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

fuzzy convex set based pattern classification for analysis of mammographic microcalcifications abstract there are many different criteria for the comparative analysis of pattern classifiers they include generalization ability computational complexity and understanding of the feature space in some applications such as the medical diagnostic systems it is crucial to use reliable tools whose behavior is always predictable so that the risk of misdiagnosis is minimized in such applications the use of the popular feedforward backpropagation bp neural network algorithm can be seen as questionable this is because it is not inherent for the backpropagation method to analyze the problem s feature space during training which can sometimes result in inadequate decision surfaces a novel convex set based neuro fuzzy algorithm for classification of difficult to diagnose instances of breast cancer is described in this paper with its structural approach to feature space the new method offers rational advantages over the backpropagation algorithm the classification performance computational and structural efficiencies are analyzed and compared with that of the bp network a 20 dimensional set of difficult to diagnose mammographic microcalcifications was used to evaluate the neuro fuzzy pattern classifier nfpc and the bp methods in order to evaluate the learning ability of both methods the relative size of training sets was varied from 40 to 90 the comparative results obtained using receiver operating characteristic roc analysis show that the ability of the convex set based method to infer knowledge was better than that of backpropagation in all of the tests performed making it more suitable for use in real diagnostic systems

speed observation and position feedback stabilization of partially linearizable mechanical systems the problems of speed observation and position feedback stabilization of mechanical systems are addressed in this paper our interest is centered on systems that can be rendered linear in the velocities via a partial change of coordinates it is shown that the class is fully characterized by the solvability of a set of partial differential equations pdes and strictly contains the class studied in the existing literature on linearization for speed observation or control a reduced order globally exponentially stable observer constructed using the immersion and invariance methodology is proposed the design requires the solution of another set of pdes which are shown to be solvable in several practical examples it is also proven that the full order observer with dynamic scaling recently proposed by karagiannis and astolfi obviates the need to solve the latter pdes finally it is shown that the observer can be used in conjunction with an asymptotically stabilizing full state feedback interconnection and damping assignment passivity based controller preserving asymptotic stability

a globally exponentially stable speed observer for a class of mechanical systems experimental and simulation comparison with high gain and sliding mode designs abstractit is shown in the paper that the problem of speed observation for mechanical systems that are partially linearisable via coordinate changes admits a very simple and robust exponentially s

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

adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parametrization in this paper we propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics models of uncertainties are allowed to be nonlinearly parameterized and required to be smooth and monotonic functions of linear functionals of the parameters the mere assumption of existence of nonlinear operator gains for the target dynamics is sufficient to guarantee that system solutions are bounded reach a neighborhood of the target set and the mismatches between the modeled uncertainties and their compensator converge to zero with respect to parameter convergence a standard persistent excitation condition suffices to ensure that it is exponential when a weaker nonlinear version of persistent excitation is satisfied asymptotic convergence is guaranteed the spectrum of possible applications ranges from tyre road slip control to asynchronous message transmission in spiking neural oscillators

estimation of states and parameters for linear systems with nonlinearly parameterized perturbations we consider systems that can be described by a linear part with a nonlinear perturbation where the perturbation is parameterized by a vector of unknown constant parameters under a set of technical assumptions about the perturbation and its relationship to the outputs we present a modular design technique for estimating the system states and the unknown parameters the design consists of a high gain observer that estimates the states of the system together with the full perturbation and a parameter estimator constructed by the designer to invert a nonlinear equation we illustrate the technique on a simulated dc motor with friction

on the existence of a kazantzis kravaris luenberger observer we state sufficient conditions for the existence on a given open set of the extension to nonlinear systems of the luenberger observer as it has been proposed by kazantzis and kravaris we prove it is sufficient to choose the dimension of the system giving the observer less than or equal to 2 twice the dimension of the state to be observed we show that it is sufficient to know only an approximation of the solution of a pde needed for the implementation we establish a link with high gain observers finally we extend our results to systems satisfying an unboundedness observability property

state feedback control of non linear systems a design method for state feedback controllers for single input non linear systems is proposed the method makes use of the transformations of the non linear system into controllable like canonical forms the resulting non linear state feedback is designed in such a way that the eigenvalues of the linearized closed loop model are invariant with respect to any constant operating point the method constitutes an alternative approach to the design methodology recently proposed by baumann and rugh also a review of different transformation methods for non linear systems is presented an example and simulation results of different control strategies are provided to illustrate the design technique

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

geometric criteria for the quasi linearization of the equations of motion of mechanical systems a linear transformation of velocity for a mechanical system is said to quasi linearize the equations of motion of the system if it eliminates all terms quadratic in the velocity it is well known that controller observer synthesis becomes tractable when the dynamics of a mechanical system are in quasi linearized form in this technical note we show that the quasi linearization property is equivalent to the property that the lie algebra of killing vector fields is pointwise equal to the tangent space to the configuration manifold with the riemannian metric induced by the mass tensor of the mechanical system a sufficient condition for this property is that the riemannian manifold be locally symmetric we further show that a necessary and sufficient condition for quasi linearizability on 2 d riemannian manifolds is that the scalar curvature is constant the above results extend the zero riemannian curvature condition that has been extensively applied since its introduction in 1992 moreover the local symmetricity condition and the constant scalar curvature condition can be easily verified using differentiation

consensus based distributed cooperative learning from closed loop neural control systems in this paper the neural tracking problem is addressed for a group of uncertain nonlinear systems where the system structures are identical but the reference signals are different this paper focuses on studying the learning capability of neural networks nns during the control process first we propose a novel control scheme called distributed cooperative learning dcl control scheme by establishing the communication topology among adaptive laws of nn weights to share their learned knowledge online it is further proved that if the communication topology is undirected and connected all estimated weights of nns can converge to small neighborhoods around their optimal values over a domain consisting of the union of all state orbits second as a corollary it is shown that the conclusion on the deterministic learning still holds in the decentralized adaptive neural control scheme where however the estimated weights of nns just converge to small neighborhoods of the optimal values along their own state orbits thus the learned controllers obtained by dcl scheme have the better generalization capability than ones obtained by decentralized learning method a simulation example is provided to verify the effectiveness and advantages of the control schemes proposed in this paper

existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations in connection with the maximizing problem for the functional r u u lq u lp in w01 p 0 we consider the equation div u p 2 u x u q 2 u x x 1 p resp q p e has no nontrivial resp nonnegative nontrivial solution belonging to the class p u w01 p lq xi u q 2u lp p 1 i 1 2 n w01 p provided that is star shaped the crucial point of the proof of our result is to obtain an l estimate of weak solutions and to verify a certain pohozaev type inequality for weak solutions belonging to p

on adaptive control of nonlinearly parameterized nonlinear systems towards a constructive procedure abstract a new framework to design immersion and invariance adaptive controllers for nonlinearly parameterized nonlinear systems was recently proposed by the authors the key step is the construction of a monotone mapping via a suitable selection of a controller tuning function which has to satisfy some integrability conditions this translates into the need to solve a partial differential equation pde in this paper this result is extended providing some answers to the questions of characterization of monotonizable systems and solvability of the pde first adding to the design a nonlinear dynamic scaling we obviate the need to solve the pde second for the case of factorizable nonlinearities the following results are established i it is shown that the monotonicity condition is satisfied if a linear matrix inequality is feasible ii directly verifiable involutivity conditions that ensure the solution of the pde are presented iii an explicit formula for the required tuning function is given provided the regressor matrix satisfies some rank conditions hence adding a dynamic scaling this yields a constructive solution to the problem

positive solutions for a class of equations with a p laplace like operator and weights abstract in this paper we will study the problem of existence of positive solutions to the problem d a r u b r g u 0 a e in 0 r lim r 0 a r u r 0 u r 0 where is an odd increasing homeomorphism of r and g c r is such that g z 0 for all z 0 with g 0 0 the functions a and b that we will refer to as weight functions satisfy a r 0 b r 0 for all r 0 r and are such that a b c 1 0 r l 1 0 r if has the form z z m z and a r r n 1 a r b r r n 1 b r n 2 then solutions of problem d provide solutions with radial symmetry for the problem p div a x m u u b x g u 0 x u 0 x where b 0 r denotes the ball with center 0 and radius r 0 in r n

relaxing the conditions for parameter estimation based observers of nonlinear systems via signal injection parameter estimation based observers are a new kind of state reconstruction methods where the state observation task is translated into an on line parameter estimation problem a key step for its application is the transformation of the system dynamics into a particular cascade form which involves the solution of a partial differential equation that moreover should satisfy some injective requirement in this note we use a recently proposed technique of signal injection to generate new outputs and simplify these tasks in this way we make this observer applicable to a wider class of nonlinear systems even with indistinguishable states the application of the proposed approach is illustrated with the design of a novel sensorless controller for magnetic levitation systems

adaptive observers and parameter estimation for a class of systems nonlinear in the parameters we consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations a solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time reconstruction of state and parameter values is based on the concepts of weakly attracting sets and non uniform convergence and is subjected to persistency of excitation conditions in the absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes in this respect the proposed method constitutes a generalization of the conventional canonical adaptive observer design

convergence analysis of the extended kalman filter used as an observer for nonlinear deterministic discrete time systems in this paper convergence analysis of the extended kalman filter ekf when used as an observer for nonlinear deterministic discrete time systems is presented based on a new formulation of the first order linearization technique sufficient conditions to ensure local asymptotic convergence are established furthermore it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified ekf significantly the efficiency of this approach compared to the classical version of the ekf is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete time systems

a robust nonlinear position observer for synchronous motors with relaxed excitation conditions abstracta robust nonlinear and globally convergent rotor position observer for surface mounted permanent magnet synchronous motors was recently proposed by the authors the key feature of this observer is that it requires only the knowledge of the motor s resistance and inductance using some particular properties of the mathematical model it is shown that the problem of state observation can be translated into one of estimation of two constant parameters which is carried out with a standard gradient algorithm in this work we propose to replace this estimator with a new one called dynamic regressor extension and mixing which has the following advantages with respect to gradient estimators 1 the stringent persistence of excitation pe condition of the regressor is not necessary to ensure parameter convergence 2 the latter is guaranteed requiring instead a non square integrability condition that has a clear physical meaning in terms of signal energy 3 if the regressor is pe the new observer

multiple time scalings of a multi output observer form time scalings in the multi output observer form for uncontrolled nonlinear continuous time systems are considered in this technical note it is the multi output version of an existing single input result time scaling broadens the class of systems which admits an exact error linearization observer design by including time scaling transformations the existence conditions of the time scaling transformation and the change of state coordinates to time scaled observer form are provided

quantum neural networks qnns inherently fuzzy feedforward neural networks this paper introduces quantum neural networks qnns a class of feedforward neural networks ffnns inherently capable of estimating the structure of a feature space in the form of fuzzy sets the hidden units of these networks develop quantized representations of the sample information provided by the training data set in various graded levels of certainty unlike other approaches attempting to merge fuzzy logic and neural networks qnns can be used in pattern classification problems without any restricting assumptions such as the availability of a priori knowledge or desired membership profile convexity of classes a limited number of classes etc experimental results presented here show that qnns are capable of recognizing structures in data a property that conventional ffnns with sigmoidal hidden units lack

dynamic observer error linearization in this paper a new framework of observer error linearization problem is proposed the main idea of our approach is twofold the one is to introduce an auxiliary dynamics whose input is the system output and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics it is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output it is also shown that whenever an n dimensional system is immersible into an n d dimensional linear system up to an output injection then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics moreover we show that the converse is not true by providing a counterexample which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method

adaptive state observers using dynamic regressor extension and mixing abstract in this paper we propose an adaptive state observer for a class of nonlinear systems with unknown parameters assuming that the system variables satisfy an algebraic constraint a linear regression involving unknown parameters and unmeasurable states is established the design proceeds adopting a gradient descent approach to minimize a quadratic criterion that is suggested by this regression to separate the problems of state and parameter estimation we use the recently proposed dynamic regressor extension and mixing approach whose main feature is that it allows to generate out of an n dimensional linear vector regression n scalar regression models moreover under a weak interval excitation assumption it ensures finite time parameter convergence it is shown that the proposed observer is applicable to several practically interesting physical systems

non zero sum nash q learning for unknown deterministic continuous time linear systems this work proposes a novel q learning algorithm to solve the problem of non zero sum nash games of linear time invariant systems with n players control inputs and centralized uncertain unknown dynamics we first formulate the q function of each player as a parametrization of the state and all other the control inputs or players an integral reinforcement learning approach is used to develop a model free structure of n actors n critics to estimate the parameters of the n coupled q functions online while also guaranteeing closed loop stability and convergence of the control policies to a nash equilibrium a 4th order simulation example with five players is presented to show the efficacy of the proposed approach

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

brief paper observer forms for perspective systems the estimation of three dimensional position information from two dimensional images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system the multi output state estimation problem has been treated by several authors using methods for nonlinear observer design this paper shows that a perspective system can be transformed to two observer forms and provides constructive methods for arriving at the transformations these observer forms lead to straightforward observer designs first it is shown that using an output transformation the system admits an observer form which leads to an observer with linear error dynamics a second observer design is based on a time scaled block triangular form both designs assume a commonly used observability condition the designs are demonstrated in simulation

technical communique explicit convergence rates for mrac type systems it is well known since many years ago that for the linear time varying system email protected ae b t q email protected b t e with a hurwitz and b t bounded and globally lipschitz it is necessary and sufficient for global exponential stability that b t satisfy the so called persistency of excitation condition in this note we revisit this question and provide explicit bounds for the convergence rate and on the overshoot of the transient behaviour of the solutions e t q t as functions of the richness of b we believe that the result that we present is useful since knowing convergence rates aids in the construction of converse lyapunov functions moreover the type of systems that we study here appear for instance in model reference adaptive control mrac

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

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

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

infinitely many radially symmetric solutions for a quasilinear elliptic problem in a ball the authors improve the results of struwe under the hypothesis that f ismerely a locally lipschitz function they are able to deal with cases wherethe growth of f exceeds the sobolev limit exponent in fact their resultssuggest that it is sufficient to have the growth conditions only for u 0 orfor u 0 oru 0 0 our aim here is to extend the results of castro and kurepa to theproblem e

incorporating fuzzy membership functions into the perceptron algorithm the perceptron algorithm one of the class of gradient descent techniques has been widely used in pattern recognition to determine linear decision boundaries while this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable it exhibits erratic behavior if the data are not linearly separable fuzzy set theory is introduced into the perceptron algorithm to produce a fuzzy algorithm which ameliorates the convergence problem in the nonseparable case it is shown that the fuzzy perceptron like its crisp counterpart converges in the separable case a method of generating membership functions is developed and experimental results comparing the crisp to the fuzzy perceptron are presented

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

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

a state observer for nonlinear dynamical systems the problem of state observation for nonlinear systems is of main importance in automatic control in recent years many contributions have been presented in literature that solve the design problem for classes of nonlinear systems most works can be roughly classi ed into two categories in one the geometrical properties of vector elds de ning the system are exploited and therefore mathematical tools of the di erential geometry are extensively employed in the other one the functional properties of the input state and state output maps which de ne the system are mainly used while the geometrical methods often provide a general solution of the problem for systems that belong to restricted classes characterized by geometrical properties 1 2 3 4 5 6 7 13 14 17 18 19 the second approach gives solutions for classes of nonlinear systems whose geometrical nature is not investigated and only macroscopic parameters norms gains lipschitz constants and so on are involved in the design procedure 8 9 11 12 21 one main problem in state observation for nonlinear systems is that the property of driftobservability does not imply observability for any input function as shown in 16 19 thus it is interesting to investigate when the drift observability property allows the solution of the state observation problem nding conditions that restricts the class of input functions due to the mathematical tools employed this work may be considered as belonging to both the categories above mentioned in this paper nonlinear systems of the form

adaptive control of continuous time systems with convex concave parametrization this paper deals with adaptive control of a class of nonlinear dynamic systems with nonlinear parametrization in this class the state variables are assumed to be accessible and the nonlinearity in the parameters is assumed to be either convex or concave by introducing a tuning function and an adaptive law based on a min max strategy it is shown that such a class of dynamic systems can be adaptively controlled in a stable manner global boundedness of the overall adaptive system and tracking to within a desired precision are established with the new adaptive controller the proposed controller is applied to a precise positioning problem in the presence of nonlinearly parametrized friction dynamics it is shown that the controller leads to position errors and friction compensation that are orders of magnitude better than those based on estimation of linear parametrizations the fact that the new parameter estimation strategy used is distinct from the traditionally used gradient schemes permits the expansion of the scope of adaptive control which has been restricted hitherto in most cases to systems with linear parametrization

a parameter estimation approach to state observation of nonlinear systems abstract a novel approach to the problem of partial state estimation of nonlinear systems is proposed the main idea is to translate the state estimation problem into one of estimation of constant unknown parameters related to the systems initial conditions the class of systems for which the method is applicable is identified via two assumptions related to the transformability of the system into a suitable cascaded form and our ability to estimate the unknown parameters the first condition involves the solvability of a partial differential equation while the second one requires some persistency of excitation like conditions the proposed observer is shown to be applicable to position estimation of a class of electromechanical systems for the reconstruction of the state of power converters and for speed observation of a class of mechanical systems

lyapunov functions for persistently excited cascaded time varying systems application to consensus we present some results on stability of linear time varying systems with particular structures such systems appear in diverse problems which include the analysis of adaptive systems persistently excited observers and consensus of systems interconnected through time varying links the originality of our statements rely in the fact that we provide smooth strict lyapunov functions hence our proofs are constructive and direct moreover we establish uniform global exponential stability with explicit stability and decay estimates for illustration we address a brief but representative case study of consensus of lagrangian systems interconnected through unreliable links

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

neurofuzzy networks with nonlinear quantum learning nonlinear quantum processing allows the solution of an optimization problem by the exhaustive search on all its possible solutions hence it can replace advantageously the algorithms for learning from a training set in order to pursue this possibility in the case of neurofuzzy networks we propose in this paper to tailor their architectures to the requirements of quantum processing in particular superposition is introduced to pursue parallelism and entanglement to associate the network performance with each solution present in the superposition two aspects of the proposed method are considered in detail the binary structure of membership functions and fuzzy reasoning and the use of a particular nonlinear quantum algorithm for extracting the optimal neurofuzzy network by exhaustive search

nonlinear observer design for state and disturbance estimation a new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed the nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in n kazantzis c kravaris nonlinear observer design using lyapunov s auxiliary theorem systems control lett 34 1998 241 a j krener m xiao nonlinear observer design in the siegel domain siam j control optim 41 2002 932 for state estimation purposes only from a mathematical standpoint the problem under consideration is addressed through a system of first order singular pdes for which a rather general set of solvability conditions is derived a nonlinear observer is then designed with a state dependent gain that is computed from the solution of the system of singular pdes under the aforementioned conditions both state and disturbance estimation errors converge to zero with assignable rates the convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor

immersion and invariance adaptive control of nonlinearly parameterized nonlinear systems a new framework to design adaptive controllers for nonlinearly parameterized systems is proposed in this technical note the key step is the construction of a monotone mapping which explicitly depends on some of the estimator tuning parameters convexity that is related to monotonicity has been explored by several authors the property is assumed a priori and is useful for the design only in some region of state space which is completed switching the controller in our approach monotonicity can be used in the whole state space and moreover is enforced by the designer effectively becoming a synthesis tool one consequence of these features is that the controller does not rely on state dependent switching in order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced immersion and invariance approach

existence and uniqueness for a class of quasilinear elliptic boundary value problems abstract we prove existence and uniqueness of positive solutions for the boundary value problem r n 1 u r n 1 f u u 0 u 1 0 where x x p 2x f x xp 1 may not be decreasing on 0 and is a large parameter

brief paper redesign of adaptive observers for improved parameter identification in nonlinear systems we propose a method for redesigning adaptive observers for nonlinear systems the redesign uses an adaptive law that is based on delayed observers this increases the computational burden but gives significantly better parameter identification and robustness properties in particular given that a special persistency of excitation condition is satisfied we prove uniform global asymptotic stability and semi global exponential stability of the origin of the state and parameter estimation error and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics for initial conditions with a known upper bound we prove tunable exponential convergence rate to illustrate the use of the proposed method we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system the simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design

on sufficient conditions for the existence of radially symmetric solutions of the p laplace equation abstract we consider the dirichlet problem for the p laplace equation with a nonlinear source new a priori estimates for solutions are established in particular we obtain an explicit formula which shows the dependence of the existence of a weak bounded radially symmetric solution on the dimension of the problem

symbolic computing of nonlinear observable and observer forms observer design for highly nonlinear dynamics is an important issue particularly when the locally observable dynamics are not linearly observable in such circumstances the ability to reduce the system to observable or observer form is a useful first step to observer design we describe and illustrate symbolic computing tools to do that

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

a nonlinear position and attitude observer on se 3 using landmark measurements this paper addresses the problem of position and attitude estimation based on landmark readings and velocity measurements a derivation of a nonlinear observer on se 3 is presented using a lyapunov function conveniently expressed as a function of the difference between the estimated and the measured landmark coordinates the resulting feedback laws are explicit functions of the landmark measurements and velocity readings exploiting the sensor information directly in the observer the proposed observer yields almost global asymptotic stabilization of the position and attitude errors and exponential convergence in any closed ball inside the region of attraction also it is shown that the asymptotic convergence of the estimation error trajectories is shaped by the landmark geometry and observer design parameters the problem of non ideal velocity readings is also considered and the observer is augmented to compensate for bias in the angular and linear velocity measurements the resulting position attitude and bias estimation errors are shown to converge exponentially fast to the desired equilibrium points for bounded initial estimation errors simulation results are presented to illustrate the stability and convergence properties of the observer

a block triangular form for nonlinear observer design this note reconsiders existence conditions for an established block triangular form btf for a broad class of multi output nonlinear systems systems transformable into btf coordinates allow for decentralized observer design performed subsystem at a time effectively treating upper subsystem states as measurements sufficient conditions are given to ensure that the output is linear in btf coordinates an example illustrates the btf construction and a typical observer design

possibility and necessity pattern classification using neural networks abstract we propose two learning algorithms of neural networks for two group discriminant problems from the view point of possibility and necessity one algorithm corresponds to the possibility analysis and the other to the necessity analysis the proposed algorithms are similar to the back propagation algorithm and the difference stems from a formulation of a cost function to be minimized in each algorithm each cost function of the proposed algorithms is the weighted sum of squared errors that is the sum of squared errors with different penalties when we discuss the possibility of group 1 the penalty for the squared errors relating to the patterns in group 1 is greater than that of group 2 this means that in the possibility analysis of group 1 we attach greater importance to the patterns in group 1 than to those in group 2 on the other hand when we discuss the necessity of group 1 the penalty for the squared errors relating to the patterns in group 2 is greater than that of group 1

quantum learning for neural associative memories abstract quantum information processing in neural structures results in an exponential increase of patterns storage capacity and can explain the extensive memorization and inferencing capabilities of humans an example can be found in neural associative memories if the synaptic weights are taken to be fuzzy variables in that case the weights update is carried out with the use of a fuzzy learning algorithm which satisfies basic postulates of quantum mechanics the resulting weight matrix can be decomposed into a superposition of associative memories thus the fundamental memory patterns attractors can be mapped into different vector spaces which are related to each other via unitary rotations quantum learning increases the storage capacity of associative memories by a factor of 2 n where n is the number of neurons

on the existence of sign changing bound state solutions of a quasilinear equation abstract in this paper we establish the existence of bound state solutions having a prescribed number of sign changes for p m u f u 0 x r n n m 1 where m u u m 2 u our result is new even for the case of the laplacian m 2

on a class of semilinear elliptic systems abstract this paper deals with the existence of positive solutions to a dirichlet problem for the superlinear elliptic system u f v v g u on a ball where is a positive parameter and f 0 g 0 may be negative

infinitely many radial solutions for a p laplacian problem p superlinear at the origin abstract we prove the existence of infinitely many radial solutions for a p laplacian dirichlet problem which is p superlinear at the origin the main tool that we use is the shooting method we extend for more general nonlinearities the results of j iaia in j iaia radial solutions to a p laplacian dirichlet problem appl anal 58 1995 335 350 previous developments require a behavior of the nonlinearity at zero and infinity while our main result only needs a condition of the nonlinearity at zero

reformulated radial basis neural networks trained by gradient descent this paper presents an axiomatic approach for constructing radial basis function rbf neural networks this approach results in a broad variety of admissible rbf models including those employing gaussian rbfs the form of the rbfs is determined by a generator function new rbf models can be developed according to the proposed approach by selecting generator functions other than exponential ones which lead to gaussian rbfs this paper also proposes a supervised learning algorithm based on gradient descent for training reformulated rbf neural networks constructed using the proposed approach a sensitivity analysis of the proposed algorithm relates the properties of rbfs with the convergence of gradient descent learning experiments involving a variety of reformulated rbf networks generated by linear and exponential generator functions indicate that gradient descent learning is simple easily implementable and produces rbf networks that perform considerably better than conventional rbf models trained by existing algorithms

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

design of asymptotic estimators an approach based on neural networks and nonlinear programming a methodology to design state estimators for a class of nonlinear continuous time dynamic systems that is based on neural networks and nonlinear programming is proposed the estimator has the structure of a luenberger observer with a linear gain and a parameterized in general nonlinear function whose argument is an innovation term representing the difference between the current measurement and its prediction the problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error toward this end if a neural network is used to take on this function the parameters i e the neural weights are chosen together with the gain by constraining the derivative of a quadratic lyapunov function for the estimation error to be negative definite on a given compact set it is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points the gain is determined by solving a lyapunov equation the neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid point constraints that are not satisfied techniques based on low discrepancy sequences are applied to deal with a small number of sampling points and hence to reduce the computational burden required to optimize the parameters numerical results are reported and comparisons with those obtained by the extended kalman filter are made

on feedback equivalence to port controlled hamiltonian systems in the last few years port controlled hamiltonian pch systems have emerged as an interesting class of nonlinear models suitable for a large number of physical applications in this paper we study the question of feedback equivalence of nonlinear systems to pch systems more precisely we give conditions under which a general nonlinear system can be transformed into a pch system via static state feedback we consider the two extreme cases where the target pch system is completely a priori fixed or completely free as well as the case where it is only partially predetermined when the energy function is free a set of partial differential equations needs to be solved on the other hand if it is fixed we have to deal with a set of algebraic equations in the former case we give some verifiable necessary and sufficient conditions for solvability as a by product of our analysis we obtain some stabilization results for nonlinear systems

positive radial solutions for dirichlet problems with mean curvature operators in minkowski space abstract in this paper by using leray schauder degree arguments and critical point theory for convex lower semicontinuous perturbations of c 1 functionals we obtain existence of classical positive radial solutions for dirichlet problems of type div v 1 v 2 f x v 0 in b r v 0 on b r here b r x r n x r and f 0 r 0 r is a continuous function which is positive on 0 r 0

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

on the state observation and output feedback problems for nonlinear uncertain dynamic systems abstract in this paper we examine the problems of state observation and state trajectory control by output feedback for the class of non linear systems in 3 11 we begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is globally exponentially stable ges we then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the ges sense specific time varying bounds on the observation error and the state trajectory are also developed revealing how the corresponding observer or control parameters can be adjusted to improve the system performance

observability through delayed measurements a new approach to state observers design an original approach for the construction of state observers for dynamic systems is presented in this article new notions of observability delay observability and delay drift observability useful for the development of the observer equations and for the convergence proof are introduced and compared with other standard observability concepts in particular it is shown that delay drift observability is an extension of the well known drift observability property the construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form which is a common feature of many other approaches a numerical example is reported where a system that is not drift observable is considered in this case the proposed observer is easily constructed and performs well

observers for a class of lipschitz systems with extension to h performance analysis abstract in this paper observer design for a class of lipschitz nonlinear dynamical systems is investigated one of the main contributions lies in the use of the differential mean value theorem dmvt which allows transforming the nonlinear error dynamics into a linear parameter varying lpv system this has the advantage of introducing a general lipschitz like condition on the jacobian matrix for differentiable systems to ensure asymptotic convergence in both continuous and discrete time systems such sufficient conditions expressed in terms of linear matrix inequalities lmis are established an extension to h filtering design is obtained also for systems with nonlinear outputs a comparison with respect to the observer method of gauthier et al a simple observer for nonlinear systems applications to bioreactors ieee trans automat control 37 6 1992 875 880 is presented to show that the proposed approach avoids high gain for a class of triangular globally lipschitz systems in the last section academic examples are given to show the performances and some limits of the proposed approach the last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain

technical communique an observation algorithm for nonlinear systems with unknown inputs this paper deals with the design of unknown input observers for nonlinear systems an algorithm which determines if the state and the unknown input of the system can be recovered in finite time is introduced this algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers the proposed method is useful to relax some restrictive conditions of the existing nonlinear unknown input observer design procedures

generalised observer design for dissipative lipschitz nonlinear systems in the presence of measurement noise this paper presents two novel observer concepts first it develops a globally exponentially stable nonlinear observer for noise free dissipative nonlinear systems second for a dissipative nonlinear system with measurement noise the paper develops an observer to guarantee a desired performance namely an upper limit on the ratio of the square of the weighted l2 norm of the error to the square of the weighted l2 norm of the measurement noise the necessary and sufficient conditions for both observers are reformulated as algebraic riccati equations ares so that standard solvers can be utilised in addition the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the are and hence the observer design problem has a solution the use of the methodology developed in this paper is demonstrated through illustrative examples in literature there is no previous observer for dissipative system that provides both necessary and sufficient condition

existence and uniqueness of fast decay entire solutions of quasilinear elliptic equations we prove the existence and uniqueness of fast decay solutions and clarify the structure of positive radial solutions of the quasilinear elliptic equation mu f u 0 in rn where m denotes the m laplace operator and f has a supercritical growth for small u 0 and a subcritical growth for large u our proofs use only elementary arguments based on several variational identities and a maximum principle of peletier and serrin