universal neural network control of mimo uncertain nonlinear systems in this brief a continuous tracking control law is proposed for a class of high order multi input multi output uncertain nonlinear dynamic systems with external disturbance and unknown varying control direction matrix the proposed controller consists of high gain feedback nussbaum gain matrix selector online approximator ola model and a robust term the ola model is represented by a two layer neural network the continuousness of the control signal is guaranteed to relax the requirement for the actuator bandwidth and avoid the incurred chattering effect asymptotic tracking performance is achieved theoretically by standard lyapunov analysis the control feasibility is also verified in simulation environment

the stationary arrival process of independent diffusers from a continuum to an absorbing boundary is poissonian we consider the arrival process of infinitely many identical independent diffusion processes from an infinite bath to an absorbing boundary previous results on this problem were confined to independent brownian particles arriving at an absorbing sphere the present paper extends these results to general diffusion processes without any symmetries and without resorting to explicit expressions for solutions to the relevant equations it is shown that for general absorbing boundaries and force fields the steady stream of arrivals is poissonian with rate equal to the total flux on the absorbing boundary as calculated from the continuum theory of diffusion with transport the considered arrival problem arises in the theory of langevin simulations of ions in electrolytic solutions in a langevin simulation ions enter and exit the simulation region and it is necessary to compute the probability laws for their entrance times into the simulation while the simulated ions inside the small simulation region inte

approximate eigensolutions for arbitrarily damped nearly proportional systems two efficient methods for determining the approximate eigenvalues and eigenvectors for arbitrarily damped nearly proportional systems are developed both approaches are formulated by means of a first order perturbation technique whereby the real modes of vibration of the undamped system are used to derive approximate expressions for the complex eigenvalues and eigenvectors of a nearly proportionally damped system using either approach the unperturbed configuration corresponds to a damped one whose damping matrix can be diagonalized by the same transformation that uncouples the undamped system and the perturbation consists of the deviation of this diagonalizable damping matrix from the actual damping matrix the proposed approaches are easy to code implement and solve and do not require forming state equations numerical examples are presented to validate the effectiveness of the current methods

particularities of newton s method in space frame force determination utilising eigenpair functions abstract redundant space frame dynamics are modelled through the structural eigenproblem which is formulated to account for the geometric stiffness due to self equilibrating membrane forces the resulting mathematical eigenvalues and eigenvectors respectively indicative of natural frequencies and modes of oscillation are then assumed to be continuous functions of a scalar factor upon a normalised set of forces in equilibrium newton s method or sensitivity analysis provides a means for minimising the difference between mathematical and physically observed eigenvalues whereupon the axial forces are inferred from the model issues of convergence and root uniqueness are anticipated eigenvalue coalescence in which eigenvalues transitorily coalesce to permute their arbitrarily numerical ordering is seen to define non smooth eigenvalue functions and hence encumber newton s method mode tracing strategies to overcome this are discussed the existence of various degrees of eigenvalue degeneracy owing to frame cyclic symmetry or otherwise is anticipated in terms of the influence upon newton s method if the degree of frame static redundancy is greater than one and there exist a number of linearly independent force distributions then the required force determination is a multidimensional newton method problems encountered in these manifold dimensions including those arising from frame spatial periodicity and the adversity of newton s method are overcome emphasis is placed upon minimising the dimensionality of newton s method through enforcement of equilibrium constraints illustrative numerical simulations are given and some applications of the method are proposed

second order sensitivity analysis in vibration and buckling problems a perturbation approach for the first and second order sensitivity analysis of eigenvalue problems as they arise in buckling and vibration of structural systems is presented a particular feature introduced in the formulation is the dependence of all matrices that model the problem not only on the design parameter but also on a pre critical state thus the sensitivity of the response of the fundamental path in buckling problems or a pre stressed state in vibration problems are introduced in the analysis two techniques are considered in this work the direct and the adjoint methods first and second order sensitivity equations for eigenvalues and eigenvectors are obtained and it is shown that second order sensitivity of an eigenvalue can be accomplished by using only one adjoint problem

adaptive neural network tracking control of mimo nonlinear systems with unknown dead zones and control directions in this paper adaptive neural network nn tracking control is investigated for a class of uncertain multiple input multiple output mimo nonlinear systems in triangular control structure with unknown nonsymmetric dead zones and control directions 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 it is shown that the dead zone output can be represented as a simple linear system with a static time varying gain and bounded disturbance by introducing characteristic function by utilizing the integral type lyapunov function and introducing an adaptive compensation term for the upper bound of the optimal approximation error and the dead zone disturbance the closed loop control system is proved to be semiglobally uniformly ultimately bounded with tracking errors converging to zero under the condition that the slopes of unknown dead zones are equal simulation results demonstrate the effectiveness of the approach

universal repetitive learning control for nonparametric uncertainty and unknown state dependent control direction matrix we propose a continuous universal repetitive learning control to track periodic trajectory for a class of nonlinear dynamical systems with nonparametric uncertainty and unknown state dependent control direction matrix the proposed controller is an integration of high gain feedback repetitive learning and nussbaum gain matrix selector the control signal is always continuous thus it avoids the potential chattering effect caused by discontinuity asymptotic convergence of the tracking error is achieved by the controller and the control performance is illustrated by simulation although the proposed method is derived for input state systems it can be readily extended to multi input multi output systems under appropriate assumption

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

multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology abstract the main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano to micrometers few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets such as buffers or active sites bridging the small and large spatial scales is achieved by rare events representing brownian particles finding small targets and characterized by long time distribution these rare events are the bottleneck of numerical simulations a naive stochastic simulation requires running many brownian particles together which is computationally greedy and inefficient solving the associated partial differential equations is also difficult due to the time dependent boundary conditions narrow passages and mixed boundary conditions at small windows we present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains the first approach is based on a markov mass action law equations coupled to a markov chain the second is a gillespie s method based on the narrow escape theory for coarse graining the geometry of the domain into poissonian rates the main application concerns diffusion in cellular biology where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release

comparison of several methods for calculating vibration mode shape derivatives four methods for the calculation of derivatives of vibration mode shapes eigenvectors with respect to design parameters are described these are finite difference method modal method a modified modal method and nelson s method the methods are implemented in a general purpose commercial finite element program and applied to the following test problems a cantilever beam and a stiffened cylinder with a cutout design variables are a beam tip mass a beam root height and specific dimensions of the cylinder model the methods are compared on the basis of central processor cp seconds required to obtain the derivatives and two of the methods are also evaluated for the rapidity of convergence data is presented showing the amount of cp time used to compute the first four eigenvector derivatives for each example problem a scalar measure of the error in the mode shape derivative is defined and numerical results illustrating the rapidity of convergence of the approximate derivative to the exact derivative are presented results indicate an advantage in using nelson s method because this method is exact and requires less cp time especially when derivatives with respect to several design variables are computed

passive vibration suppression of flexible space structures via optimal geometric redesign acomputationalframework is presented for the design of large flexible space structures with nonperiodicgeometries to achieve passive vibration suppression the present system combines an approximationmodel management framework ammf developed for evolutionary optimization algorithms eas with reduced basis approximate dynamic reanalysis techniques a coevolutionary genetic search strategy is employed to ensure that design changes during the optimization iterations lead to low rank perturbations of the structural system matrices for which thereduced basis methods give high quality approximations the k means algorithm is employed for cluster analysis of the population of designs to determine design points at which exact analysis should be carried out the fitness of the designs in an ea generation is then approximated using reduced basis models constructed around the points where exact analysis is carried out results are presented for the optimal design of a two dimensional cantilevered space structure to achieve passive vibration suppression it is shown that significant vibration isolation of the order of 50 db over a 100 hz bandwidth can be achieved further it is demonstrated that the ammf can potentially arrive at a better design compared to conventional approaches when a constraint is imposed on the computational budget available for optimization

adaptive dynamic output feedback neural network control of uncertain mimo nonlinear systems with prescribed performance an adaptive dynamic output feedback neural network controller for a class of multi input multi output affine in the control uncertain nonlinear systems is designed capable of guaranteeing prescribed performance bounds on the system s output as well as boundedness of all other closed loop signals it is proved that simply guaranteeing a boundedness property for the states of a specifically defined augmented closed loop system is necessary and sufficient to solve the problem under consideration the proposed dynamic controller is of switching type however its continuity is guaranteed thus alleviating any issues related to the existence and uniqueness of solutions simulations on a planar two link articulated manipulator illustrate the approach

mode tracking issues in structural optimization within the context of optimization of the structural dynamics properties of finite element models methodology is developed for the tracking of eigenpairs through changes in the structural eigenvalue problem the goal is to eliminate difficulties caused by mode switching i e frequency crossing out of several candidate methods two methods for mode tracking are successful the first method the higher order eigenpair perturbation algorithm is based on a perturbation expansion of the eigenproblem it iteratively computes changes in the eigenpairs due to parameter perturbations with the important feature of maintaining the correspondence between the baseline and perturbed eigenpairs the second method is a cross orthogonality check method which uses mass orthogonality to reestablish correspondence after a standard reanalysis modified eigenpair extraction routines lanczos subspace iteration inverse power were unsuccessful in tracking modes applications of mode tracking technology that are presented are frequency constrained optimization and optimization with mode shape constraints each application procedure is outlined and examples are given recommendations are made based on method efficiency and robustness in the example problems

reinforcement learning design based adaptive tracking control with less learning parameters for nonlinear discrete time mimo systems based on the neural network nn approximator an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output mimo nonlinear discrete time systems with unknown functions and disturbances in the design procedure two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function an optimal control signal and adaptation laws can be generated based on two nns in the previous approaches the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design consequently compared with the existing results the main contributions of this paper are 1 only two parameters are needed to be adjusted and thus the number of the adaptation laws is smaller than the previous results and 2 the updating parameters do not depend on the number of the subsystems for mimo systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks it is proven that the tracking errors the adaptation laws and the control inputs are uniformly bounded using lyapunov analysis method the simulation examples are employed to illustrate the effectiveness of the proposed algorithm

higher order eigenpair perturbations a matrix method is presented for the exact calculation of large eigenpair perturbations arising from design variable changes this method of forward analysis is presented that takes into account all order of the perturbation expansion

high gain adaptive stabilization of multivariable linear systems revisited abstract we consider the class of multi input multi output finite dimensional state space systems of the form x ax bu y cx where the state dimension is unknown the system is minumum phase and it is known that det cb 0 for this class a universal adaptive high gain controller not based on identification or estimation algorithms is presented which ensures exponential decay of the motion of the closed loop system it is shown that the controller is robust with respect to certain nonlinear perturbations

robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities in this paper robust adaptive neural network nn control is investigated for a general class of uncertain multiple input multiple output mimo nonlinear systems with unknown control coefficient matrices and input nonlinearities for nonsymmetric input nonlinearities of saturation and deadzone variable structure control vsc in combination with backstepping and lyapunov synthesis is proposed for adaptive nn control design with guaranteed stability in the proposed adaptive nn control the usual assumption on nonsingularity of nn approximation for unknown control coefficient matrices and boundary assumption between nn approximation error and control input have been eliminated command filters are presented to implement physical constraints on the virtual control laws then the tedious analytic computations of time derivatives of virtual control laws are canceled it is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed loop system finally simulation results are presented to illustrate the effectiveness of the proposed adaptive nn control

an approximate solution scheme for the algebraic random eigenvalue problem a reduced basis formulation is presented for the efficient solution of large scale algebraic random eigenvalue problems this formulation aims to improve the accuracy of the first order perturbation method and also allow the efficient computation of higher order statistical moments of the eigenparameters in the present method the two terms of the first order perturbation approximation for the eigenvector are used as basis vectors for ritz analysis of the governing random eigenvalue problem this leads to a sequence of reduced order random eigenvalue problems to be solved for each eigenmode of interest since only two basis vectors are used to represent each eigenvector explicit expressions for the random eigenvalues and eigenvectors can readily be derived this enables the statistics of the random eigenparameters and the forced response to be efficiently computed numerical studies are presented for free and forced vibration analysis of a linear stochastic structural system it is demonstrated that the reduced basis method gives better results as compared to the first order perturbation method

new mode tracking methods in aeroelastic analysis within the context of analysis of finite element models a methodology is developed for the tracking of complex eigenvalues and eigenvectors through changes in aeroelastic eigenvalue problems the goal is to eliminate difficulties caused by mode switching i e frequency crossing two new methods for mode tracking are presented and compared with an existing method the first new method the complex higher order eigenpair perturbation algorithm is based on a perturbation expansion of the eigenproblem it iteratively computes changes in the eigenpairs due to parameter perturbations with the important feature of maintaining the correspondence between the baseline and perturbed eigenpairs the second new method is the complex cross orthogonality check method which uses mass biorthogonality of the left and right eigenvectors to re establish correspondence after a standard reanalysis applications of mode tracking technology are presented in v g and fc subsonic aeroelastic analyses each application procedure is outlined and examples are given recommendations are made based on method ease of use and robustness in the example problems

hybrid perturbation polynomial chaos approaches to the random algebraic eigenvalue problem the analysis of structures is affected by uncertainty in the structure s material properties geometric parameters boundary conditions and applied loads these uncertainties can be modelled by random variables and random fields amongst the various problems affected by uncertainty the random eigenvalue problem is specially important when analyzing the dynamic behavior or the buckling of a structure the methods that stand out in dealing with the random eigenvalue problem are the perturbation method and methods based on monte carlo simulation in the past few years methods based on polynomial chaos pc have been developed for this problem where each eigenvalue and eigenvector are represented by a pc expansion in this paper four variants of a method hybridizing perturbation and pc expansion approaches are proposed and compared the methods use rayleigh quotient the power method the inverse power method and the eigenvalue equation pc expansions of eigenvalues and eigenvectors are obtained with the proposed methods the new methods are applied to the problem of an euler bernoulli beam and a thin plate with stochastic properties

mode traces in degenerate eigensystems and augmented assurance eigenpairs contextually indicative of the frequencies and oscillatory modes of structural systems are considered as functions of a single parameter undesired permutation of modal designations is noted to arise following events of transitory eigenvalue coalescence with respect to the parameter resulting in the definition of nonsmooth functions the tracing of eigenpairs across such events is outlined for the permanently degenerate general eigenproblem as the general case the cases of transitorily degenerate and distinct eigenvalues are thus accounted for the foundation for mode tracing is the assumption of eigenvector consistency across parameter intervals used as a means of eigenpair reconciliation the resulting traced modes are smooth and their variations physically pertinent which is necessary in iterative schemes in which convergence may otherwise be jeopardized the proposal of an augmented modal assurance routine that potentially augments the assurance of tracing and therefore the maximum permissible parameter perturbation is given a threefold increase in the insight to consistency entails the notion of the routine is to forward and backward cast eigenvectors utilizing their derivatives in affine modeling a numerical example of the modes of a cyclic frame as functions of a cyclic distribution of membrane forces demonstrates the concepts and utility of the proposal

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

asymptotic tracking for uncertain dynamic systems via a multilayer neural network feedforward and rise feedback control structure the use of a neural network nn as a feedforward control element to compensate for nonlinear system uncertainties has been investigated for over a decade typical nn based controllers yield uniformly ultimately bounded uub stability results due to residual functional reconstruction inaccuracies and an inability to compensate for some system disturbances several researchers have proposed discontinuous feedback controllers e g variable structure or sliding mode controllers to reject the residual errors and yield asymptotic results the research in this paper describes how a recently developed continuous robust integral of the sign of the error rise feedback term can be incorporated with a nn based feedforward term to achieve semi global asymptotic tracking to achieve this result the typical stability analysis for the rise method is modified to enable the incorporation of the nn based feedforward terms and a projection algorithm is developed to guarantee bounded nn weight estimates

a unified approach to adaptive neural control for nonlinear discrete time systems with nonlinear dead zone input in this paper an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete time systems which contain unknown functions unknown dead zone input and unknown control direction different from linear dead zone the dead zone in this paper is a kind of nonlinear dead zone to overcome the noncausal problem which leads to the control scheme infeasible the systems can be transformed into a m step ahead predictor due to nonlinear dead zone appearance the transformed predictor still contains the nonaffine function in addition it is assumed that the gain function of dead zone input and the control direction are unknown these conditions bring about the difficulties and the complicacy in the controller design thus the implicit function theorem is applied to deal with nonaffine dead zone appearance the problem caused by the unknown control direction can be resolved through applying the discrete nussbaum gain and the neural networks are used to approximate the unknown function based on the lyapunov theory all the signals of the resulting closed loop system are proved to be semiglobal uniformly ultimately bounded moreover the tracking error is proved to be regulated to a small neighborhood around zero the feasibility of the proposed approach is demonstrated by a simulation example

the narrow escape problem the narrow escape problem in diffusion theory is to calculate the mean first passage time of a diffusion process to a small target on the reflecting boundary of a bounded domain the problem is equivalent to solving the mixed dirichlet neumann boundary value problem for the poisson equation with small dirichlet and large neumann parts the mixed boundary value problem which goes back to lord rayleigh originates in the theory of sound and is closely connected to the eigenvalue problem for the mixed problem and for the neumann problem in domains with bottlenecks we review here recent developments in the non standard asymptotics of the problem which are based on several ingredients a better resolution of the singularity of neumann s function resolution of the boundary layer near the small target by conformal mappings of domains with bottlenecks and the breakup of composite domains into simpler components the new methodology applies to two and higher dimensional problems selected applications are r

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

adaptive neural output feedback tracking control for a class of uncertain discrete time nonlinear systems this brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi input multi output mimo systems in the discrete time form the considered mimo systems are composed of n subsystems with the couplings of inputs and states among subsystems in order to solve the noncausal problem and decouple the couplings it needs to transform the systems into a predictor form the higher order neural networks are utilized to approximate the desired controllers by using lyapunov analysis it is proven that all the signals in the closed loop system is the semi globally uniformly ultimately bounded and the output errors converge to a compact set in contrast to the existing results the advantage of the scheme is that the number of the adjustable parameters is highly reduced the effectiveness of the scheme is verified by a simulation example

data driven model free adaptive control for a class of mimo nonlinear discrete time systems in this paper a data driven model free adaptive control mfac approach is proposed based on a new dynamic linearization technique dlt with a novel concept called pseudo partial derivative for a class of general multiple input and multiple output nonlinear discrete time systems the dlt includes compact form dynamic linearization partial form dynamic linearization and full form dynamic linearization the main feature of the approach is that the controller design depends only on the measured input output data of the controlled plant analysis and extensive simulations have shown that mfac guarantees the bounded input bounded output stability and the tracking error convergence

improvement of normalization methods for eigenvector derivatives the subject algorithms are all forward analysis i e the eigenvector changes are being driven by design parameter perturbations the new method emphasizes proper mass normalization and is most needed when iteratively computing eigenvector perturbations within a reduced dimension space

improved first order approximation of eigenvalues and eigenvectors a method based on reduced basis approximation concepts is presented for improved first order approximation of eigenvalues and eigenvectors of modified structural dynamic systems the terms of a local approximation based on taylor or matrix power series are used as basis vectors for approximating the perturbed eigenparameters for each eigenmode a reduced eigensystem is generated by using the baseline eigenvector and the first order approximation term as ritz vectors the solution of the reduced eigensystem leads to two possible estimates of each perturbed eigenvalue and eigenvector criteria for selection of the best approximation are presented the zero and first order rayleigh quotient approximation can be directly recovered as special cases of the present method results are presented for approximate dynamic reanalysis of a 25 bar planar truss structure it is shown that high quality approximation of the perturbed eigenparameters can be obtained for moderate perturbations in the stiffness and mass matrices for very large local perturbations of the structure including deletion of some structural members it is shown that the present method yields reasonable quality approximations