition applications

tree graphs and the solution to the hamilton jacobi equation a combinatorial method is used to construct solutions of the hamilton jacobi equation an exact expression for hamilton s principal function s is obtained for classical systems of finitely many particles interacting via a certain class of time dependent potentials if x p and t are the position momentum and time variables for n point particles of mass m it is shown that hamiltonians of the form h x p t 1 2m p2 v x t have complete integrals s that are analytic functions of the inverse mass parameter m 1 in a punctured disk about the origin if v x t is bounded c in the x variable and has controlled x derivative growth then the coefficients of the laurent expansion of s about m 1 0 may be expressed in terms of gradient structures associated with tree graphs this series expansion for s x t y t0 converges absolutely and uniformly for all x y for time displacements t t0 t 2k 1 m eu 1 2 where k and u are bounds associated with the space derivatives of the potential for t t0 t the classi

an asymptotic analysis of quantum evolution with electromagnetic fields a singular perturbation expansion of solutions to the schrodinger initial value problem is constructed using an approximate propagator for a nonrelativistic quantum system interacting with time dependent external electromagnetic fields this approximate propagator defines a gauge invariant semiclassical expansion that is realized by large mass scaling the asymptotic nature of this approximation is established by constructing error estimates that bound the hilbert space norm difference between the exact and approximate evolved states the maximum order of the approximation is determined explicitly as a function of the number of derivatives supported by the scalar and vector potentials the asymptotic expansion is obtained when the configuration space rd and also for problems where is a proper subset of rd and the self adjoint hamiltonian is defined using a supplementary boundary condition typically dirichlet or periodic

design of a new fuzzy suction controller using fuzzy modeling for nonlinear boundary layer there are two types of fuzzy modeling 1 imitating an expert experiment or fulfilling an engineering knowledge and 2 modeling a complex or unknown system in this paper based on the first type of fuzzy modeling a new fuzzy suction controller nfsc is proposed using its linguistic rules to design nonlinear boundary layer two kinds of nonlinear boundary layers are discussed the first kind is designed by three rules derived according to a new interpretation of the switching conditions for a suction controller such that the new controller reduces chattering and spends less energy than a suction controller does a design procedure summarizes the nfsc design the second kind of nonlinear boundary layer is the linguistic rules designed to have sliding sectors to control a mobile robot for trajectory tracking the discussion emphasizes the advantage of nonlinear boundary layers compared with traditional suction controllers usually using linear boundary in addition the proposed nfsc provides a flexible way to adjust the controller functions using linguistic rules based on the first type of fuzzy modeling

a new and simple algorithm for sliding mode trajectory control of the robot arm a simple sliding mode trajectory control of the robot arm that needs no inverse of the inertia matrix is derived the assumptions underlying the derivation are outlined

a quantum wkb approximation without classical trajectories the time evolution of a coherent state is studied in the limit 0 for a spinless nonrelativistic quantum system in euclidean space with smooth bounded time dependent scalar interaction v x t the lowest order wkb approximation is derived rigorously complete with an explicit bound on its l2 norm error over a specified finite time interval the method is based on a constructive series representation of the classical action thereby avoiding the need to analyze the behavior of classical trajectories the amplitude of the initial states considered is neither assumed to be of rapid decrease nor to depend on

robust adaptive control of plants with unknown order and high frequency gain abstract an adaptive control scheme is presented which has a simple structure and guarantees global stability of the closed loop plant and asymptotic zero tracking error for a class of reference signals the plants to be controlled are of minimum phase and relative degree one no a priori knowledge for the order the parameters of the plant or the sign of the high frequency gain is required the number of adjustable control parameters is proportional to the number of frequencies in the reference signal and is independent of the order of the plant the proposed algorithm is then modified by using a variable structure for generating the control signal to guarantee robust stability of the closed loop plant and asymptotic zero tracking error in the presence of bounded disturbances and unmodeled dynamics

extracting non negative basis images using pixel dispersion penalty non negativity matrix factorization nmf and its variants have been explored in the last decade and are still attractive due to its ability of extracting non negative basis images however most existing nmf based methods are not ready for encoding higher order data information one reason is that they do not directly explicitly model structured data information during learning and therefore the extracted basis images may not completely describe the parts in an image 1 very well in order to solve this problem the structured sparse nmf has been recently proposed in order to learn structured basis images it however depends on some special prior knowledge i e one needs to exhaustively define a set of structured patterns in advance in this paper we wish to perform structured sparsity learning as automatically as possible to that end we propose a pixel dispersion penalty pdp which effectively describes the spatial dispersion of pixels in an image without using any manually predefined structured patterns as constraints in pdp we consider each part based feature pattern of an image as a cluster of non zero pixels that is the non zero pixels of a local pattern should be spatially close to each other furthermore by incorporating the proposed pdp we develop a spatial non negative matrix factorization spatial nmf and a spatial non negative component analysis spatial nca in spatial nca the non negativity constraint is only imposed on basis images and such constraint on coefficients is released so both subtractive and additive combinations of non negative basis images are allowed for reconstructing any images extensive experiments are conducted to validate the effectiveness of the proposed pixel dispersion penalty we also experimentally show that spatial nca is more flexible for extracting non negative basis images and obtains better and more stable performance

on the wkb approximation to the propagator for arbitrary hamiltonians this paper presents a general expression for the wkb approximation to the propagator corresponding to an arbitrary hamiltonian operator h for example if the correspondence rule used to pass from the classical hamiltonian hc to h is such that it associates apiq j 1 a q jpi to piq j then the formula gives kwkb kvvexp 1 2 a ft 2hc qi pi qc t pc t t dt where kvv 2 ih n 2 det m 1 2exp isc h is van vleck s well known formula sc being the action functional evaluated at the classical path qc pc and mij 2sc qa i qbj more generally the formula presented here applies to any system with n degrees of freedom described by a function f x t whose time evolution is given by h x k x t k t f x t 0 regardless of the form of h the schrodinger equation of quantum mechanics and the fokker planck equation of diffusion are obvious examples many examples are discussed this generalizes results obtained in a previous publication j math phys 18 786 90 1977

on the validity of the wkb approximation we consider the wkb approximation to the non relativistic schrodinger equation for an n particle system with a possibly time dependent potential a recent rigorous and explicit error estimate given by molzahn 1988 is investigated by means of examples to this end we extend the class of potentials considered by molzahn and find that his estimates are almost optimal however these examples also reveal an inherent drawback of the wkb method

a unifying design of sliding mode and classical controllers a theory is given to unify output sliding mode control and classical control the idea is based on defining the sliding variable in such a way that once the system begins to slide the classical controller transfer function is realized this idea leads to the development of a hybrid sliding and classical controller which retains the merits of both types of controllers but eliminates their respective limitations the proposed method is robust and applies to non minimum phase single input single output siso systems no state measurement is required

a performance approach to fuzzy control design for nonlinear systems abstract this paper presents a systematic methodology to the design of a decentralized fuzzy logic controller for large scale nonlinear systems a new method which is based on a performance index of sliding mode control is used to derive fuzzy rules and an adaptive algorithm is used to reduce the chattering phenomenon the simulation results of a two inverted pendulum system and a two link manipulator demonstrate that the attractive features of the proposed approach include a smaller residual error and robustness against nonlinear interactions

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

disturbance observer based sliding mode control for t s fuzzy discrete time systems with application to circuit system abstract in this paper the problem of disturbance observer based sliding mode control smc is studied for a class of takagi sugeno t s fuzzy discrete time systems subject to dead zone input and external disturbance the disturbance is monitored by a disturbance observer do then a do based sliding mode controller is derived by selecting the suitable gain matrices the do can approximate the external disturbance effectively and the stability of the system can be guaranteed finally the validity of the proposed smc scheme is verified with the simulation results of the tunnel diode circuit system

variable structure control of robot manipulators with nonlinear sliding manifolds performance characteristics of a sliding mode controller depend essentially on a selected sliding manifold customarily the variable structure controllers operate with linear sliding surfaces however using nonlinear or time varying manifolds may provide definite advantages in particular they may provide faster convergence in this paper a control algorithm is presented which guarantees the occurrence of the sliding mode on nonlinear or time varying manifolds the bounds needed for calculating the switching gains are determined in terms of parameter variations rather than bounds on the system matrices the parameter bounds are usually evident and can be easily established or estimated while matrix bounds can rarely be justified in practical problems in this paper we also present an adaptive version of the controller which provides an automatic estimation of the parameter bounds the robustness of the controller with respect to a class of state dependent uncertainties is analysed by the lyapunov m

error estimates for approximate solutions of the riccati equation with real or complex potentials a method is presented for obtaining rigorous error estimates for approximate solutions of the riccati equation with real or complex potentials our main tool is to derive invariant region estimates for complex solutions of the riccati equation we explain the general strategy for applying these estimates and illustrate the method in typical examples where the approximate solutions are obtained by gluing together wkb and airy solutions of corresponding one dimensional schrodinger equations our method is motivated by and has applications to the analysis of linear wave equations in the geometry of a rotating black hole

a new controller design for manipulators using the theory of variable structure systems a controller design for manipulators using the theory of variable structure systems vss is presented to deal with the set point regulation problem the major obstacle of vss vector control with strong dynamic coupling is overcome for a class of systems with positive symmetric inertia matrices parameter variations can easily be considered in the design methodology which is readily extendable to a higher number of links the problem of chattering is solved by the introduction of sliding sectors

exponential cluster solutions to quantum transport equations connected graph methods are used to solve the transport equation arising in a semiclassical representation of the schrodinger propagator k t s x y for a spinless quantum system whose hamiltonian is a smooth position and momentum dependent perturbation of the laplacian in rd exponential cluster expansions for k are obtained these formally exact solutions to the time dependent schrodinger equation employ explicit graphically determined derivatives of the hamiltonian s symbol integrated along geodesics for the special case of particles interacting with external electromagnetic fields the propagator s gauge invariant derivative expansion coefficients are determined in closed form in terms of the lorentz force a tree graph formula for hamilton s principal function is extracted from this result

robust trajectory following of robots using computed torque structure with vss a control approach is proposed for robust accurate trajectory tracking of manipulators based on the computed torque technique and variable structure systems vss theory the computed torque structure of the control scheme most importantly provides greater insight to the control of manipulators and serves as a unifying framework for control law development looking at the control structure from a computed torque perspective also enables the extension of the technique from joint space to direct end effector control of both non redundant and redundant robots in task or operational space the technique perhaps may be further augmented to incorporate force control to achieve hybrid force position control the use of sliding modes in the control scheme in its idealized form ensures accurate tracking while achieving insensitivity to parameter variations uncertainties and bounded disturbances in the development of the control laws some useful properties of the robot dynamics viz positive definiteness