observer design using a generalized time scaled block triangular observer form this paper presents an observer design for uncontrolled nonlinear multi output continuous time systems based on a time scaled block triangular observer form tbtof the tbtof generalizes an established block triangular observer form btof by including generalized time scaling functions tsfs which have both state and output dependence introducing these stability preserving tsfs broadens the class of systems which admits a btof based observer design necessary conditions for the tsfs are provided when a tbtof exists an observer can be constructed subsystem at a time sufficient conditions are given to prove estimate error stability a physical example illustrates the tbtof construction and observer design

mixing times for the mean field blume capel model via aggregate path coupling we investigate the relationship between the mixing times of the glauber dynamics of a statistical mechanical system with its thermodynamic equilibrium structure for this we consider the mean field blume capel model one of the simplest statistical mechanical models that exhibits the following intricate phase transition structure within a two dimensional parameter space there exists a curve at which the model undergoes a second order continuous phase transition a curve where the model undergoes a first order discontinuous phase transition and a tricritical point which separates the two curves we determine the interface between the regions of slow and rapid mixing in order to completely determine the region of rapid mixing we employ a novel extension of the path coupling method successfully proving rapid mixing even in the absence of contraction between neighboring states

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

restricted dynamic observer error linearizability following the general dynamic observer error linearization problem state equivalence to a triangular nonlinear observer canonical form with index d and the restricted dynamic observer error linearization problem are defined in this paper the necessary and sufficient conditions for the above two problems are given since our proofs are constructive a desired state transformation can also be found in the theorem

complete analysis of phase transitions and ensemble equivalence for the curie weiss potts model using the theory of large deviations we analyze the phase transition structure of the curie weiss potts spin model which is a mean field approximation to the nearest neighbor potts model it is equivalent to the potts model on the complete graph on n vertices the analysis is carried out both for the canonical ensemble and the microcanonical ensemble besides giving explicit formulas for the microcanonical entropy and for the equilibrium macrostates with respect to the two ensembles we analyze ensemble equivalence and nonequivalence at the level of equilibrium macrostates relating these to concavity and support properties of the microcanonical entropy the curie weiss potts model is the first statistical mechanical model for which such a detailed and rigorous analysis has been carried out

sliding observer based feedback control for flexible joints manipulator abstract high precision measurements of joint displacements and elastic forces are available on a flexible joints manipulator in contrast velocity measurements and elastic forces derivative are in many cases contaminated by noise or unavailable technical or economical constraint it is therefore interesting to investigate the possibility of controlling robot dynamics by only using position and elastic force measurements this paper presents a singular perturbation approach for trajectory tracking control combined with non linear sliding state observer the stability of the closed loop system is investigated

algebraic conditions for state equivalence to a discrete time nonlinear observer canonical form abstract algebraic necessary and sufficient conditions for a single output discrete time system to be state equivalent to a generalized nonlinear observer canonical form with or without output transformation are derived our algebraic conditions are easier to verify for researchers unaccustomed to differential geometry in addition our proofs are constructive and contain the state and output transformations for generalized nonlinear observer canonical forms

nonlinear observer design for a general class of discrete time nonlinear systems with real parametric uncertainty this paper is a geometric study of the local observer design for a general class of discrete time nonlinear systems with real parametric uncertainty explicitly we study the observer design problem for a general class of discrete time nonlinear systems with real parametric uncertainty and with an input generator exosystem in this paper we show that for the classical case when the state equilibrium does not change with the parametric uncertainty and when the plant output is purely a function of the state there is no local asymptotic observer for the plant next we show that in sharp contrast to this case for the general case of problems where we allow the state equilibrium to change with the parametric uncertainty there typically exist local exponential observers even when the plant output is purely a function of the state we also present a characterization and construction procedure for local exponential observers for the general class of discrete time nonlinear systems with real parametric uncertainty under some stability assumptions we also show that for the general class of discrete time nonlinear systems considered under some stability assumptions the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs finally we generalize our results to a general class of discrete time nonlinear systems with input generator and with exogenous disturbance

a block triangular nonlinear observer normal form abstract the nonlinear observer normal form is generalized to a block triangular observer normal form which can be interpreted as a series connection of subsystems in observer form based on this new form exponential observers can be designed using methods from the linear case necessary and sufficient conditions for the existence of state transformations into this normal form are given

the aggregate path coupling method for the potts model on bipartite graph in this paper we derive the large deviation principle for the potts model on the complete bipartite graph kn n as n increases to infinity next for the potts model on kn n we provide an extension of the method of aggregate path coupling that was originally developed in the work of kovchegov otto and titus j stat phys 144 5 1009 1027 2011 for the mean field blume capel model and in kovchegov and otto j stat phys 161 3 553 576 2015 for a general mean field setting that included the generalized curie weiss potts model analyzed in the work of jahnel et al markov process relat fields 20 601 632 2014 we use the aggregate path coupling method to identify and determine the threshold value s separating the rapid and slow mixing regimes for the glauber dynamics of the potts model on kn n

sampled data observer error linearization the effects of time sampling on the solvability conditions for the observer linearization design methodology are investigated it is shown that the class of systems for which this design method can be applied for an open set of sampling times is quite small in particular when the dimension of the state space is two it consists only of those systems that are state equivalent to a linear system the practical implication is that digital implementations of this methodology will have to be approximate

an efficient method for observer design with approximately linear error dynamics exact error linearization is a well known full order observer design method which yields linear time invariant stable error dynamics in normal form coordinates the difficult procedure associated with exact error linearization has led to the simpler extended luenberger observer design however extended luenberger observers can only guarantee a first order approximation to the exact error linearization design this paper provides an explicit formula involving only derivative lie derivative and bracket and matrix inversion operations for computing an nth order approximation of the exact error linearization observer hence the proposed method is a computational simple tool for designing observers for systems admitting exact error linearization observers two examples demonstrate the application of the method

necessary and sufficient conditions for state equivalence to a nonlinear discrete time observer canonical form in this technical note we obtain necessary and sufficient conditions for a multi input multi output discrete time nonlinear system to be state equivalent to a nonlinear observer form and for an uncontrolled multi output system to be state equivalent to a linear observer form we adopt a geometric approach and the proofs are constructive with respect to the required coordinate change

nonlinear observer design for a general class of nonlinear systems with real parametric uncertainty this paper is a geometric study of the local observer design for a general class of nonlinear systems with real parametric uncertainty explicitly we study the observer design problem for a general class of nonlinear systems with real parametric uncertainty and with an input generator exosystem in this paper we show that for the classical case when the state equilibrium does not change with the parametric uncertainty and when the plant output is purely a function of the state there is no local asymptotic observer for the plant next we show that in sharp contrast to this case for the general case of problems where we allow the state equilibrium to change with the parametric uncertainty there typically exist local exponential observers even when the plant output is purely a function of the state we also present a characterization and construction procedure for local exponential observers for the general class of nonlinear systems with real parametric uncertainty under some stability assumptions we also show that for the general class of nonlinear systems considered under some stability assumptions the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs finally we generalize our results to a general class of nonlinear systems with input generator and with exogenous disturbance

non linear observer design by observer canonical forms this paper studies the non linear observer design problem by observer canonical forms we present necessary and sufficient conditions in terms of the ranks of matrices for the existence of a non linear state coordinate change under which a time variable system is transformed into an observer canonical form these conditions give the multiple versions of li and tao 1986 for the single output case then a comparison is made with the lie algebraic conditions obtained by krener and respondek 1985 and modified by the authors in a recent paper xia and gao 1987

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

observing non linear time variable systems through a canonical form observer abstract bestle and zeitz have introduced a non linear time variable observer canonical form which permits through a non linear state transformation the use of the eigenvalue assignment method to design observers for non linear time variable dynamic systems in this paper a necessary and sufficient condition under which the transformation exists is given it is also proved that the transformation could be determined by integrating single variable functions instead of solving a set of partial differential equations as shown by bestle and zeitz examples are included to show how to do the transformation

observer linearization by output dependent time scale transformations we study the problem of observer linearization for single output dynamical systems in the presence of output dependent time scaling changes an alternative algorithm for the solution of the observer linearization problem is introduced the algorithm employs an exterior calculus approach that provides a simple procedure for the solution of the observer linearization problem by means of an output dependent time scale transformation

a new reduced order observer normal form for nonlinear discrete time systems this paper presents a new observability normal form for discrete time nonlinear systems this form enables us to design a reduced order observer necessary and sufficient geometrical conditions for the existence of a coordinate change to transform a discrete time nonlinear system into such normal form are given an illustrative example is given to show the effectiveness of our approach

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 unifying model of generalised random walks the authors propose a unifying model for generalised static random walks in which each walk has a weight exp g sigma ni alpha where ni is the occupation number of a site and alpha and g are variable parameters special cases of this general walk include the ordinary brownian random walk the self avoiding walk the lattice domb joyce model 1972 and the interacting random walk model recently introduced by stanley et al 1983 the asymptotic properties of the walk are studied in one dimension by effective medium arguments and exact enumeration methods for repulsive correlations the authors find saw behaviour while for attractive correlations the model is self trapping for 1 alpha or 2 and exhibits anomalous diffusion with continuously varying exponents for 0 or alpha 1 in higher dimensions comments are made about effective medium predictions and their relationship to other generalised random walk models

glauber dynamics of 2d kac blume capel model and their stochastic pde limits abstract we study the glauber dynamics of a two dimensional blume capel model or dilute ising model with kac potential parametrized by the inverse temperature and the chemical potential we prove that the locally averaged spin field rescales to the solution of the dynamical 4 equation near a curve in the plane and to the solution of the dynamical 6 equation near one point on this curve our proof relies on a discrete implementation of da prato debussche method 13 as in 33 but an additional coupling argument is needed to show convergence of the linearized dynamics

comments on state observers and state feedback controllers for a class of non linear systems the new non linear observer canonical form introduced by hauksdottir and fenton 1988 is compared with the known non linear observer canonical form it is pointed out that the new canonical form does not satisfy essential requirements for an observer canonical form and hence should not be denoted as such

nonlinear observers for two classesof perturbed systems in this paper we study two important classes of nonlinear systems with perturbation namely perturbation with output injection and perturbation of pure feedback systems with sufficiently good initial error estimates and sufficiently restricted external inputs and perturbation parameter nonlinear observers for each class of perturbed systems are designed so that the error between the exact states and the estimated states goes to zero our simulation results illustrate the applicability of our technique in building nonlinear observers for these two classes of perturbed systems

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

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

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

on a random process interpolating between markovian and non markovian random walks the authors give the exact solution in one dimension of the continuum analogue of a model of stanley et al 1983 which interpolates between markovian polya and self avoiding random walks on lattices and make some heuristic comments on the nature of phase transitions in the model in higher dimensions

observer design in convergent series for a class of nonlinear systems this paper deals with convergence analysis for power series solutions to a partial differential equation for nonlinear observer design with linear observer error dynamics this power series solution is used to design the gain matrix for a luenberger like observer for nonlinear systems an explicit domain of convergence around the origin is identified which is related to the relative sizes of high order terms in the original nonlinear system with respect to the linearized model the convergent conditions can provide a guideline for nonlinear observer design with a truncated series for the observer gain

glauber dynamics for the mean field ising model cut off critical power law and metastability we study the glauber dynamics for the ising model on the complete graph also known as the curie weiss model for 1 we study metastability in particular we show that the glauber dynamics restricted to states of non negative magnetization has mixing time o n log n

non linear observer design by reduced generalized observer canonical form a non linear canonical form observer design approach for multi input multi output systems y h x u with linearizable error dynamics is proposed in the paper the method involves a transformation of the original non linear system in a reduced generalized observer canonical form rgocf by a non linear state transformation the name reduced comes from the fact that this non linear canonical form has a reduced dependency on derivatives of the inputs necessary and sufficient conditions for transformability are derived and a transformation algorithm based on those conditions is developed the non linear observer is firstly designed in the canonical coordinates of the rgocf and then it is presented in the original and observability coordinates a final example including simulation is given for illustration

verifiable conditions for multioutput observer error linearizability the verifiable necessary and sufficient conditions for the multioutput observer error linearization problem have not been found over the last three decades in this technical note we give the unverifiable necessary and sufficient conditions which are more specific than the ones in the literature using these conditions a verifiable sufficient condition also necessary with additional restriction on the problem is derived since our proofs are constructive a desired state transformation can also be found in the theorem also our algorithmic conditions can be easily implemented by a matlab programming

a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems abstract an adaptive observer for a class of single input single output siso nonlinear systems is proposed using a generalized dynamic recurrent neural network drnn the neural network nn weights are tuned on line with no off line learning required no exact knowledge of non linearities in the observed system is required furthermore no linearity with respect to unknown system parameters is assumed the drnn observer does not assume that nonlinearities in the system are restricted to the system output only the overall adaptive observer scheme is shown to be uniformly ultimately bounded simulation results have verified the performance of the drnn observer

exponential estimates for the wiener sausage letc e t be the wiener sausage of radius e inr d up to timet we obtain bounds on the asymptotics ofe exp c e t ast for all 0

on exponential observers for nonlinear systems abstract the aim of the paper is to identify the class of nonlinear systems that have exponential observers a concept introduced by previous authors it is shown that a necessary condition for the existence of an exponential observer for a nonlinear system is that the corresponding linearized system is detectable and for local exponential stabilization problems the condition is also sufficient this paper gives also a theorem on the separation property for the exponential design problem and it enables us to tell exactly to what extent the classical local linearization approach is applicable

a state observer for nonlinear systems a state observer design methodology for a class of nonlinear systems is proposed the nonlinear observer design methodology is in fact an extension of linear observer design techniques using transformations related to linear observability matrices

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

observer with linear error dynamics for nonlinear multi output systems based upon nonlinear state coordinate transformations and a condensed dual brunovsk form for multi output systems a method for designing nonlinear state observers with linear error dynamics is presented necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained

diffusion with random traps transient one dimensional kinetics in a linear potential the problem of one dimensional diffusion with random traps is solved without and with a constant field of force using an eigenvalue expansion for long times and the method of images for short times we give an exact straightforward solution for the time dependence of the mean survival probability and the mean probability density for returning to the origin using the backward equation approach we determine the mean survival time and the mean residence time density at the origin we comment on the relation between these solutions and those for one dimensional diffusion with random reflectors