design of state detectors for nonlinear systems using symmetries and semi invariants two techniques are proposed for the design of asymptotic state detectors for nonlinear systems both in the continuous time and discrete time cases the first technique allows one to design linear state detectors for nonlinear systems belonging to a given class which is studied and characterized in the paper the second technique extends the ideas of the first by using semi invariants to compute invariant sets and study their stability

scalar curvature of a metric with unit volume the problem of finding riemannian metrics on a closed manifold with prescribed scalar curvature function is now fairly well understood from the works of kazdan and warner in 1970 s 10 and references cited in it in this paper we shall consider the same problem under a constraint on the volume for this purpose it is useful to introduce an invariant p m of a smooth closed manifold m which will be called the yamabe number of m defined as the supremum of m c of all conformal classes c of riemannian metrics on m

aubin s lemma for the yamabe constants of infinite coverings and a positive mass theorem aubin s lemma says that if the yamabe constant of a closed conformal manifold m c is positive then it is strictly less than the yamabe constant of any of its non trivial finite conformal coverings we generalize this lemma to the one for the yamabe constant of any m c of its infinite conformal coverings provided that 1 m has a descending chain of finite index subgroups tending to 1 m moreover if the covering m is normal the limit of the yamabe constants of the finite conformal coverings associated to the descending chain is equal to that of m c for the proof of this we also establish a version of positive mass theorem for a specific class of asymptotically flat manifolds with singularities

existence theorems for nonselfadjoint semilinear elliptic boundary value problems where e is a real elliptic linear differential operator in a bounded domain g of r with a given system of linear homogeneous conditions say bx 0 on the boundary ag of g and where n is a nemitsky type nonnecessarily linear operator we shall make use here of the alternative method and particularly we shall make use for the elliptic case of new remarks these remarks suggest that both the auxiliary and bifurcation equations can be analyzed under different topologies and by a more specific construction of the operator s y0 x0 actually some of these remarks have been already used implicitly in previous papers on the semilinear wave equation in r2 cesari and kannan 5 cesari and pucci 6 for selfadjoint elliptic problems landesman and lazer 9 proved also by the alternative method a remarkable theorem which was then extended by williams 14 by the same method and by others by different arguments later shaw 12 proved again by the alternative method that landesman s and lazer s theorem extends even to nonselfadjoint problems with equal fredholm indices and whose eigenfunctions share regions of positivity and negativity with their corresponding adjoint eigenfunctions in the present paper we definitely aim at elliptic problems which are not necessarily selfadjoint and do not necessarily satisfy shaw s requirements the sufficient conditions we obtain are more quantitative in character and concern the cases nx f t g t d x and nx f f g t x t t e g however as we show by examples for the case nx f t g t x t our sufficient conditions for existence allow a great freedom on g on which no monotonicity is required

a block triangular observer form for non linear observer design this paper discusses observer design for unforced non linear multi output systems using a block triangular observer form btof the btof allows an established exact error linearization observer design method to be generalized to a larger class of multi output systems observer design proceeds in a decentralized manner or subsystem at a time starting with the uppermost subsystem designs for each subsystem effectively treat upper subsystem states as known measurements and are relatively simple given their reduced dimension exponential error stability results are given new necessary and sufficient existence conditions are given for the btof examples illustrate the construction of the btof coordinates and the advantages of a btof based design compared to a generally applicable method

global periodic solutions of the nonlinear wave equation on considere le probleme u tt u t g u t r 2 u t t u t u t t t t t t t ou u et sont des fonctions scalaires de r 2 et g une fonction scalaire sur r on suppose que g et sont continues et on determine des conditions suffisantes sous forme d inegalites pour garantir que ce probleme a des solutions continues

smooth yamabe invariant and surgery we prove a surgery formula for the smooth yamabe invariant sigma m of a compact manifold m assume that n is obtained from m by surgery of codimension at least 3 we prove the existence of a positive number lambda n depending only on the dimension n of m such that sigma n geq min sigma m lambda n

a stable neural network based observer with application to flexible joint manipulators a stable neural network nn based observer for general multivariable nonlinear systems is presented in this paper unlike most previous neural network observers the proposed observer uses a nonlinear in parameters neural network nlpnn therefore it can be applied to systems with higher degrees of nonlinearity without any a priori knowledge about system dynamics the learning rule for the neural network is a novel approach based on the modified backpropagation bp algorithm an e modification term is added to guarantee robustness of the observer no strictly positive real spr or any other strong assumption is imposed on the proposed approach the stability of the recurrent neural network observer is shown by lyapunov s direct method simulation results for a flexible joint manipulator are presented to demonstrate the enhanced performance achieved by utilizing the proposed neural network observer

high gain observers in the state and estimation of robots having elastic joints the paper deals with the state and parameter estimation of robots having elastic joints the estimation of the unknown parameters of the robot is reduced to the estimation of its state variables by a state space immersion the luenberger observer is used in the state estimation of the extended robot model the use of high gains is studied in the cancellation of nonlinearities in order to simplify the observer design the high gain induces a time scale separation between the robot model and the observer and therefore the singular perturbation theory can be used in the stability analysis of the estimate error dynamics in particular it is shown that the error dynamics reaches the stable equilibrium in a very fast transient ensuring that the slow dynamics of the observer is just that of the given robot

moduli spaces of critical riemannian metrics in dimension four abstract we obtain a compactness result for various classes of riemannian metrics in dimension four in particular our method applies to anti self dual metrics kahler metrics with constant scalar curvature and metrics with harmonic curvature with certain geometric non collapsing assumptions the moduli space can be compactified by adding metrics with orbifold like singularities similar results were obtained for einstein metrics in j amer math soc 2 3 1989 455 invent math 97 2 1989 313 invent math 101 1 1990 101 but our analysis differs substantially from the einstein case in that we do not assume any pointwise ricci curvature bound

a new method for linearizing non linear systems the pseudolinearization consider the single input non linear system x f x u it has been shown that under mild conditions there exist transformations z t x v s x u such that in the z space the linear tangent model is independent of the operating point a constructive procedure to obtain the above transformations is described this new method is computationally attractive and effective in many practical cases

discrete time observer error linearizability via restricted dynamic systems in this technical note we define the observer error linearization problem of a discrete time autonomous nonlinear system via a restricted dynamic system this is the dual to restricted dynamic feedback linearization in a loose sense necessary and sufficient conditions for this problem are obtained in terms of the index

neural network observer based optimal control for unknown nonlinear systems using adaptive dynamic programming in this paper an observer based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming adp algorithm first a neural network nn observer is designed to estimate system states then based on the observed states a neuro controller is constructed via adp method to obtain the optimal control in this design two nn structures are used a three layer nn is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics and a critic nn is employed to approximate the value function the optimal control law is computed using the critic nn and the observer nn uniform ultimate boundedness of the closed loop system is guaranteed the actor critic and observer structures are all implemented in real time continuously and simultaneously finally simulation results are presented to demonstrate the effectiveness of the proposed control scheme

classification of prime 3 manifolds with σ invariant greater than rp 3 in this paper we compute the invariants sometimes also called the smooth yamabe invariants of rp 3 and rp 2 s 1 which are equal and show that the only prime 3 manifolds with larger invariants are s 3 s 2 s 1 and s 2 s 1 the nonorientable s 2 bundle over s 1 more generally we show that any 3 manifold with invariant greater than rp 3 is either s 3 a connect sum with an s 2 bundle over s 1 or has more than one nonorientable prime compo

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input abstract the transformation of nonlinear multi input multi output systems x f x u y h x u into an observer canonical form with reduced dependency on derivatives of the input is studied necessary and sufficient conditions for its existence and a straightforward algorithm for obtaining the canonical model are derived the proposed method involves the solution of a nonlinear algebraic equation system and systems of first order linear partial differential equations the nonlinear canonical form obtained permits global observer error linearization and it is a stage in the design of nonlinear observers the method is illustrated by an example

partial state observers for nonlinear systems this note deals with the design of reduced order observers for a class of nonlinear systems the order reduction of the observer is achieved by only estimating a required partial set of the state vector necessary and sufficient conditions are derived for the existence of reduced order observers an observer design procedure based on linear matrix inequalities is given a numerical example is given to illustrate the design method

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

input output linearization approach to state observer design for nonlinear system presents a state observer for a class of nonlinear systems based on the input output linearization while the previous result presented state observers for nonlinear systems of full relative degree we proposed a procedure fur the design of nonlinear state observers which do not require the hypothesis of full relative degree assuming that there exists a global state observer for internal dynamics and that some functions are globally lipschitz we can design a globally convergent state observer it is also shown that if the zero dynamics are locally exponentially stable then there exists a local state observer an example is given to illustrate the proposed design of nonlinear state observers

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

the extended luenberger observer for nonlinear systems abstract for nonlinear single input single output systems dot x f x u y h x u the relationships for a state transformation into the nonlinear observer canonical form are developed it is possible to dimension a nonlinear observer by an eigenvalue assignment without solving the nonlinear partial differential equations for the transformation if the transformed nonlinearities are linearized about the reconstructed state with reference to the extended kalman filter algorithm this nonlinear observer design is called the extended luenberger observer

periodic solutions of nonlinear wave equations on obtient des conditions suffisantes pour l existence de solutions doublement periodiques de l equation d onde non lineaire u ts f t s u u t t s u t s u t s t ou f est une fonction continue donnee dans r 3 et f est t periodique en t et s

reduced order observer in the sliding mode control of nonlinear nonaffine systems the note considers the variable structure control of nonlinear known nonaffine systems when the state vector is not completely available and the use of observers is required the strategy of introducing integrators in the input channel is exploited to enlarge the class of tractable control systems a new reduced order observer is proposed and conditions are found under which it is proven the convergence to the unique ideal solution of both system and observer the control problem is solved by forcing a sliding regime for the observer while satisfying an exponential stability criterion for the observation error state equation

an approximate observer for a class of nonlinear systems abstract for a class of nonlinear multi input multi output systems an approximate observer is derived the design utilizes a change of coordinates by which the error differential equation is transformed in the observable canonical form neglecting higher order terms with respect to the set of operating points the note is completed by an example referred to elastic robots

proof of the positive mass theorem ii the positive mass theorem states that for a nontrivial isolated physical system the total energy which includes contributions from both matter and gravitation is positive this assertion was demonstrated in our previous paper in the important case when the space time admits a maximal slice here this assumption is removed and the general theorem is demonstrated abstracts of the results of this paper appeared in 11 and 13

a semilinear elliptic problem which is not selfadjoint cesari 7 i in a preceding paper established conditions sufficient that a semilinear elliptic boundary value problem possibly not selfadjoint shall have a solution

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

brief paper full order observer design for a class of port hamiltonian systems we consider a special class of port hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full order observers using a passivity based approach the essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state space on which the state estimation error is zero we first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state space and then perform a partial state feedback passivation which leads to the construction of the observer we then illustrate this observer design procedure on two physical examples the magnetic levitation system and the inverted pendulum on the cart system

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

a hybrid scheme for reducing peaking in high gain observers for a class of nonlinear systems for a family of nonlinearly interconnected second order plants we propose a hybrid modification of the well known high gain observer design which leads to guaranteed asymptotic stability properties of the error dynamics as well as exhibiting significantly reduced peaking the hybrid modification results in suitable jumps of the observer state which therefore corresponds to a discontinuous function of ordinary time the jump conditions depend on the plant output and on extra states incorporated in the observer that evolve according to some suitable combination of the output error and of its integral our result is illustrated on a well known case study taken from the literature and also on a planar robot with rigid links

a deformation of flat conformal structures we consider deformations of flat conformal structures from a viewpoint of connected sum decomposition of conformally flat manifolds

nonlinear second order elliptic partial differential equations at resonance on etudie la resolubilite de problemes aux valeurs limites pour des equations aux derivees partielles elliptiques d ordre 2 semi lineaires de type resonance dans lesquelles la perturbation non lineaire ne satisfait pas necessairement la condition de landesman lazer ou l hypothese de monotonicite

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package