adaptive control design based on adaptive optimization principles recently we introduced an adaptive control design for linearly parameterized multi input nonlinear systems admitting a known control lyapunov function clf that depends on the unknown system parameters the main advantage of that design is that it overcomes the problem where the estimation model becomes uncontrollable at regions of the state space where the actual system is controllable however the resulted adaptive control design is quite complicated and moreover it exhibited poor transient behavior in various applications in this technical note we propose and analyze a new computationally efficient adaptive control design that overcomes the aforementioned shortcomings the proposed design is based on an adaptive optimization algorithm introduced recently by the author which makes sure that the parameters to be optimized which correspond to the controller parameters in this technical note are modified so as to both lead to a decrease of the function to be minimized and satisfy a persistence of excitation condition the main advantage of the proposed adaptive control design is that it can produce arbitrarily good transient performance outside a the regions of the state space where the actual system becomes uncontrollable and b a region of the parameter estimates space which shrinks exponentially fast it is also worth noting that the class of systems where the proposed algorithm is applicable is more general than that of our previous work however it has to be emphasized that due to the fact that the proposed algorithm involves the use of random sequences all the established stability and convergence results are guaranteed to hold with probability one

step fluctuations for a faceted crystal a statistical mechanics model for a faceted crystal is the 3d ising model at zero temperature it is assumed that in one octant all sites are occupied by atoms the remaining ones being empty allowed atom configurations are such that they can be obtained from the filled octant through successive removals of atoms with breaking of precisely three bonds if v denotes the number of atoms removed then the grand canonical boltzmann weight is q v 0 q 1 as shown by cerf and kenyon in the limit q 1 a deterministic shape is attained which has the three facets 100 010 001 and a rounded piece interpolating between them we analyse the step statistics as q 1 in the rounded piece it is given by a determinantal process based on the discrete sine kernel exactly at the facet edge the steps have more space to meander their statistics is again determinantal but this time based on the airy kernel in particular the border step is well approximated by the airy process which has been obtained previously in the context of growth models our results are based on the asymptotic analysis for space time inhomogeneous transfer matrices

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

gibbs ensembles of nonintersecting paths we consider a family of determinantal random point processes on the two dimensional lattice and prove that members of our family can be interpreted as a kind of gibbs ensembles of nonintersecting paths examples include probability measures on lozenge and domino tilings of the plane some of which are non translation invariant the correlation kernels of our processes can be viewed as extensions of the discrete sine kernel and we show that the gibbs property is a consequence of simple linear relations satisfied by these kernels the processes depend on infinitely many parameters which are closely related to parametrization of totally positive toeplitz matrices

the arctic circle boundary and the airy process we prove that the appropriately rescaled boundary of the north polar region in the aztec diamond converges to the airy process the proof uses certain determinantal point processes given by the extended krawtchouk kernel we also prove a version of propp s conjecture concerning the structure of the tiling at the center of the aztec diamond 1 introduction and results domino tilings of the aztec diamond were introduced in 8 9 asymptotic properties of random domino tilings of the aztec diamond have been studied in 5 12 15 in particular in 12 the existence of the so called arctic circle was proved the arctic circle is the asymptotic boundary of the disordered so called temperate region of the tiling outside this boundary the tiling forms a completely regular brick wall pattern the methods in 12 combined with the results in 13 show that the fluctuations of the point of intersection of the boundary of the temperate region with a line converge to the tracy widom distribution of random matrix theory in this paper we extend this result to show that the fluctuations of the boundary around the arctic circle converges to the airy process introduced in 23 the paper is a continuation of the approach used in 14 and 15 where certain point processes with determinantal correlation functions 24 and the krawtchouk ensemble were used we will use the general techniques developed in 16 and investigate an extended point process which also has determinantal correlation functions given by a kernel which we call the extended krawtchouk kernel the aztec diamond an of order n is the union of all lattice squares m m 1 l l 1 m l 2 z that lie inside the region x1 y1 x1 y1

markov chain algorithms for planar lattice structures consider the following markov chain whose states are all domino tilings of a 2n 2n chessboard starting from some arbitrary tiling pick a 2 2 window uniformly at random if the four squares appearing in this window are covered by two parallel dominoes rotate the dominoes 90 rm o in place repeat many times this process is used in practice to generate a random tiling and is a widely used tool in the study of the combinatorics of tilings and the behavior of dimer systems in statistical physics analogous markov chains are used to randomly generate other structures on various two dimensional lattices this paper presents techniques which prove for the first time that in many interesting cases a small number of random moves suffice to obtain a uniform distribution

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

asymptotic controllability implies feedback stabilization it is shown that every asymptotically controllable system can be globally stabilized by means of some discontinuous feedback law the stabilizing strategy is based on pointwise optimization of a smoothed version of a control lyapunov function iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium a major technical problem and one of the contributions of the present paper concerns the precise meaning of solution when using a discontinuous controller

decentralized measurement feedback stabilization of large scale systems via control vector lyapunov functions abstract this paper studies the problem of decentralized measurement feedback stabilization of nonlinear interconnected systems as a natural extension of the recent development on control vector lyapunov functions the notion of output control vector lyapunov function ocvlf is introduced for investigating decentralized measurement feedback stabilization problems sufficient conditions on local stabilizability are discussed which are based on the proposed notion of ocvlf it is shown that a decentralized controller for a nonlinear interconnected system can be constructed using these conditions under an additional vector dissipation like condition to illustrate the proposed method two examples are given

brief paper an adaptive optimization scheme with satisfactory transient performance adaptive optimization ao schemes based on stochastic approximation principles such as the random directions kiefer wolfowitz rdkw the simultaneous perturbation stochastic approximation spsa and the adaptive fine tuning aft algorithms possess the serious disadvantage of not guaranteeing satisfactory transient behavior due to their requirement for using random or random like perturbations of the parameter vector the use of random or random like perturbations may lead to particularly large values of the objective function which may result to severe poor performance or stability problems when these methods are applied to closed loop controller optimization applications in this paper we introduce and analyze a new algorithm for alleviating this problem mathematical analysis establishes satisfactory transient performance and convergence of the proposed scheme under a general set of assumptions application of the proposed scheme to the adaptive optimization of a large scale complex control system demonstrates the efficiency of the proposed scheme

generalized receding horizon control of fuzzy systems based on numerical optimization algorithm the optimal control of fuzzy systems with constraints is still an open problem our focus concerns the optimal control problem of fuzzy systems derived from receding horizon control rhc schemes we consider methods to numerically compute the value function for general fuzzy systems the numerical method that is developed using the finite difference with sigmoidal transformation is a stable and convergent algorithm for the hamilton jacobi bellman hjb equation an optimization procedure is developed to increase the calculation accuracy with less computation time a parallel processing method is employed in the optimization procedure the optimization results are applied to the controller design of general fuzzy dynamic systems employing the principle of conventional rhc schemes rhc form controllers are designed for some classes of fuzzy dynamic systems the basic ideas are as follows first the value function is calculated by numerical methods then the value function is used as controller design parameters to redesign rhc controllers for fuzzy systems which is motivated by the inverse lyapunov function design method it is proven that the closed loop system is asymptotically stable an engineering implementation of the controller redesign scheme is discussed meanwhile the parallel processing framework that can improve the closed loop performance is also introduced

degree of approximation results for feedforward networks approximating unknown mappings and their derivatives recently barron 1993 has given rates for hidden layer feedforward networks with sigmoid activation functions approximating a class of functions satisfying a certain smoothness condition these rates do not depend on the dimension of the input space we extend barron s results to feedforward networks with possibly nonsigmoid activation functions approximating mappings and their derivatives simultaneously our conditions are similar but not identical to barron s but we obtain the same rates of approximation showing that the approximation error decreases at rates as fast as n 1 2 where n is the number of hidden units the dimension of the input space appears only in the constants of our bounds

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

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

lyapunov design of stabilizing controllers for cascaded systems the design of a state feedback law for an affine nonlinear system to render a as small as possible compact neighborhood of the equilibrium of interest globally attractive is discussed following z artstein s theorem 1983 the problem can be solved by designing a so called control lyapunov function for systems which are in a cascade form a lyapunov function meeting artstein s conditions is designed assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem in particular for planar systems this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized

neural networks for optimal approximation of smooth and analytic functions we prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives if the activation function evaluated by each principal element satisfies certain technical conditions under these conditions it is also possible to construct networks that provide a geometric order of approximation for analytic target functions the permissible activation functions include the squashing function 1 e x 1 as well as a variety of radial basis functions our proofs are constructive the weights and thresholds of our networks are chosen independently of the target function we give explicit formulas for the coefficients as simple continuous linear functionals of the target function

control for a class of second order systems via a state dependent riccati equation approach this study investigates the state dependent riccati equation sdre controller for a class of second order nonlinear systems by fully exploiting the design degree of freedom dof arising from the nonunique state dependent coefficient sdc matrices we explicitly calculate the ranges of control input via the sdre scheme moreover when a permissible control input is determined we also explicitly parameterize the sdc matrices that result in the designated control value in terms of system states and parameters so the engineer can easily implement the scheme notably this is the first analytical result that explores the range of control input using the design dof of sdc matrices in addition by applying the analytical results it is shown that the second order systems are always globally stabilizable without any supplementary assumptions on weighting matrices as extended from existing sdre global results and the corresponding stabilizing sdc matrices are also explicitly presented finally illustr

hierarchical mixtures of experts and the em algorithm we present a tree structured architecture for supervised learning the statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models glim s learning is treated as a maximum likelihood problem in particular we present an expectation maximization em algorithm for adjusting the parameters of the architecture we also develop an on line learning algorithm in which the parameters are updated incrementally comparative simulation results are presented in the robot dynamics domain

the quantum dark side of the optimal control theory abstract in a recent article a generic optimal control problem was studied from a physicist s point of view contreras et al 2017 through this optic the pontryagin equations are equivalent to the hamilton equations of a classical constrained system by quantizing this constrained system using the right ordering of the operators the corresponding quantum dynamics given by the schrodinger equation is equivalent to that given by the hamilton jacobi bellman equation of bellman s theory the conclusion drawn there were based on certain analogies between the equations of motion of both theories in this paper a closer and more detailed examination of the quantization problem is carried out by considering three possible quantization procedures right quantization left quantization and feynman s path integral approach the bellman theory turns out to be the classical limit 0 of these three different quantum theories also the exact relation of the phase s x t of the wave function x t e i s x t of the quantum theory with bellman s cost function j x t is obtained in fact s x t satisfies a conjugate form of the hamilton jacobi bellman equation which implies that the cost functional j x t must necessarily satisfy the usual hamilton jacobi bellman equation thus the bellman theory effectively corresponds to a quantum view of the optimal control problem

approximation by network operators with logistic activation functions this paper aims to study the construction and multivariate approximation of a class of network operators with logistic sigmoidal functions first a class of even and bell shaped function with support on r is constructed by using appropriate translation and combination of the logistic function then the constructed function is employed as activation function to construct a kind of so called cardaliaguet euvrard type network operators finally these network operators are used to approximate bivariate functions in c 1 1 2 and a jackson type theorem for the approximation errors is established

clf based designs with robustness to dynamic input uncertainties abstract the problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation stabilizing control laws may not be robust to this type of uncertainty especially if cancellation of nonlinearities is used in the design by exploiting a connection between robustness and optimality domination redesign of the control lyapunov function clf based sontag s formula has been shown to possess robustness to static and dynamic input uncertainties in this paper we provide a sufficient condition for the domination redesign to apply this condition relies on properties of local homogeneous approximations of the system and of the clf we show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these conditions may guide the choice of a clf which is suitable for domination redesign

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

approximation of conditional densities by smooth mixtures of regressions this paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the kullback leibler distance by different specifications of finite mixtures of normal regressions in which normal means and variances and mixing probabilities can depend on variables in the conditioning set covariates these models are a special case of models known as mixtures of experts in statistics and computer science literature flexible specifications include models in which only mixing probabilities modeled by multinomial logit depend on the covariates and in the univariate case models in which only means of the mixed normals depend flexibly on the covariates modeling the variance of the mixed normals by flexible functions of the covariates can weaken restrictions on the class of the approximable densities obtained results can be generalized to mixtures of general location scale densities rates of convergence and easy to interpret bounds are also obtained for different model specifications these approximation results can be useful for proving consistency of bayesian and maximum likelihood density estimators based on these models the results also have interesting implications for applied researchers

locally optimal controllers and globally inverse optimal controllers in this paper we consider the problem of global asymptotic stabilization with prescribed local behavior we show that this problem can be formulated in terms of control lyapunov functions moreover we show that if the local control law has been synthesized employing an lq approach then the associated lyapunov function can be seen as the value function of an optimal problem with some specific local properties we illustrate these results on two specific classes of systems backstepping and feedforward systems finally we show how this framework can be employed when considering the orbital transfer problem

clf based control design for unknown multiinput nonlinear systems with good transient performance this technical note tackles the problem of constructing state feedback stabilizers that guarantee good transient closed loop performance when applied to general unknown nonlinear multiinput state feedback stabilizable systems an adaptive control lyapunov function based control scheme is proposed in order to address this problem mathematical analysis establishes that the proposed control scheme guarantees good closed loop transient performance outside the regions where the system is uncontrollable provided the controlled system admits a controllability like property

approximation by neural networks with scattered data in this paper the approximation capability of feed forward neural networks fnns formed as k 1 nc k f x x k is considered where f is an even periodic continuous function and x k s are scattered data the best approximation error of trigonometric polynomials and the continuous modulus of the activation function f are introduced to describe the approximation capability of fnns

brownian gibbs property for airy line ensembles consider a collection of n brownian bridges b i n n to mathbb r b i n b i n 0 1 i n conditioned not to intersect the edge scaling limit of this system is obtained by taking a weak limit as n of the collection of curves scaled so that the point 0 21 2 n is fixed and space is squeezed horizontally by a factor of n 2 3 and vertically by n 1 3 if a parabola is added to each of the curves of this scaling limit an x translation invariant process sometimes called the multi line airy process is obtained we prove the existence of a version of this process which we call the airy line ensemble in which the curves are almost surely everywhere continuous and non intersecting this process naturally arises in the study of growth processes and random matrix ensembles as do related processes with wanderers and outliers we formulate our results to treat these relatives as well note that the law of the finite collection of brownian bridges above has the property called the brownian gibbs property of being invariant under the following action select an index 1 k n and erase b k on a fixed time interval a b n n then replace this erased curve with a new curve on a b according to the law of a brownian bridge between the two existing endpoints a b k a and b b k b conditioned to intersect neither the curve above nor the one below we show that this property is preserved under the edge scaling limit and thus establish that the airy line ensemble has the brownian gibbs property an immediate consequence of the brownian gibbs property is a confirmation of the prediction of m prahofer and h spohn that each line of the airy line ensemble is locally absolutely continuous with respect to brownian motion we also obtain a proof of the long standing conjecture of k johansson that the top line of the airy line ensemble minus a parabola attains its maximum at a unique point this establishes the asymptotic law of the transversal fluctuation of last passage percolation with geometric weights our probabilistic approach complements the perspective of exactly solvable systems which is often taken in studying the multi line airy process and readily yields several other interesting properties of this process

error bounds for functional approximation and estimation using mixtures of experts we examine some mathematical aspects of learning unknown mappings with the mixture of experts model mem specifically we observe that the mem is at least as powerful as a class of neural networks in a sense that will be made precise upper bounds on the approximation error are established for a wide class of target functions the general theorem states that spl par f f sub n spl par sub p spl les c n sup r d for f spl isin w sub p sup r l a sobolev class over 1 1 sup d and f sub n belongs to an n dimensional manifold of normalized ridge functions the same bound holds for the mem as a special case of the above the stochastic error in the context of learning from independent and identically distributed i i d examples is also examined an asymptotic analysis establishes the limiting behavior of this error in terms of certain pseudo information matrices these results substantiate the intuition behind the mem and motivate applications

observer based stabilization of sector bounded nonlinear stochastic systems in the presence of intermittent measurements abstract this paper focuses on the stabilization problem of sector bounded stochastic nonlinear systems in which the measured output can be only intermittently available an intermittent observer is constructed to estimate the unmeasurable states by employing a piecewise time dependent lyapunov function method mean square exponential stability and almost sure exponential stability criteria are established in terms of linear matrix inequalities lmis it shows that the almost sure stability criterion is less conservative than the mean square stability criterion with the help of the singular value decomposition technique the controller and observer gains can be achieved by solving a set of lmis finally two numerical examples are provided to illustrate the validity of the proposed scheme

analysis of sdc matrices for successfully implementing the sdre scheme abstract the state dependent riccati equation sdre approach for stabilization of nonlinear affine systems was recently reported to be effective in many practical applications however there is no guideline on the construction of state dependent coefficient sdc matrix when the sdre solvability condition is violated which may result in the sdre scheme being terminated in this study we present several easy checking conditions so that the sdre scheme can be successfully implemented additionally when the presented checking conditions are satisfied the sets of all feasible sdc matrices and their structures are explicitly depicted for the planar system

accuracy analysis for wavelet approximations constructive wavelet networks are investigated as a universal tool for function approximation the parameters of such networks are obtained via some direct monte carlo procedures approximation bounds are given typically it is shown that such networks with one layer of wavelons achieve an l sub 2 error of order o n sup spl rhod where n is the number of nodes d is the problem dimension and spl rho is the number of summable derivatives of the approximated function an algorithm is also proposed to estimate this approximation based on noisy input output data observed from the function under consideration unlike neural network training this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated backpropagation and it completely avoids the problem of poor convergence or undesirable local minima

controller design for nonlinear affine systems by control lyapunov functions abstract this paper addresses the stabilization problems for nonlinear affine systems first of all the explicit feedback controller is developed for a nonlinear multiple input affine system by assuming that there exists a control lyapunov function next based upon the homogeneous property sufficient conditions for the continuity of the derived controller are developed and then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems it is shown that under some homogeneous assumptions on control lyapunov functions and the interconnection term the cascaded system can be globally stabilized finally some interesting results of finite time stabilization for nonlinear affine systems are also obtained

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

the low temperature expansion of the wulff crystal in the 3d ising model we compute the expansion of the surface tension of the 3d random cluster model for q 1 in the limit where p goes to 1 we also compute the asymptotic shape of a plane partition of n as n goes to this same shape determines the wulff crystal to order o in the 3d ising model and more generally in the 3d random cluster model for q 1 at temperature

robust switching adaptive control of multi input nonlinear systems during the last decade a considerable progress has been made in the design of stabilizing controllers for nonlinear systems with known and unknown constant parameters new design tools such as adaptive feedback linearization adaptive back stepping control lyapunov functions clfs and robust control lyapunov functions rclfs nonlinear damping and switching adaptive control have been introduced most of the results developed are applicable to single input feedback linearizable systems and parametric strict feedback systems these results however cannot be applied to multi input feedback linearizable systems parametric pure feedback systems and systems that admit a linear in the parameters clf in this paper we develop a general procedure for designing robust adaptive controllers for a large class of multi input nonlinear systems this class of nonlinear systems includes as a special case multi input feedback linearizable systems parametric pure feedback systems and systems that admit a linear in the parameters clf the proposed approach uses tools from the theory of rclf and the switching adaptive controllers proposed by the authors for overcoming the problem of computing the feedback control law when the estimation model becomes uncontrollable the proposed control approach has also been shown to be robust with respect to exogenous bounded input disturbances

path integral approach to dynamics in a sparse random network we study the dynamics involved in a sparse random network model we extend the standard mean field approximation for the dynamics of a random network by employing the path integral approach the result indicates that the distribution of the variable is essentially identical to that obtained from globally coupled oscillators with random gaussian interaction we present the results of a numerical simulation of the kuramoto transition in a random network which is found to be consistent with this analysis

sampled data feedback practical semi global controllability and stabilization for time varying systems we deal with the problems of the closed loop controllability and stabilization for time varying systems whose dynamics are in general unbounded with respect to time it is shown that a general notion of global asymptotic controllability being in general non uniform with respect to initial values of time implies existence of a family of continuous control lyapunov functions and this enables the establishment of practical semi global closed loop controllability by means of a sampled data time varying feedback moreover the usual concept of global asymptotic controllability being uniform with respect to the initial values of time implies practical semi global stabilization by sampled data feedback the work is a continuation of a recent paper of the author in the same journal and extends krichman s 2000 result relying practical stabilization of time varying systems with bounded in time dynamics

brief practical l2 disturbance attenuation for nonlinear systems in this work a notion of generalized l 2 gain for nonlinear systems where the gain is considered as a function of the state instead of a global constant is presented this new notion seems to be adequate to characterize the gain properties of several nonlinear systems which do not possess a uniform l 2 gain property i e the l 2 gain depends on the operating point moreover a notion of practical l 2 gain attenuation which extends the standard definition and parallels mutatae mutandis the concepts of practical stability is also proposed

random surface growth with a wall and plancherel measures for o we consider a markov evolution of lozenge tilings of a quarter plane and study its asymptotics at large times one of the boundary rays serves as a reflecting wall we observe frozen and liquid regions prove convergence of the local correlations to translation invariant gibbs measures in the liquid region and obtain new discrete jacobi and symmetric pearcey determinantal point processes near the wall the model can be viewed as the one parameter family of plancherel measures for the infinite dimensional orthogonal group and we use this interpretation to derive the determinantal formula for the correlation functions at any finite time moment

strict lyapunov function constructions under lasalle conditions with an application to lotka volterra systems we provide new techniques for building explicit global strict lyapunov functions for broad classes of periodic time varying nonlinear systems satisfying lasalle conditions we illustrate our work using the lotka volterra model which plays a fundamental role in bioengineering we use our strict lyapunov constructions to prove robustness of the lotka volterra tracking dynamics to uncertainty in the death rates

risk bounds for model selection via penalization performance bounds for criteria for model selection are devel oped using recent theory for sieves the model selection criteria are based on an empirical loss or contrast function with an added penalty term moti vated by empirical process theory and roughly proportional to the number of parameters needed to describe the model divided by the number of ob servations most of our examples involve density or regression estimation settings and we focus on the problem of estimating the unknown density or regression function we show that the quadratic risk of the minimum penal ized empirical contrast estimatoris bounded by an index of the accuracy of the sieve this accuracy index quanties the trade off among the candidate models between the approximation error and parameter dimension relative to sample size if we choose a list of models which exhibit good approximation prop erties with respect to different classes of smoothness the estimator can be simultaneously minimax rate optimal in each of those classes this is what is usually called adaptation the type of classes of smoothness in which one gets adaptation depends heavily on the list of models if too many models are involved in order to get accurate approximation of many wide classes of functions simultaneously it may happen that the estimator is only approx

the errors of simultaneous approximation of multivariate functions by neural networks there have been many studies on the simultaneous approximation capability of feed forward neural networks fnns most of these however are only concerned with the density or feasibility of performing simultaneous approximations this paper considers the simultaneous approximation of algebraic polynomials employing taylor expansion and an algebraic constructive approach to construct a class of fnns which realize the simultaneous approximation of any smooth multivariate function and all of its derivatives we also present an upper bound on the approximation accuracy of the fnns expressed in terms of the modulus of continuity of the functions to be approximated

local characteristics entropy and limit theorems for spanning trees and domino tilings via transfer impedances let g be a finite graph or an infinite graph on which mathbb z d acts with finite fundamental domain if g is finite let mathbf t be a random spanning tree chosen uniformly from all spanning trees of g if g is infinite methods from pemantle show that this still makes sense producing a random essential spanning forest of g a method for calculating local characteristics i e finite dimensional marginals of mathbf t from the transfer impedance matrix is presented this differs from the classical matrix tree theorem in that only small pieces of the matrix n dimensional minors are needed to compute small n dimensional marginals calculation of the matrix entries relies on the calculation of the green s function for g which is not a local calculation however it is shown how the calculation of the green s function may be reduced to a finite computation in the case when g is an infinite graph admitting a z d action with finite quotient the same computation also gives the entropy of the law of mathbf t these results are applied to the problem of tiling certain lattices by dominos the so called dimer problem another application of these results is to prove modified versions of conjectures of aldous on the limiting distribution of degrees of a vertex and on the local structure near a vertex of a uniform random spanning tree in a lattice whose dimension is going to infinity included is a generalization of moments to tree valued random variables and criteria for these generalized moments to determine a distribution

approximation bounds for smooth functions in c r sup d by neural and mixture networks we consider the approximation of smooth multivariate functions in c r sup d by feedforward neural networks with a single hidden layer of nonlinear ridge functions under certain assumptions on the smoothness of the functions being approximated and on the activation functions in the neural network we present upper bounds on the degree of approximation achieved over the domain r sup d thereby generalizing available results for compact domains we extend the approximation results to the so called mixture of expert architecture which has received considerable attention in recent years showing that the same type of approximation bound may be achieved

stochastic nonlinear stabilization ii inverse optimality after considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper in this second part we address the classical question of when is a stabilizing in probability controller optimal and show that for every system with a stochastic control lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional then we return to the problem from part i and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin

technical communique stabilizing controllers design for switched nonlinear systems in strict feedback form this paper considers the stabilization problem for a class of switched nonlinear systems under arbitrary switching based on the backstepping method and the control lyapunov function approach it is shown that under a simultaneous domination assumption a switched nonlinear system in strict feedback form can be globally uniformly asymptotically stabilized by a continuous state feedback controller a universal formula for constructing stabilizing feedback laws is presented one example is included for verifying the obtained results

a variational principle for domino tilings 1 1 description of results a domino is a 1 x 2 or 2 x 1 rectangle and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps in 1961 kasteleyn kal found a formula for the number of domino tilings of an m x n rectangle with mn even as shown in figure 1 for rm n 68 temperley and fisher tf used a differenit method and arrived at the same result at almost exactly the same time both lines of calculation showed that the logarithm of number of tilings divided by the number of dominos in a tiling that is mn 2 converges to 2g 7r 0 58 here g is catalan s constant on the other hand in 1992 elkies et al eklp studied domino tilings of regions they called aztec diamonds figure 2 shows an aztec diamond of order 48 and showed that the logarithm of the number of tilings divided by the number of dominos converges to the smaller number log 2 2 0 35 thus even though the region in figure 1 has slightly smaller area than the region in figure 2 the former has far more domino tilings for regions with other shapes neither of these asymptotic formulas may apply in the present paper we consider simply connected regions of arbitrary shape we give an exact formula for the limiting value of the logarithm of the number of tilings per unit area as a function of the shape of the boundary of the region as the size of the region goes to infinity in particular we show that computation of this limit is intimately linked with an understanding of long range variations in the local statistics of random domino tilings such variations can be seen by comparing figures 1 and 2 each of the two tilings is random in the sense that the algorithm pwi that was used to create it generates each of the possible tilings of the region being tiled with the same probability hence one can expect each tiling to be qualitatively typical of the overwhelming majority of tilings of the region in

strong effects of network architecture in the entrainment of coupled oscillator systems random networks of coupled phase oscillators representing an approximation for systems of coupled limit cycle oscillators are considered entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated for a large class of interaction functions we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization however the entrainment is significantly facilitated if the networks are directionally biased i e closer to the feedforward networks furthermore we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes the neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

asymptotic stabilization of two dimensional real analytic systems abstract we investigate the local asymptotic stabilizability of a real analytic control system around an equilibrium point and give necessary and sufficient conditions for local asymptotic stabilization using continuous feedback

hysteresis switching adaptive control of linear multivariable systems this paper presents a model reference adaptive control scheme for deterministic continuous time multivariable systems represented by square strictly proper minimum phase transfer function matrices a typical requirement of existing algorithms is to assume that the zero structure at infinity and the high frequency gain matrix are fully or at least partially known it is well known that these requirements may be very restrictive since in general both the zero structure at infinity and the high frequency gain matrix depend on plant parameters in this paper we show that these restrictive assumptions may be considerably weakened using morse et al s hysteresis switching control strategy 1992 the strategy entails running a finite number of parameter estimators in parallel and using a switching algorithm to select between candidate estimators based on their associated prediction errors hysteresis in the switching algorithm precludes switching arbitrarily rapidly between estimators and all switching ceases within a finite time the results represent a significant step forward in understanding the minimal amount of prior knowledge necessary to design a stabilizing controller for a linear multivariable system

emergence of synchronization in complex networks of interacting dynamical systems abstract we study the emergence of coherence in large complex networks of interacting heterogeneous dynamical systems we show that for a large class of dynamical systems and network topologies there is a critical coupling strength at which the systems undergo a transition from incoherent to coherent behavior we find that the critical coupling strength at which this transition takes place is k c z 1 where z depends only on the uncoupled dynamics of the individual systems on each node while is the largest eigenvalue of the network adjacency matrix thus we achieve a separation of the problem into two parts one depending solely on the node dynamics and one depending solely on network topology

convex design control for practical nonlinear systems this paper describes a new control scheme for approximately optimal control aoc of nonlinear systems convex control design convcd the key idea of convcd is to transform the approximate optimal control problem into a convex semi definite programming sdp problem contrary to the majority of existing aoc designs where the problem that is addressed is to provide a control design which approximates the performance of the optimal controller by increasing the controller complexity the proposed approach addresses a different problem given a controller of fixed complexity it provides a control design that renders the controller as close to the optimal as possible and moreover the resulted closed loop system stable two numerical examples are used to show the effectiveness of the method

asymptotically exact stabilisation for constrained discrete takagisugeno systems via set invariance given a takagisugeno ts system this paper proposes a novel methodology to obtain the state feedback controller guaranteeing asymptotically as a polya related complexity parameter grows the largest membership shape independent possible domain of attraction with contraction rate performance based on polyhedral contractive sets from constrained linear systems literature the resulting controller is valid for any realisation of the memberships as usual in most ts literature for a finite complexity parameter an inner estimate of such largest set is obtained the frontier of such approximation can be understood as the level set of a polyhedral control lyapunov function convergence of a proposed iterative algorithm is asymptotically necessary and sufficient for ts system stabilisation for a high enough value of the complexity parameter any conceivable shape independent lyapunov controller design procedure will yield a proven domain of attraction smaller or equal to the algorithm s output

stability region analysis using polynomial and composite polynomial lyapunov functions and sum of squares programming we propose using bilinear sum of squares programming for obtaining inner bounds of roas for dynamical systems with polynomial vector fields we search for polynomial as well as composite lyapunov functions comprised of pointwise maximums of polynomial functions results for several examples from the literature are presented using the proposed methods and the penbmi solver

the approximation operators with sigmoidal functions the aim of this paper is to investigate the error which results from the method of approximation operators with logarithmic sigmoidal function by means of the method of extending functions a class of feed forward neural network operators is introduced using these operators as approximation tools the upper bounds of errors in uniform norm approximating continuous functions are estimated also a class of quasi interpolation operators with logarithmic sigmoidal function is constructed for approximating continuous functions defined on the total real axis

brief strict lyapunov functions for time varying systems uniformly asymptotically stable periodic time varying systems for which is known a lyapunov function with a derivative along the trajectories non positive and negative definite in the state variable on non empty open intervals of the time are considered for these systems strict lyapunov functions are constructed

geometric variational problems of statistical mechanics and of combinatorics we present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics together with the wulff construction which predicts the shape of the crystals we discuss the construction which exhibits the shape of a typical young diagram and of a typical skyscraper

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn