econometrics and decision theory abstract the paper considers the role of econometrics in decision making under uncertainty this leads to a focus on predictive distributions the decision maker s subjective distribution is only partly specified it belongs to a set s of distributions s can also be regarded as a set of plausible data generating processes criteria are needed to evaluate procedures for constructing predictive distributions we use risk robustness and minimax regret risk relative to s to obtain procedures for constructing predictive distributions we use bayes procedures based on parametric models with approximate prior distributions the priors are nested with a first stage that incorporates qualitative information such as exchangeability and a second stage that is quite diffuse special points in the parameter space such as boundary points can be accommodated with second stage priors that have one or more mass points but are otherwise quite diffuse an application of these ideas is presented motivated by an individual s consumption decision the problem is to construct a distribution for that individual s future earnings based on his earnings history and on a longitudinal data set that provides earnings histories for a sample of individuals

on some techniques for approximating boundary conditions in the finite element method we discuss the stabilization of finite element methods in which essential boundary conditions are approximated by babuska s method of lagrange multipliers and we show that there is a close connection with this technique and a classical method by nitsche

a mixed method for dirichlet problems with radial basis functions we present a simple discretization by radial basis functions for the poisson equation with dirichlet boundary condition a lagrangian multiplier using piecewise polynomials is used to accommodate the boundary condition this simplifies previous attempts to use radial basis functions in the interior domain to approximate the solution and on the boundary to approximate the multiplier which technically requires that the mesh norm in the interior domain is significantly smaller than that on the boundary numerical experiments confirm the theoretical results

adaptive fuzzy tracking control of switched uncertain nonlinear systems with unstable subsystems this paper is concerned with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems where the solvability of the fuzzy tracking control problem for subsystems is unnecessary fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a new adaptive fuzzy tracking control technique for the problem under study is set up based on the technique above we design a switching law and construct adaptive fuzzy controllers of subsystems explicitly by a recursive design algorithm to guarantee that all the signals in the resulting closed loop system remain bounded and the system output of the closed loop system converges to a small neighborhood of the reference signal multiple lyapunov functions are exploited to get out of the conservativeness caused by adoption of a common lyapunov function for all subsystems which is commonly required when applying the backstepping like recursive design scheme a mass spring damper system is provided to demonstrate the effectiveness of the proposed design method

a meshless galerkin method for dirichlet problems using radial basis functions in this paper a numerical method is given for partial differential equations which combines the use of lagrange multipliers with radial basis functions it is a new method to deal with difficulties that arise in the galerkin radial basis function approximation applied to dirichlet also mixed boundary value problems convergence analysis results are given several examples show the efficiency of the method using tps or sobolev splines

globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

meshless galerkin method using radial basis functions based on domain decomposition in this present paper we will give an overview about the combination of rbf meshless method with domain decomposition especially galerkin method based on the analysis for this method before we will consider the combination of projection domain decomposition method with radial basis function both of galerkin approximation and collocation method are discussed some examples are given to show the efficiency of this method

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

on unsymmetric collocation by radial basis functions solving partial differential equations by collocation with radial basis functions can be efficiently done by a technique first proposed by kansa in 1990 it rewrites the problem as a generalized interpolation problem and the solution is obtained by solving a possibly large linear system the method has been used successfully in a variety of applications but a proof of nonsingularity of the linear system was still missing this paper shows that a general proof of this fact is impossible however numerical evidence shows that cases of singularity are rare and have to be constructed with quite some effort

boundary lagrange multipliers in finite element methods error analysis in natural norms a finite element procedure for circumventing the babuska brezzi condition in mixed formulations with lagrange multipliers defined on the boundary is presented residual terms constructed from the euler lagrange equations are added to the classical galerkin formulation in order to attain coercivity in a mesh dependent norm convergence is proven for the primal variable and the multiplier in the natural mesh independent norm of the problem generalizing results of a previous paper

brief paper backstepping controller design for a class of stochastic nonlinear systems with markovian switching a more general class of stochastic nonlinear systems with irreducible homogenous markovian switching are considered in this paper as preliminaries the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a lyapunov function the state feedback controller is designed by regarding markovian switching as constant such that the closed loop system has a unique solution and the equilibrium is asymptotically stable in probability in the large the output feedback controller is designed based on a quadratic plus quartic form lyapunov function such that the closed loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded in probability solution in the biased case

adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small gain approach this paper considers the adaptive fuzzy robust control problem for a class of single input and single output siso stochastic nonlinear systems in strict feedback form the systems under study possess unstructured uncertainties unknown dead zone uncertain dynamics and unknown gain functions in the controller design fuzzy logic systems are adopted to approximate the unknown functions and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics by combining the backstepping technique with the stochastic small gain approach a novel adaptive fuzzy robust control scheme is developed it is shown that the proposed control approach can guarantee that the closed loop system is input state practically stable isps in probability and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters simulation results are provided to illustrate the effectiveness of the proposed control approach

a note on the meshless method using radial basis functions in this paper we prove some inverse inequalities for the finite dimensional subspace interpolated by radial basis functions the properties of these inequalities are worse than those in finite element spaces these bad properties result in a huge condition number for both the collocation method and galerkin method using radial basis functions as applications theoretical estimates of the condition numbers of a meshless method using radial basis functions are given

a particle partition of unity method for the solution of elliptic parabolic and hyperbolic pdes in this paper we present a meshless discretization technique for instationary convection diffusion problems it is based on operator splitting the method of characteristics and a generalized partition of unity method we focus on the discretization process and its quality the method may be used as an h version or a p version even for general particle distributions the convergence behavior of the different versions corresponds to that of the respective version of the finite element method on a uniform grid we discuss the implementational aspects of the proposed method furthermore we present the results of numerical examples where we considered instationary convection diffusion instationary diffusion linear advection and elliptic problems

a new spectral meshless radial point interpolation smrpi method for the two dimensional fredholm integral equations on general domains with error analysis in this article we present a numerical method to solve two dimensional fredholm integral equations of the second kind on general domains the method utilizes meshless and spectral collocation techniques but it is not traditional meshless collocation method the point interpolation method with the help of strictly positive definite radial basis functions is used to construct shape functions as a basis functions in the frame of spectral collocation methods these basis functions shape functions have kronecker delta function property since the proposed method is meshless it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional integral equation to the solution of a linear system of algebraic equations convergence analysis with error estimates are given with full discussion furthermore some numerical examples are presented to show the validity and efficiency of smrpi

on the convergence analysis stability and implementation of meshless local radial point interpolation on a class of three dimensional wave equations summary in this article the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt ut u uxx uyy uzz f x y z t xt x y z rd d 2 3 t 0 subject to given initial and dirichlet boundary conditions the main difficulty of the great number of methods in full 3 d problems is the large computational costs in meshless local radial point interpolation method it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions the point interpolation method with the help of radial basis functions is proposed to construct shape functions that have kronecker delta function property a weak formulation with the heaviside step function converts the set of governing equations into local integral equations on local subdomains a two step time discretization method is employed to evaluate the time derivatives this suggests crank nicolson technique to be applied on the right hand side of the equation the convergence analysis and stability of the method are fully discussed three illustrative examples are presented and satisfactory agreements are achieved it is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones copyright 2015 john wiley sons ltd

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

adaptive output feedback tracking of stochastic nonlinear systems we address the adaptive stabilization and tracking problems for a class of output feedback canonical systems driven by wiener noises of unknown covariance filtered transformation and backstepping techniques are employed in the stochastic control design we obtain two adaptive controllers that guarantee the global stability in probability for vanishing perturbations or the input to state stability in probability for nonvanishing perturbations respectively the tracking error can converge to a small residual set around the origin in the sense of mean quartic value

meshless galerkin methods using radial basis functions we combine the theory of radial basis functions with the field of galerkin methods to solve partial differential equations after a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions

existence uniqueness and exponential stability analysis for complex valued memristor based bam neural networks with time delays this article explores the exponential stability problem of complex valued bidirectional associative memory bam neural networks with time delays this analysis is on the basis of the m matrix approach the differential inclusions theory and the homeomorphism property by constructing a novel lyapunov functional a sufficient criterion for the existence uniqueness and exponential stability for the equilibrium point of the considered system is derived moreover similar results in terms of m matrix are also obtained for the exponential stability problem of delayed complex valued bam neural networks without memristors in the end two numerical examples are provided to demonstrate the availability of the obtained results

ranges of posterior probabilities for quasiunimodal priors with specified quantiles abstract suppose several quantiles of the prior distribution for are specified or equivalently the prior probabilities of a partitioning collection of intervals ii are given in addition suppose that the prior distribution is assumed to be unimodal rather than selecting a single prior distribution to perform a bayesian analysis it is of interest to consider the class of all prior distributions compatible with these inputs for this class and unimodal likelihood functions the ranges of the posterior probabilities of the ii and the ranges of the posterior cdf at the specified prior quantiles were determined in berger and o hagan in press unfortunately calculations with this class can be difficult here a similar much more easily analyzed class of quasiunimodal prior distributions is considered and compared with other classes

adaptive fuzzy tracking control for a class of pure feedback stochastic nonlinear systems with non lower triangular structure this paper considers the problem of the adaptive fuzzy tracking control for a class of nonaffine stochastic nonlinear systems without lower triangular form by using fuzzy logic systems universal approximation property an adaptive fuzzy controller is proposed which guarantees that all the signals in the closed loop system are bounded in the sense of mean quartic value and the output tracking error eventually converges to a small neighborhood around the origin simulation results are provided to illustrate the effectiveness of the proposed scheme

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

optimal adaptive fuzzy ftc design for strict feedback nonlinear uncertain systems with actuator faults abstract in this paper the optimal fault tolerant control ftc design problem is investigated for strict feedback nonlinear systems the considered nonlinear systems contain actuator faults which are bias fault and gain fault the problem of actuator faults is solved by utilizing the adaptive compensation technique applying the backstepping design technique a main fault tolerant controller is established via the designed main fault tolerant control strategy the controlled nonlinear system can be converted to an equivalent nonlinear system in affine form subsequently a fuzzy logic system fls is introduced to approximate the unknown cost function and an adaptive fuzzy feedback optimal controller is developed the whole adaptive fuzzy fault tolerant optimal control scheme consists of a main controller and a feedback optimal controller based on the lyapunov theory it is proved that all the signals in the closed loop system are bounded the system output can track a bounded reference signal in addition the proposed control method can guarantee the cost function is the smallest simulation results are provided to illustrate the effectiveness of the proposed fault tolerant optimal control scheme

ranges of posterior measures for priors with unimodal contaminations we consider the problem of robustness or sensitivity of given bayesian posterior criteria to specification of the prior distribution criteria considered include the posterior mean variance and probability of a set for credible regions and hypothesis testing uncertainty in an elicited prior go is modelled by an e contamination class f x 1 c 1t0 eq q e q where reflects the amount of probabilistic uncertainty in g and q is a class

adaptive neural network control for a class of low triangular structured nonlinear systems in this paper a class of unknown perturbed nonlinear systems is theoretically stabilized by using adaptive neural network control the systems with disturbances and nonaffine unknown functions have low triangular structure which generalizes both strict feedback uncertain systems and pure feedback ones there do not exist any effective methods to stabilize this kind of systems with some new conclusions for nussbaum gain functions ngf and the idea of backstepping semiglobal uniformal and ultimate boundedness of all the signals in the closed loop is proved at equilibrium point the two problems control directions and control singularity are well dealt with the effectiveness of proposed scheme is shown by simulation on a proper nonlinear system

nn based adaptive tracking control of uncertain nonlinear systems disturbed by unknown covariance noise a class of uncertain nonlinear systems that are additionally driven by unknown covariance noise is considered based on the backstepping technique adaptive neural control schemes are developed to solve the output tracking control problem of such systems as it is proven by stability analysis the proposed controller guarantees that all the error variables are bounded with desired probability in a compact set while the tracking error is mean square semiglobally uniformly ultimately bounded m sguub the tracking performance and the effectiveness of the proposed design are evaluated by simulation results

coupling three field formulation and meshless mixed galerkin methods using radial basis functions in this work we solve the elliptic partial differential equation by coupling the meshless mixed galerkin approximation using radial basis function with the three field domain decomposition method the formulation has been adopted to increase the efficiency of the numerical technique by decreasing the error and dealing with the ill conditioning of the linear system caused by the radial basis function convergence analysis of the coupled technique is treated and numerical results of some solved examples are given at the end of this paper

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

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

improved error bounds for scattered data interpolation by radial basis functions if additional smoothness requirements and boundary conditions are met the well known approximation orders of scattered data interpolants by radial functions can roughly be doubled

the finite element method with lagrange multipliers for domains with corners we study the convergence of the finite element method with lagrange multipliers for approximately solving the dirichlet problem for a second order elliptic equation in a plane domain with piecewise smooth boundary assuming mesh refinements around the corners we construct families of boundary subspaces that are compatible with triangular lagrange elements in the interior and we carry out the error analysis of the resulting approximations in weighted sobolev spaces

on the accuracy of least squares methods in the presence of corner singularities abstract this paper treats elliptic problems with corner singularities finite element approximations based on variational principles of the least squares type tend to display poor convergence properties in such contexts moreover mesh refinement or the use of special singular elements do not appreciably improve matters here we show that if the least squares formulation is done in appropriately weighted spaces then optimal convergence results in unweighted spaces like l2

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

on condition number of meshless collocation method using radial basis functions in this paper we will give an estimate for the condition number of meshless collocation method using radial basis functions

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

reduced order observer based control design for nonlinear stochastic systems in this paper we investigate the stabilization control design problem of nonlinear stochastic siso systems in strict feedback form by introducing a novel reduced order observer an output feedback based control is constructively designed which renders the closed loop system asymptotically stable in the large when the nonlinearities and stochastic disturbance equal zero at the equilibrium point of the open loop system and bounded in probability otherwise besides the obtained controller preserves the equilibrium point of the open loop nonlinear system