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

global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weights recently a dynamic neural system was presented and analyzed due to its good performance in optimization computation and low complexity for implementation the global asymptotic stability of such a dynamic neural system with symmetric connection weights was well studied in this note based on a new lyapunov function we investigate the global asymptotic stability of the dynamic neural system with asymmetric connection weights since the dynamic neural system with asymmetric weights is more general than that with symmetric ones the new results are significant in both theory and applications specially the new result can cover the asymptotic stability results of linear systems as special cases

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

on exponential convergence conditions of an extended projection neural network recently the extended projection neural network was proposed to solve constrained monotone variational inequality problems and a class of constrained nonmonotontic variational inequality problems its exponential convergence was developed under the positive definiteness condition of the jacobian matrix of the nonlinear mapping this note proposes new results on the exponential convergence of the output trajectory of the extended projection neural network under the weak conditions that the jacobian matrix of the nonlinear mapping may be positive semidefinite or not therefore new results further demonstrate that the extended projection neural network has a fast convergence rate when solving a class of constrained monotone variational inequality problems and nonmonotonic variational inequality problems illustrative examples show the significance of the obtained results

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

adaptive observers for ts fuzzy systems with unknown polynomial inputs a large class of nonlinear systems can be well approximated by takagi sugeno ts fuzzy models with linear or affine consequents however in practical applications the process under consideration may be affected by unknown inputs such as disturbances faults or unmodeled dynamics in this paper we consider the problem of simultaneously estimating the state and unknown inputs in ts systems the inputs considered in this paper are 1 polynomials in time such as a bias in the model or an unknown ramp input acting on the model and 2 unmodeled dynamics the proposed observer is designed based on the known part of the fuzzy model conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal the results are illustrated on a simulation example

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

robust adaptive observers for nonlinear systems with bounded disturbances since existing adaptive observers for nonlinear systems may generate unbounded parameter estimates in the presence of bounded disturbances robust adaptive observers are presented which prevent parameter estimate drift in addition the input to state stability of the error dynamics with respect to disturbances and parameter time derivatives is guaranteed by generalizing a persistency of excitation result asymptotic convergence of state estimation errors is still achieved for systems in adaptive observer form when disturbances are not present by a suitable extension of barbalat s lemma

free group algebras in division rings with valuation i abstract let r be an algebra over a commutative ring k suppose that r is endowed with a descending filtration indexed on an ordered group g such that the restriction to k is positive we show that the existence of free algebras on a certain set of generators in the induced graded ring grad r implies the existence of free group algebras in r our best results are obtained for division rings endowed with a valuation

free group algebras in the field of fractions of differential polynomial rings and enveloping algebras abstract we construct free group algebras in the quotient ring of the differential polynomial ring k x for suitable division rings k and nonzero derivations in k

free skew fields have many orderings abstract the notion of a ordering on a skew field with involution was introduced by s holland in j algebra 101 1986 16 46 as an analogue to the notion of a total ordering on a skew field and developed further in a series of papers of t craven i idris m marshall and t smith while it is well known that every free skew field has a total ordering see j lewin trans amer math soc 192 1974 339 346 it has not been known so far whether every free skew field with some natural involution has a ordering the aim of this paper is to give an explicit construction of a class of orderings on free associative algebras and to prove that orderings from this class extend uniquely to the corresponding free skew fields the problem was posed by t craven and t smith in j algebra 238 2001 314 327

on universal fields of fractions for free algebras abstract let l be an arbitrary lie algebra then by cohn s theorem its universal enveloping algebra can be embedded in a skew field d l we study this skew field in the case when l is a free lie algebra and prove that in this case d l is isomorphic to the universal field of fractions for the free associative algebra u l we apply this theorem to obtain new results on free fields

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

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

global adaptive observers for nonlinear systems via filtered transformations the problem of determining global adaptive observers for a class of single output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation under additional geometric conditions the original state can be observed as well the results obtained are based on a nonlinear change of coordinates driven by auxiliary filters filtered transformations

neural network for quadratic optimization with bound constraints a recurrent neural network is presented which performs quadratic optimization subject to bound constraints on each of the optimization variables the network is shown to be globally convergent and conditions on the quadratic problem and the network parameters are established under which exponential asymptotic stability is achieved through suitable choice of the network parameters the system of differential equations governing the network activations is preconditioned in order to reduce its sensitivity to noise and to roundoff errors the optimization method employed by the neural network is shown to fall into the general class of gradient methods for constrained nonlinear optimization and in contrast with penalty function methods is guaranteed to yield only feasible solutions

finite time parameter estimation in adaptive control of nonlinear systems this note presents a parameter estimation routine that allows exact reconstruction of the unknown parameters in finite time provided a given excitation condition is satisfied the robustness of the routine to an unknown bounded disturbance or modeling error is also shown the result is independent of the control and identifier structures employed the true parameter value is obtained without requiring the measurement or computation of the velocity state vector moreover the technique provides a direct solution to the problem of removing auxiliary perturbation signals when parameter convergence is achieved

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

parameterization of computational domain in isogeometric analysis methods and comparison parameterization of computational domain plays an important role in isogeometric analysis as mesh generation in finite element analysis in this paper we investigate this problem in the 2d case i e how to parametrize the computational domains by planar b spline surface from the given cad objects four boundary planar b spline curves firstly two kinds of sufficient conditions for injective b spline parameterization are derived with respect to the control points then we show how to find good parameterization of computational domain by solving a constraint optimization problem in which the constraint condition is the injectivity sufficient conditions of planar b spline parametrization and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of planar b spline parameterization by using this method the resulted parameterization has no self intersections and the isoparametric net has good uniformity and orthogonality after introducing a posteriori error estimation for isogeometric analysis we propose r refinement method to optimize the parameterization by repositioning the inner control points such that the estimated error is minimized several examples are tested on isogeometric heat conduction problem to show the effectiveness of the proposed methods and the impact of the parameterization on the quality of the approximation solution comparison examples with known exact solutions are also presented

development and analysis of a neural dynamical approach to nonlinear programming problems this technical note develops a neural dynamical approach to nonlinear programming np problems whose equilibrium points coincide with karush kuhn tucker points of the np problem a rigorous analysis on the global convergence and the convergence rate of the proposed neural dynamical approach is carried out under the condition that the associated lagrangian function is convex analysis results show that the proposed neural dynamical approach can solve general convex programming problems and a class of nonconvex programming problems two nonconvex programming examples are provided to demonstrate the performance of the developed neural dynamical approach

free products of units in algebras i quaternion algebras abstract letabe a quaternion algebra over a commutative unital ring we find sufficient conditions for pairs of units ofato generate a free group using the well known isomorphism betweenso 3 r and the group of real quaternions of norm 1 we obtain free groups of rotations of the euclidean 3 space specialization techniques allow us to find similar free subgroups in skew polynomial rings a consequence is the following letkgbe the group algebra of a residually torsion free nilpotent groupgover a fieldkwhose characteristic is not 2 ifxandyare any pair of noncommuting elements ofg andc d k then 1 cxand 1 dygenerate a free subgroup of the malcev neumann field of fractions ofkg

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

valuation methods in group rings and in skew fields i abstract in this first in a series of two papers we construct a family of discrete valuations in group rings of residually torsion free nilpotent groups and extend these valuations to the malcev neumann power series skew fields of these group rings we apply these valuations to the study of these skew fields in the second paper we will use our results and methods to study free fields and the universal fields of fractions k x of the magnus power series ring

adaptive observers for single output nonlinear systems an adaptive version of the nonlinear observer obtained by a j krener et al 1983 is presented this version involves the cancellation of nonlinear terms by output injection as an intermediate step necessary and sufficient conditions are given for transforming a nonlinear system by state space change of coordinates into the special adaptive observer form that was used by y bastin et al 1988 to design adaptive observers

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

an analysis of a class of neural networks for solving linear programming problems a class of neural networks that solve linear programming problems is analyzed the neural networks considered are modeled by dynamic gradient systems that are constructed using a parametric family of exact nondifferentiable penalty functions it is proved that for a given linear programming problem and sufficiently large penalty parameters any trajectory of the neural network converges in finite time to its solution set for the analysis lyapunov type theorems are developed for finite time convergence of nonsmooth sliding mode dynamic systems to invariant sets the results are illustrated via numerical simulation examples

a method for inversion of periodic open boundary conditions in two dimensional tidal models for parameter estimation problems it is of great importance to reduce the number of spatially varying control variables because of the ill posedness of inverse problem a new method for the inversion of periodic open boundary conditions in two dimensional tidal models is developed in this work in this method the open boundary curves are generated by linearly interpolating the values at feature points fps the fps are selected by calculating the second order derivatives of discrete curves the advantage is that most of the variations of the curves can be reproduced by the minimum number of control points the adjoint based 4dvar data assimilation method is then applied to simulate the tides in the bohai yellow and east china seas by optimizing the fourier coefficients at fps the model and the method are calibrated in twin experiments where the prescribed distributions along open boundaries are successfully inverted the results of twin experiments demonstrate that the effect of inversion is in inverse proportion with the number of fps which characterizes the complexity of open boundary curves in order to test the method in practical application real experiments are performed and the fps are selected by analyzing the background information from a global tidal model dtu10 during the assimilation both the data misfit between observations and modeling results and l2 norm of gradients of cost function with respect to control variables have decreased significantly the relation between the number of control variables and parameter inversion is discussed it is concluded the method developed in this work will be especially useful and effective when dealing with complex open boundary forcing or applying in highly refined models

a novel neural network for a class of convex quadratic minimax problems based on the inherent properties of convex quadratic minimax problems this article presents a new neural network model for a class of convex quadratic minimax problems we show that the new model is stable in the sense of lyapunov and will converge to an exact saddle point in finite time by defining a proper convex energy function furthermore global exponential stability of the new model is shown under mild conditions compared with the existing neural networks for the convex quadratic minimax problem the proposed neural network has finite time convergence a simpler structure and lower complexity thus the proposed neural network is more suitable for parallel implementation by using simple hardware units the validity and transient behavior of the proposed neural network are illustrated by some simulation results

optimal reset adaptive observer design abstract a reset adaptive observer reao is an adaptive observer consisting of an integrator and a reset law that resets the output of the integrator depending on a predefined reset condition the inclusion of reset elements can improve the observer performance but it can also destroy the stability of the estimation process if the reao is not properly tuned as contribution a method to optimally tune the parameters and gains of the reao is presented they are optimally chosen by solving the l 2 gain minimization problem which can be rewritten as an equivalent lmi problem the effectiveness of the proposed method is checked by simulations comparing the results of an optimal reao with an optimal traditional adaptive observer

bounded state reconstruction error for lpv systems with estimated parameters the note deals with the state reconstruction of a class of discrete time systems with time varying parameters while usually the parameters are assumed to be online available and exactly known the special and realistic situation when the parameters are known with a finite accuracy is considered the main objective of the note is to show that despite of the resulting mismatch between the true system and the model the state reconstruction error boundedness can be guaranteed and an explicit bound can be derived the proof is based upon the concept of input to state stability

ideal theory of right cones and associated rings abstract right cones are semigroups with a left cancellation law such that for any two elements a b there exists an element c with b ac or a bc valuation rings cones of ordered or left ordered groups semigroups of ordinal numbers and hjelmslev rings are examples the ideal theory of these semigroups is described in terms of prime and completely prime ideals and a classification of prime segments is given that can be used to solve a problem raised by skornyakov the archimedean case can be dealt with in a satisfactory way with the help of holder s theorem right cones of rank 1 are classified we then consider the problem of constructing for a given right cone h a right chain ring r with the same right ideal and ideal structure as h

the analysis of an ill posed problem using multi scale resolution and second order adjoint techniques abstract a wavelet regularization approach is presented for dealing with an ill posed problem of adjoint parameter estimation applied to estimating inflow parameters from down flow data in an inverse convection case applied to the two dimensional parabolized navier stokes equations the wavelet method provides a decomposition into two subspaces by identifying both a well posed as well as an ill posed subspace the scale of which is determined by finding the minimal eigenvalues of the hessian of a cost functional measuring the lack of fit between model prediction and observed parameters the control space is transformed into a wavelet space the hessian of the cost is obtained either by a discrete differentiation of the gradients of the cost derived from the first order adjoint or by using the full second order adjoint the minimum eigenvalues of the hessian are obtained either by employing a shifted iteration method x zou i m navon f x le dimet tellus 44a 4 1992 273 or by using the rayleigh quotient the numerical results obtained show the usefulness and applicability of this algorithm if the hessian minimal eigenvalue is greater or equal to the square of the data error dispersion in which case the problem can be considered as well posed i e regularized if the regularization fails i e the minimal hessian eigenvalue is less than the square of the data error dispersion of the problem the following wavelet scale should be neglected followed by another algorithm iteration the use of wavelets also allowed computational efficiency due to reduction of the control dimension obtained by neglecting the small scale wavelet coefficients

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

on convergence rate of projection neural networks this note presents an analysis of the convergence rate for a projection neural network with application to constrained optimization and related problems it is shown that the state trajectory of the projection neural network is exponentially convergent to its equilibrium point if the jacobian matrix of the nonlinear mapping is positive definite while the convergence rate is proportional to a design parameter if the jacobian matrix is only positive semidefinite moreover the convergence time is guaranteed to be finite if the design parameter is chosen to be sufficiently large furthermore if a diagonal block of the jacobian matrix is positive definite then the corresponding partial state trajectory of the projection neural network is also exponentially convergent three optimization examples are used to show the convergence performance of the projection neural network

fuzzy iterative learning control applied in a biological reactor using a reduced number of measures iterative learning control applied to a biotechnological process it was used a sample time of one hour to known the concentrations in the process because there are not on line sensors fuzzy logic improves convergence in the control a theorem is given to have an idea for the gain that guarantees convergence due theoretic results interpolation is made to satisfy the theorem proposed there exist some processes difficult to control as the chemical ones a common problem takes place when the output cannot be measured on line and so closed loop control cannot be implemented in this work an iterative learning control type proportional derivative is analyzed and theoretical results are shown this control is applied to a biological reactor to degrade phenol by working in discontinuous batch state as the measures of the substrata concentrations are taken by hand it was proposed to have a sample time of one hour to guarantee convergence and to improve the control cubic splines were used to interpolate the measures fuzzy logic was used to compute the control gains used to build the control signal simulation results are shown and the control signals are presented through iterations here it is possible to see that the error is smaller using fuzzy logic to compute the control signal when iterations run

open boundary control problem for navier stokes equations including a free surface data assimilation this paper develops the data assimilation procedure in order to allow for the assimilation of measurements of currents and free surface elevations into an unsteady flow solution governed by the free surface barotropic navier stokes equations the flow is considered in a 2d vertical section in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface since a possible application is to the construction of a coastal limited area circulation model the open boundary control problem is the main scope of the paper the assimilation algorithm is built on the limited memory quasi newton lbfgs method guided by the adjoint sensitivities the analytical step search which is based on the solution of the tangent linear model is used we process the gradients to regularize the solution in numerical experiments we consider different wave patterns with a purpose to specify a set of incomplete measurements which could be sufficient for boundary control identification as a result of these experiments we formulate some important practical conclusions

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

robust observer design for non linear interconnected systems using structural characteristics in this paper a kind of robust observer design scheme based on a constrained lyapunov equation is presented for a class of non linear interconnected systems using structural characteristics the non linear interconnected system is not required to be affine or linearizable both matched and unmatched uncertainties are considered and a method to deal with uncertain interconnections is proposed the bounding functions of all the uncertainties may be arbitrarily large since non linear gain functions are introduced to eliminate the effects of the uncertainties by exploiting their structural characteristics simulation is given to demonstrate the effectiveness of the proposed scheme