a hybrid redesign of newton observers in the absence of an exact discrete time model abstract we study the newton observer design developed by moraal and grizzle when the exact discrete time model of the sampled data plant is not known analytically we eliminate the dependence on this exact model with a hybrid reconstruction that makes use of continuous time filters to produce the numerical value of the exact model we then implement the newton method with finite difference and secant approximations for the jacobian despite the continuous time filters the proposed hybrid redesign preserves the sampled data characteristic of the newton observer because it only employs discrete time measurements of the output it also offers flexibility to be implemented with nonuniform or event driven sampling we finally study how a line search scheme can be incorporated in this hybrid newton observer to enlarge the region of convergence

adaptive observer for multiple input multiple output mimo linear time varying systems for joint state parameter estimation in linear time varying ltv multiple input multiple output mimo systems an approach to the design of adaptive observers is proposed it is conceptually simple and computationally efficient its global exponential convergence is established for noise free systems in the presence of noises it is proved that the estimation errors are bounded and converge in the mean to zero if the noises are bounded and have zero means potential applications are fault detection and isolation and adaptive control

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

on the quasilinear elliptic problems with critical sobolev hardy exponents and hardy terms abstract let r n be a smooth bounded domain such that 0 n 3 in this paper we study the critical quasilinear elliptic problems p u u p 2 u x p u p t 2 x t u u q 2 x s u u w 0 1 p with dirichlet boundary condition where p u div u p 2 u 1 p n 0 n p p p 0 0 s t p p q p s p n s n p p t p n t n p p s and p t are the critical sobolev hardy exponents via variational methods we deal with the conditions that ensure the existence of positive solutions for the equation the results depend crucially on the parameters p q s and

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

symmetric solutions for a class of singular biharmonic elliptic systems involving critical exponents this paper deals with a class of singular biharmonic elliptic systems involving critical exponents in a bounded symmetric domain by using the variational method and the symmetric criticality principle of palais we obtain several existence and multiplicity results of g symmetric solutions for the systems

solutions to critical elliptic equations with multi singular inverse square potentials abstract let be an open bounded domain in r n n 3 with smooth boundary we are concerned with the multi singular critical elliptic problem u i 1 k i u x a i 2 q x u 2 2 u u h 0 1 where i r 2 2 n n 2 a i 1 i k and q x is a positive bounded function on using moser iteration we prove the asymptotic behavior of solutions for at points a i 1 i k by exploiting the effect of the coefficient of the critical nonlinearity we by means of a variational method establish the existence of positive and sign changing solutions for problem

a framework for nonlinear sampled data observer design via approximate discrete time models and emulation we study observer design for sampled data nonlinear systems using two approaches i the observer is designed via an approximate discrete time model of the plant ii the observer is designed based on the continuous time plant model and then discretized for sampled data implementation emulation we investigate under what conditions and in what sense these designs achieve convergence for the unknown exact discrete time model we present examples which show that designs that violate our conditions may indeed lead to instability when implemented on the exact model

stable adaptive observers for nonlinear time varying systems an adaptive observer identifier for single input single output observable nonlinear systems that can be transformed to a certain observable canonical form is described sufficient conditions for stability of this observer are provided these conditions are in terms of the structure of the system and canonical form the boundedness of the parameter variations and the sufficient richness of some signals the scope of the canonical form and the use of the observer identifier is motivated by the presentation of applications to time invariant bilinear systems nonlinear systems in phase variable form a biotechnological process and a robot manipulator in each case the specific stability conditions are presented

existence of solutions for singular elliptic systems with critical exponents abstract let 0 be an open bounded domain in r n n 3 and 2 2 n n 2 we consider the following elliptic system of two equations in h 0 1 h 0 1 u t u x 2 2 u 2 u v u v t v x 2 2 u v 2 v v where 0 and 1 satisfy 2 using moser iteration we prove the asymptotic behavior of solutions for at the origin by exploiting the mountain pass theorem we establish the existence of solutions to we also discuss sign changing solutions for in this paper

high gain estimation for nonlinear systems abstract this work is a continuation of 4 where the third author exhibits a high gain exponential observer for miso nonlinear systems affine in the input and observable for any input with continuous dynamics and measurements in this paper we establish stability results for continuous continuous and continuous discrete extended kalman filters derived from the observer of 4

elliptic systems involving the critical exponents and potentials abstract in this paper we investigate a singular elliptic system which involves the critical sobolev exponent and multiple hardy type terms by employing variational methods the existence of its positive solutions is established by the moser iteration method some asymptotic properties of its nontrivial solutions at the singular points are verified

elliptic systems involving critical nonlinearities and different hardy type terms abstract in this paper a singular system of elliptic equations is investigated which involves critical nonlinearities and deferent hardy type terms existence of positive solutions to the system is verified by variational methods and asymptotic properties of solutions at the singular point are established by the moser iteration method it is found that the functions in solutions have different singularities at the singular point

a note on the sign changing solutions to elliptic problems with critical sobolev and hardy terms let rn be a bounded domain such that 0 n 7 2 2nn 2 we obtain existence of sign changing solutions for the dirichlet problem u u x 2 u 2 2u u on u 0 on for suitable positive numbers and

on the singular elliptic systems involving multiple critical sobolev exponents in this paper a singular elliptic system is investigated which involves multiple critical sobolev exponents and hardy type terms by using variational methods and analytical techniques the existence of positive and sign changing solutions to the system is established

limit load and shakedown analysis of plastic structures under stochastic uncertainty abstract problems from plastic analysis are based on the convex linear or linearised yield strength condition and the linear equilibrium equation for the stress state vector in practice one has to take into account stochastic variations of several model parameters hence in order to get robust maximum load factors the structural analysis problem with random parameters must be replaced by an appropriate deterministic substitute problem a direct approach is proposed based on the primary costs for missing carrying capacity and the recourse costs e g costs for repair compensation for weakness within the structure damage failure etc based on the mechanical survival conditions of plasticity theory a quadratic error loss criterion is developed the minimum recourse costs can be determined then by solving an optimisation problem having a quadratic objective function and linear constraints for each vector a of model parameters and each design vector x one obtains then an explicit representation of the best internal load distribution f moreover also the expected recourse costs can be determined explicitly consequently an explicit stochastic nonlinear program results for finding a robust maximal load factor the analytical properties and possible solution procedures are discussed

quasilinear elliptic problems with critical exponents and hardy terms abstract let 0 be an open bounded domain r n n p 2 we are concerned with the multiplicity of positive solutions of p u u p 2 u x p u p 2 u q x u p 2 u u w 0 1 p where p u div u p 2 u 1 p n p np n p 0 n p p p 0 and q x is a nonnegative function on by investigating the effect of the coefficient of the critical nonlinearity we by means of variational method prove the existence of multiple positive solutions

on adaptive observers for state affine systems in this paper the problem of adaptive observer design for the class of state affine systems is discussed the discussion is based on recent results on adaptive observer with exponential rate of convergence obtained for multi input multi output linear time varying systems on the one hand and the well known kalman like design for state affine systems on the other in particular the relationship between both designs is emphasized showing how they can even be equivalent the interest of such an adaptive observer for state affine systems is illustrated by the example of state and parameter estimation for the lorenz chaotic system the observer performances are illustrated via simulation

technical communique continuous discrete adaptive observers for state affine systems the observation of a class of multi input multi output mimo state affine systems with constant unknown parameters and discrete time output measurements is addressed assuming some persistent excitation conditions to hold and the sampling steps to satisfy some boundedness hypotheses system observability is ensured and a class of global exponential observers is synthesized

a systematic approach to adaptive observer synthesis for nonlinear systems geometric techniques of controller design for nonlinear systems have enjoyed great success a serious shortcoming however has been the need for access to full state feedback this paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty an adaptive nonlinear observer is suggested for lipschitz nonlinear systems and the stability of this observer is shown to be related to finding solutions to a quadratic inequality involving two variables a coordinate transformation is used to reformulate this inequality as a linear matrix inequality a systematic algorithm is presented which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible the state estimation errors then are guaranteed to converge to zero asymptotically the convergence of the parameters however is determined by a persistence of excitation type constraint