recursive identification using feedforward neural networks the paper is concerned with the identification of an unknown nonlinear dynamical system when only the inputs and outputs are accessible for measurement under certain assumptions it is shown that generically the system can be realized by a recursive input output model furthermore relying on the approximation properties of neural networks and the existence of effective training algorithms it is demonstrated how an effective identification model can be constructed simulation results are presented to complement the theoretical discussions

neural network adaptive control for a class of nonlinear uncertain dynamical systems with asymptotic stability guarantees in this paper a neuroadaptive control framework for continuous and discrete time nonlinear uncertain dynamical systems with input to state stable internal dynamics is developed the proposed framework is lyapunov based and unlike standard neural network nn controllers guaranteeing ultimate boundedness the framework guarantees partial asymptotic stability of the closed loop system that is asymptotic stability with respect to part of the closed loop system states associated with the system plant states the neuroadaptive controllers are constructed without requiring explicit knowledge of the system dynamics other than the assumption that the plant dynamics are continuously differentiable and that the approximation error of uncertain system nonlinearities lie in a small gain type norm bounded conic sector this allows us to merge robust control synthesis tools with nn adaptive control tools to guarantee system stability finally two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach

transition thresholds and transition operators for binarization and edge detection the transition method for image binarization is based on the concept of t transition pixels a generalization of edge pixels and t transition sets we introduce a novel unsupervised thresholding for unimodal histograms to estimate the transition sets we also present dilation and incidence transition operators to refine the transition set afterward we propose the simple edge transition operator for detecting edges our experiments show that the new approach increases the effectiveness of ocr applications outperforming several top ranked binarization algorithms

technical communique adaptive ilc for a class of discrete time systems with iteration varying trajectory and random initial condition in this work we present a discrete time adaptive iterative learning control ailc scheme to deal with systems with time varying parametric uncertainties using the analogy between the discrete time axis and the iterative learning axis the new adaptive ilc can incorporate a recursive least squares rls algorithm hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis when the initial states are random and the reference trajectory is iteration varying the new ailc can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis

robustifying nonlinear systems using high order neural network controllers a robust control methodology for affine control of nonlinear dynamical systems is developed in this paper a correction control signal is added to a nominal controller designed to guarantee a desired performance for the corresponding nominal system to render the actual system uniformly and ultimately bounded the control signal is smooth and does not require a priori knowledge of an upper bound on the modeling error and or optimal weight values simulations performed on a simple nonlinear system illustrate the approach

time series based bifurcation diagram reconstruction abstract we consider the problem of reconstructing bifurcation diagrams bds of maps using time series this study goes along the same line of ideas presented by tokunaga et al physica d 79 1994 348 and tokuda et al physica d 95 1996 380 the aim is to reconstruct the bd of a dynamical system without the knowledge of its functional form and its dependence on the parameters instead time series at different parameter values assumed to be available are used a three layer fully connected neural network is employed in the approximation of the map the task of the network is to learn the dynamics of the system as function of the parameters from the available time series we determine a class of maps for which one can always find a linear subspace in the weight space of the network where the network s bifurcation structure is qualitatively the same as the bifurcation structure of the map we discuss a scheme in locating this subspace using the time series we further discuss how to recognize time series generated by this class of maps finally we propose an algorithm in reconstructing the bds of this class of maps using predictor functions obtained by neural network this algorithm is flexible so that other classes of predictors apart from neural networks can be used in the reconstruction

minimal realization of nonlinear systems described by input output difference equations we consider a general class of nonlinear discrete time systems described by their input output i o relationship we first present the necessary and sufficient conditions for existence of a local observable state space realization of the system and an explicit algorithm for computing it in cases where the i o map and its resulting realization are nonminimal we formulate an algorithm for extracting its minimal realization whenever possible the developed theory and algorithms are illustrated by means of several examples

finite interpolation with minimum uniform norm in cn given a finite sequence a a1 an in a domain cn and complex scalars v v1 vn consider the classical extremal problem of finding the smallest uniform norm of a holomorphic function verifying f aj vj for all j we show that the modulus of the solutions to this problem must approach its least upper bound along a subset of the boundary of the domain large enough so that its a hull contains a subset of the original a large enough to force the same minimum norm furthermore all the solutions must agree on a variety which contains the hull in an appropriate weaker sense of a measure supported on the maximum modulus set an example is given to show that the inclusions can be strict

multiple model adaptive control for a class of linear bounded nonlinear systems this study proposes a novel multiple model adaptive control mmac algorithm for a class of nonlinear discrete time systems the controller consists of a linear indirect adaptive controller a nonlinear indirect adaptive controller based on neural networks and a switching mechanism the control input is generated by the switching mechanism which selects the candidate controller from the two controllers the assumption of the nonlinear term is relaxed to linear bounded when a modified adaptive law is introduced the restraint that the nonlinear term of the plant should be linear with respect to the control input is removed by resorting to the pole placement control scheme the proposed control method can address the properties of non minimum phase and open loop instability in the linear part of the plant the proposed mmac algorithm can guarantee the bounded input bounded output stability of the proposed closed loop switching system a simulation example is presented to demonstrate the effectiveness of the proposed method

direct feedback control design for nonlinear systems we propose an approach for the direct design from data of controllers finalized at solving tracking problems for nonlinear systems this approach called direct feedback dfk design overcomes relevant problems typical of the standard design methods such as modeling errors non trivial parameter identification non convex optimization and difficulty in nonlinear control design considering a set membership sm approach we provide three main contributions the first one is a theoretical framework for the stability analysis of nonlinear feedback control systems in which the controller email protected is an approximation identified from data of an ideal inverse model f o in this framework we derive sufficient conditions under which email protected stabilizes the closed loop system the second contribution is a technique for the direct design of an approximate controller f from data having suitable optimality stability and sparsity properties in particular we show that f is an almost optimal controller in a worst case sense and we derive a guaranteed accuracy bound which can be used to quantify the performance level of the dfk control system we also show that when the number of data used for control design tends to infinity and these data are dense in the controller domain the closed loop stability is guaranteed for a set of trajectories of interest the technique is based on convex optimization and sparse identification methods and thus avoids the problem of local minima and allows an efficient online controller implementation in real world applications the third contribution is a simulation study regarding the application of dfk to the challenging problem of control design for a class of airborne wind energy generators

stabilizing predictive control of nonlinear arx models in this paper a predictive control algorithm for nonlinear discrete time systems is presented starting from a state space model conditions for the asymptotic tracking of constant reference signals in a neighbourhood of a given equilibrium are first derived then it is shown that the system under control can be locally described in terms of a suitable narx nonlinear arx model which in practice can be identified by means of well established techniques for the narx model a receding horizon predictive control algorithm is proposed which guarantees local stability and robust asymptotic tracking in the neighbourhood of the equilibrium conditions for local stability and tracking are given in terms of reachability observability and transmission zeros of the linearization of the original state space system around the equilibrium an example is reported to illustrate the effectiveness of the proposed method

design of a fuzzy servo controller a design method of a fuzzy servo controller for nonlinear plants has been presented the proposed method is an error feedback scheme where the controller also receives signals representing the plant operating points integrator is used in the control loop to ensure setpoint following low frequency disturbance rejection and to enhance the robustness of the closed loop system a training scheme for the fuzzy controller is derived that minimizes the output error between a reference model and the plant the training is conducted off line for a class of setpoints conforming to the normal operating condition of the plant results of simulation studies are also presented

efficient computation of adaptive threshold surfaces for image binarization the problem of binarization of gray level images acquired under non uniform illumination is reconsidered yanowitz and bruckstein proposed to use for image binarization an adaptive threshold surface determined by interpolation of the image gray levels at points where the image gradient is high the rationale is that high image gradient indicates probable object edges and there the image values are between the object and the background gray levels the threshold surface was determined by successive over relaxation as the solution of the laplace equation this work proposes a different method to determine an adaptive threshold surface in this new method inspired by multiresolution approximation the threshold surface is constructed with considerably lower computational complexity and is smooth yielding faster image binarizations and often better noise robustness

hyperbolic mean growth of bounded holomorphic functions in the ball we consider the hyperbolic hardy class q h p b 0 p it consists of holomorphic in the unit complex ball b for which 1 and sup q r 0 p d 0 r 1 b where q denotes the hyperbolic distance of the unit disc the hyperbolic version of the littlewood paley type g function and the area function are defined in terms of the invariant gradient of b and membership of qh p b is expressed by the l p property of the functions as an application we can characterize the boundedness and the compactness of the composition operator c defined by c f f o from the bloch space into the hardy space h p b

corrigendum to conical plurisubharmonic measure and new cross theorems j math anal appl 365 2010 429 434

adaptive learning control for finite interval tracking based on constructive function approximation and wavelet using a constructive function approximation network an adaptive learning control alc approach is proposed for finite interval tracking problems the constructive function approximation network consists of a set of bases and the number of bases can evolve when learning repeats the nature of the basis allows the continuous adaptive learning of parameters when the network undergoes any structural changes and consequently offers the flexibility in tuning the network structure the expandability of the bases guarantees precision of the function approximation and avoids the trial and error procedure in structure selection for any fixed structure network two classes of unknown nonlinear functions namely either global l2 or local l2 with a known bounding function are taken into consideration using the lyapunov method the existence of solution and the convergence property of the proposed alc system are discussed in a rigorous manner by virtue of the celebrated orthonormal and multiresolution properties wavelet network is used as the universal function approximator with the weights tuned by the proposed adaptive learning mechanism

discrete time model reference adaptive control of nonlinear dynamical systems using neural networks a multilayer discrete time neural net nn controller is presented for the direct model reference adaptive control of a class of multi input multi output mim0 nonlinear dynamical systems the nonlinear dynamical system is assumed to be controllable and its state vector is available for measurement the nn controller exhibits learning while functioning features instead of learning then control so that control is immediate with no explicit learning phase needed the tracking error between the output of a nonlinear plant and an ideal linear model converges within a very short time persistence of excitation pe is not needed linearity in the parameters is not required and certainty equivalence is not used this overcomes several limitations of standard adaptive control the novel weight tuning paradigm for the nn controller is based on the well known delta rule but includes a modification to the learning rate parameter plus a correction term it guarantees tracking as well as bounded nn weights in non i

markov chain network training and conservation law approximations linking microscopic and macroscopic models for evolution in this paper a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of markov chains and the approximation of conservation law equations is proposed this framework allows us to demonstrate an intrinsic link between microscopic and macroscopic models for evolution via the concept of perturbed generalized dynamic systems the main result is exemplified with a number of illustrative examples where efficient numerical approximations follow directly from network based computational models viewed here as markov chain approximations finally stability and consistency conditions of such computational models are discussed

a double threshold image binarization method based on edge detector this paper presents a new double threshold image binarization method based on the edge and intensity information we first find seeds near the image edges and present an edge connection method to close the image edges then we use closed image edges to partition the binarized image that is generated using a high threshold and obtain a primary binarization result by filling the partitioned high threshold binary image with the seeds finally the final binarization result is obtained by remedying the primary binarization result with the low threshold binary image compared with the classical binarization methods and the similar binarization methods our method is effective on the binarization of images with low contrast noise and non uniform illumination

adaptive control of nonlinear systems using neural networks layered networks are used in a nonlinear adaptive control problem the plant is an unknown feedback linearizable discrete time system represented by an input output model a state space model of the plant is obtained to define the zero dynamics which are assumed to be stable a linearizing feedback control is derived in terms of some unknown nonlinear functions to identify these functions it is assumed that they can be modelled by layered neural networks the weights of the networks are updated and used to generate the control a local convergence result is given computer simulations verify the theoretical result

shcherbina s theorem for finely holomorphic functions we prove an analogue of sadullaev s theorem concerning the size of the set where a maximal totally real manifold m can meet a pluripolar set m has to be of class c1 only this readily leads to a version of shcherbina s theorem for c1 functions f that are defined in a neighborhood of certain compact sets k subset mathbb c if the graph f k is pluripolar then frac partial f partial bar z 0 in the closure of the fine interior of k

adaptive nn control for a class of strict feedback discrete time nonlinear systems in this paper both full state and output feedback adaptive neural network nn controllers are presented for a class of strict feedback discrete time nonlinear systems firstly lyapunov based full state adaptive nn control is presented via backstepping which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete time backstepping design procedure after the strict feedback form is transformed into a cascade form another relatively simple lyapunov based direct output feedback control is developed the closed loop systems for both control schemes are proven to be semi globally uniformly ultimately bounded

non linear discrete variable structure systems in quasi sliding mode abstract the problem of inducing convergent quasi sliding regimes on smooth state space surfaces of non linear single input single output discrete time controlled systems is addressed in full generality a suitable extension of the notion of relative degree is used in establishing the most salient features of quasi sliding motions in non linearly controlled systems several examples are given

neural network adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative these models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous in this paper we develop a full state feedback neural adaptive control framework for adaptive set point regulation of nonlinear uncertain nonnegative and compartmental systems the proposed framework is lyapunov based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains in addition the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions

control of nonlinear dynamical systems using neural networks ii observability identification and control for pt i see ibid vol 4 1993 this paper considers the problems of regulation and tracking of a dynamical system when the state variables of the dynamical system are not accessible the existence of the nonlinear maps describing the identifier and controller are first established and the implications for neural network realizations are described simulation results are included to complement the theoretical discussions

a novel ring radius transform for video character reconstruction character recognition in video is a challenging task because low resolution and complex background of video cause disconnections loss of information loss of shapes of the characters etc in this paper we introduce a novel ring radius transform rrt and the concept of medial pixels on characters with broken contours in the edge domain for reconstruction for each pixel the rrt assigns a value which is the distance to the nearest edge pixel the medial pixels are those which have the maximum radius values in their neighborhood we demonstrate the application of these concepts in the problem of character reconstruction to improve the character recognition rate in video images with ring radius transform and medial pixels our approach exploits the symmetry information between the inner and outer contours of a broken character to reconstruct the gaps experimental results and comparison with two existing methods show that the proposed method outperforms the existing methods in terms of measures such as relative error and character recognition rate

adaptive degraded document image binarization this paper presents a new adaptive approach for the binarization and enhancement of degraded documents the proposed method does not require any parameter tuning by the user and can deal with degradations which occur due to shadows non uniform illumination low contrast large signal dependent noise smear and strain we follow several distinct steps a pre processing procedure using a low pass wiener filter a rough estimation of foreground regions a background surface calculation by interpolating neighboring background intensities a thresholding by combining the calculated background surface with the original image while incorporating image up sampling and finally a post processing step in order to improve the quality of text regions and preserve stroke connectivity after extensive experiments our method demonstrated superior performance against four 4 well known techniques on numerous degraded document images

nonlinear internal model control application of inverse model based fuzzy control this paper investigates the possible applications of dynamical fuzzy systems to control nonlinear plants with asymptotically stable zero dynamics using a fuzzy nonlinear internal model control strategy the developed strategy consists in including a dynamical takagi sugeno fuzzy model of the plant within the control structure in this way the controller design simply results in a fuzzy model inversion in this framework the originality of the presented work lies in the use of a dynamical fuzzy model and its inversion in order to be able to implement the control structure two crucial points have to be addressed in the considered fuzzy context on the one hand the model representation and identification on the other the model inversion as the fuzzy system can be viewed as a collection of elementary subsystems its inversion is approached here in a local way i e on the elementary subsystems capable to provide an inverse solution in this case the inversion of the global fuzzy system is thus tackled by inversion of some of its components by doing so exact inversion is obtained and offset free performances are ensured in order to guarantee a desired regulation behavior and robustness of stability of the control system the fuzzy controller is connected in series with a robustness filter the potential of the proposed method is demonstrated with simulation examples

observer based direct adaptive fuzzy neural control for nonaffine nonlinear systems in this paper an observer based direct adaptive fuzzy neural control scheme is presented for nonaffine nonlinear systems in the presence of unknown structure of nonlinearities a direct adaptive fuzzy neural controller and a class of generalized nonlinear systems which are called nonaffine nonlinear systems are instead of the indirect one and affine nonlinear systems given by leu et al by using implicit function theorem and taylor series expansion the observer based control law and the weight update law of the fuzzy neural controller are derived for the nonaffine nonlinear systems based on strictly positive real spr lyapunov theory the stability of the closed loop system can be verified moreover the overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed loop system will asymptotically track the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

output feedback control of a class of discrete mimo nonlinear systems with triangular form inputs in this paper adaptive neural network nn control is investigated for a class of discrete time multi input multi output mimo nonlinear systems with triangular form inputs each subsystem of the mimo system is in strict feedback form first through two phases of coordinate transformation the mimo system is transformed into input output representation with the triangular form input structure unchanged by using high order neural networks honns as the emulators of the desired controls effective output feedback adaptive control is developed using backstepping the closed loop system is proved to be semiglobally uniformly ultimate bounded sguub by using lyapunov method the output tracking errors are guaranteed to converge into a compact set whose size is adjustable and all the other signals in the closed loop system are proved to be bounded simulation results show the effectiveness of the proposed control scheme

integrated design of a linear neuro adaptive controller in the presence of norm bounded uncertainties adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network nn design parameters to performance requirements this study proposes a methodology for the design of an integrated linear adaptive model reference controller that guarantees component wise boundedness of the tracking error within an a priori specified compact domain the approach is based on the design of a robust invariant ellipsoidal set where both the nn reconstruction error and the neuro adaptive control are considered as bounded persistent uncertainties we show that all the performance and control requirements for the closed loop system can be expressed as linear matrix inequality constraints this brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem an advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design param

stable neural network based adaptive control for sampled data nonlinear systems for a class of mimo sampled data nonlinear systems with unknown dynamic nonlinearities a stable neural network nn based adaptive control approach which is an integration of an nn approach and the adaptive implementation of the variable structure control with a sector is developed the sampled data nonlinear system is assumed to be controllable and its state vector is available for measurement the variable structure control with a sector serves two purposes one is to force the system state to be within the state region in which the nn s are used when the system goes out of neural control and the other is to provide an additional control until the system tracking error metric is controlled inside the sector within the network approximation region the proof of a complete stability and a tracking error convergence is given and the setting of the sector and the nn parameters is discussed it is demonstrated that the asymptotic error of the system can be made dependent only on inherent network approximation errors and the frequency range of unmodeled dynamics simulation studies of a two link manipulator show the effectiveness of the proposed control approach

conical plurisubharmonic measure and new cross theorems we study the boundary behavior of the conical plurisubharmonic measure as an application we establish some new extension theorems for separately holomorphic mappings defined on cross sets

experimental studies in nonlinear discrete time adaptive prediction and control this paper presents implementation results using recently introduced discrete time adaptive prediction and control techniques using online function approximators we consider a process control experiment as our test bed and develop a discrete time adaptive predictor for liquid volume and a discrete time adaptive controller for reference volume tracking we use takagi sugeno ts fuzzy systems as our function approximators and for both prediction and control we investigate the use of a least squares update of the fuzzy system s parameters

robust adaptive control of nonaffine nonlinear plants with small input signal changes assuming small input signal magnitudes arma models can approximate the narma model of nonaffine plants recently narma l1 and narma l2 approximate models were introduced to relax such input magnitude restrictions however some applications require larger input signals than allowed by arma narma l1 and narma l2 models under certain assumptions we recently developed an affine approximate model that eliminates the small input magnitude restriction and replaces it with a requirement of small input changes such a model complements existing models using this model we present an adaptive controller for discrete nonaffine plants with unknown system equations accessible input output signals but inaccessible states our approximate model is realized by a neural network that learns the unknown input output map online a deadzone is used to make the weight update algorithm robust against modeling errors a control law is developed for asymptotic tracking of slowly varying reference trajectories

stable auto tuning of adaptive fuzzy neural controllers for nonlinear discrete time systems in direct adaptive control the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller in the indirect case however we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities in both cases approximators such as linear mappings polynomials fuzzy systems or neural networks can be used as either the parameterized nonlinear controller or identifier model in this paper we present algorithms to tune some of the parameters e g the adaptation gain and the direction of descent for a gradient based approximator parameter update law used for a class of nonlinear discrete time systems in both direct and indirect cases in our proposed algorithms the adaptation gain and the direction of descent are obtained by minimizing the instantaneous control energy we will show that updating the adaptation gain can be viewed as a special case of updating the direction of descent we will also compare the direct and indirect adaptive control schemes and illustrate their performance via a simple surge tank example

asymptotic tracking of uncertain systems with continuous control using adaptive bounding this paper presents a robust adaptive control design method for a class of multiple input multiple output uncertain nonlinear systems in the presence of parametric and nonparametric uncertainties and bounded disturbances using the approximation properties of the unknown continuous nonlinearities and the adaptive bounding technique the developed controller achieves asymptotic convergence of the tracking error to zero while ensuring boundedness of parameter estimation errors the algorithm does not assume the knowledge of any bound on the unknown quantities in designing the controller it is based on an integral technique involving the filtered tracking error and produces a continuous control theoretical developments are illustrated via simulation results

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

neural network enhanced output regulation in nonlinear systems a neural network based approach is developed to approximate the feedforward function needed for solving the nonlinear output regulation problem the approach eliminates the need for solving the regulator equations thus applying to complex uncertain nonlinear systems

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

darboux transformation and explicit solutions for the satsuma hirota coupled equation abstract a darboux transformation for the satsuma hirota coupled equation is obtained with the help of the gauge transformation between the lax pairs as an application of the darboux transformation we give some new explicit solutions including rational solutions soliton solutions and periodic solutions and others of the satsuma hirota coupled equation

transition pixel a concept for binarization based on edge detection and gray intensity histograms this paper introduces a novel binarization method based on the concept of transition pixel a generalization of edge pixels such pixels are characterized by extreme transition values computed using pixel intensity differences in a small neighborhood we show how to adjust the threshold of several binary threshold methods which compute gray intensity thresholds using the gray intensity mean and variance of the pixels in the transition set our experiments show that the new approach yields segmentation performance superior to several with current state of the art binarization algorithms

right inverse of a discrete time non linear system the concept of right invertibility functional reproducibility of a general multi variable discrete time analytic non linear system is discussed two different types of right inverses are considered one being a special case of the other the sufficient conditions for both types of right invertibility are given and for invertible systems the right inverses are constructed

identification and control of a nonlinear discrete time system based on its linearization a unified framework this paper presents a unified theoretical framework for the identification and control of a nonlinear discrete time dynamical system in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a higher order function this representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system and reveals the role played by the linearized system in a more transparent form under the assumption that the linearized system is controllable and observable it is shown that 1 the nonlinear system is also controllable and observable in a local domain 2 a feedback law exists to stabilize the nonlinear system locally and 3 the nonlinear system can exactly track a constant or a periodic sequence locally if its linearized system can do so with some additional assumptions the nonlinear system is shown to have a well defined relative degree delay and zero dynamics if the zero dynamics of the linearized system is asymptotically stable so is that of the nonlinear one and in such a case a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly in a neighborhood of the equilibrium state the tracking can be achieved by using the state vector for feedback or by using only the input and the output in which case the nonlinear autoregressive moving average narma model is established and utilized these results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete time dynamical systems

design of a neural network adaptive controller via a constrained invariant ellipsoids technique in safety critical applications control architectures based on adaptive neural networks nns must satisfy strict design specifications this paper presents a practical approach for designing a mixed linear adaptive model reference controller that recovers the performance of a reference model and guarantees the boundedness of the tracking error within an a priori specified compact domain in the presence of bounded uncertainties the linear part of the controller results from the solution of an optimization problem where specifications are expressed as linear matrix inequality constraints the linear controller is then augmented with a general adaptive nn that compensates for the uncertainties the only requirement for the nn is that its output must be confined within pre specified saturation limits toward this end a specific nn output confinement algorithm is proposed in this paper the main advantages of the proposed approach are that requirements in terms of worst case performance can be easily defined during the design phase and that the design of the adaptation mechanism is largely independent from the synthesis of the linear controller a numerical example is used to illustrate the design methodology

consistent identification of narx models via regularization networks generalization networks are nonparametric estimators obtained from the application of tychonov regularization or bayes estimation to the hypersurface reconstruction problem under symmetry assumptions they are a particular type of radial basis function neural network in this correspondence it is shown that such networks guarantee consistent identification of a very general infinite dimensional class of narx models the proofs are based on the theory of reproducing kernel hilbert spaces and the notion of frequency of time probability by means of which it is not necessary to assume that the input is sampled from a stochastic process

subsets of full measure in a generic submanifold in mathbb c n are non plurithin in this paper we prove that if i subset m is a subset of measure 0 in a c 2 smooth generic submanifold m subset mathbb c n then m setminus i is non plurithin at each point of m in mathbb c n this result improves a previous result of a edigarian and j wiegerinck who considered the case where i is pluripolar set contained in a c 1 smooth generic submanifold m subset mathbb c n edigarian and wiegernick in math z 266 2 393 398 2010 the proof of our result is essentially different

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

data based analysis of discrete time linear systems in noisy environment in this paper a data based method is developed for analyzing the controllability and observability of discrete time linear systems in noisy environment this method uses measured data to estimate the controllability matrix and the observability matrix without identifying system models the unbiasedness and consistency of this estimate with measurement noise and system noise are proven respectively as the estimated error of system parameters will not accumulate in calculating the controllability matrix and observability matrix this method has a higher precision than traditional methods especially in high dimensional state space in the simulation the advantages of the data based method in accuracy and convergence are illustrated

the full positive flows of manakov hierarchy hamiltonian structures and conservation laws based on four sets of lenard recursion sequences and zero curvature equation we derive the full positive flows of the manakov hierarchy associated with a 3x3 matrix spectral problem from which some new nonlinear evolution equations are proposed with the help of the darboux transformation soliton solutions of two new nonlinear evolution equations in the manakov hierarchy are constructed as two special reductions the full positive flows of the coupled modified korteweg de vries hierarchy and the sasa satsuma hierarchy are deduced in which some new nonlinear evolution equations are included and then we construct the hamiltonian structures of the manakov hierarchy and infinite conservation laws of several nonlinear evolution equations

feedback linearization control design for systems with fuzzy uncertainty we derive a state feedback control design for nonlinear systems with fuzzy uncertainty we use a fuzzy version of the kolmogorov forward equation and an equivalent deterministic system to represent the effects of the fuzzy uncertainty feedback linearization of the equivalent deterministic system cancels both the system nonlinearities and the effects of the fuzzy uncertainty on the state membership function our controller obtains asymptotic stability and an approximation to our controller drives the system state to a small bounded set

nsm constrained approximation of lipschitz functions from data the problem of approximating a function from a set of its values in the presence of constraints is considered solving this problem is useful in system identification state estimation and control the typical approach to this problem consists in 1 deriving an approximation without considering the constraints and 2 using the constraints to clip the approximation however using this approach may give poor results and in any case no optimality properties can be guaranteed in this paper a nonlinear set membership method is developed allowing optimal constrained approximation the effectiveness of the proposed method is shown through its application to the problem of model predictive control approximation

input output stability theory for direct neuro fuzzy controllers in an input output i o setting we undertake a detailed theoretical investigation of the stability of a given direct static multiple input single output neuro fuzzy controller operating under feedback control dependent only on the functional gain of the plant to be controlled it is shown that various stability regions in weight space are convex and necessary and sufficient conditions are given for these stability regions to be open and bounded the convexity results coupled with the stability test give a practical method for constructing the stability regions we show that an adaptive neuro fuzzy controller is stable under feedback if we constrain the weights of the controller to lie within any compact set within the stability region combining a projection operator with any standard training law can thus give a stable adaptive controller

deadzone compensation in motion control systems using neural networks a compensation scheme is presented for general nonlinear actuator deadzones of unknown width the compensator uses two neural networks nns one to estimate the unknown deadzone and another to provide adaptive compensation in the feedforward path the compensator nn has a special augmented form containing extra neurons whose activation functions provide a jump function basis set for approximating piecewise continuous functions rigorous proofs of closed loop stability for the deadzone compensator are provided and yield tuning algorithms for the weights of the two nns the technique provides a general procedure for using nns to determine the preinverse of an unknown right invertible function

direct filtering a new approach to optimal filter design for nonlinear systems optimal filters for nonlinear systems are in general difficult to derive or implement the common approach is to use approximate solutions such as extended kalman filters ensemble filters or particle filters however no optimality properties can be guaranteed by these approximations and even the stability of the estimation error cannot often be ensured another relevant issue is that in most practical situations the system whose variables have to be estimated is not known and a two step procedure is adopted based on model identification from data and filter design from the identified model however the designed filter may display large performance deteriorations in the case of modeling errors in this paper a new approach overcoming these issues is proposed allowing the design of optimal filters for nonlinear systems in both the cases of known and unknown system the approach is based on the direct filter design from a set of data generated by the system either experimental or simulated data can be used for design a bound on the number of data necessary to ensure a given filter accuracy is also provided showing that the proposed approach is not affected by the curse of dimensionality

neural network approximation of piecewise continuous functions application to friction compensation one of the most important properties of neural nets nns for control purposes is the universal approximation property unfortunately this property is generally proven for continuous functions in most real industrial control systems there are nonsmooth functions e g piecewise continuous for which approximation results in the literature are sparse examples include friction deadzone backlash and so on it is found that attempts to approximate piecewise continuous functions using smooth activation functions require many nn nodes and many training iterations and still do not yield very good results therefore a novel neural network structure is given for approximation of piecewise continuous functions of the sort that appear in friction deadzone backlash and other motion control actuator nonlinearities the novel nn consists of neurons having standard sigmoid activation functions plus some additional neurons having a special class of nonsmooth activation functions termed jump approximation basis function two types of nonsmooth jump approximation basis functions are determined a polynomial like basis and a sigmoid like basis this modified nn with additional neurons having jump approximation activation functions can approximate any piecewise continuous function with discontinuities at a finite number of known points applications of the new nn structure are made to rigid link robotic systems with friction nonlinearities friction is a nonlinear effect that can limit the performance of industrial control systems it occurs in all mechanical systems and therefore is unavoidable in control systems it can cause tracking errors limit cycles and other undesirable effects often inexact friction compensation is used with standard adaptive techniques that require models that are linear in the unknown parameters it is shown here how a certain class of augmented nn capable of approximating piecewise continuous functions can be used for friction compensation

cauchy integral equalities and applications we study bounded holomorphic functions 7t on the unit ball bn of cn satisfying the following so called cauchy integral equalities c 7r te y 7r m 0 1 2 for some sequence ym depending on i among the applications are the ahernrudin problem concerning the composition property of holomorphic functions on bn a projection theorem about the orthogonal projection of h2 bn onto the closed subspace generated by holomorphic polynomials in it and some new information about the inner functions in particular it is shown that if we interpret bmoa bn as the dual of hi bn then the map g g o i is a linear isometry of bmoa b1 into bmoa bn for every inner function it on bn such that it 0 0

an adaptive logical method for binarization of degraded document images abstract this paper describes a modified logical thresholding method for binarization of seriously degraded and very poor quality gray scale document images this method can deal with complex signal dependent noise variable background intensity caused by nonuniform illumination shadow smear or smudge and very low contrast the output image has no obvious loss of useful information firstly we analyse the clustering and connection characteristics of the character stroke from the run length histogram for selected image regions and various inhomogeneous gray scale backgrounds then we propose a modified logical thresholding method to extract the binary image adaptively from the degraded gray scale document image with complex and inhomogeneous background it can adjust the size of the local area and logical thresholding level adaptively according to the local run length histogram and the local gray scale inhomogeneity our method can threshold various poor quality gray scale document images automatically without need of any prior knowledge of the document image and manual fine tuning of parameters it keeps useful information more accurately without overconnected and broken strokes of the characters and thus has a wider range of applications compared with other methods

technical communique robust adaptive regulation of discrete time nonlinear systems with arbitrary nonlinearities this note develops a new recursive estimator with a dead zone by using the estimator a robust adaptive regulator for a class of simple discrete time nonlinear systems with bounded disturbance is presented a global stability result of the closed loop system is obtained through lyapunov analysis without assuming any growth conditions on the nonlinearities the regulation performance is also presented through a simulation example

adaptive mnn control for a class of non affine narmax systems with disturbances in this paper adaptive multi layer neural network mnn control is developed for a class of discrete time non affine nonlinear systems in nonlinear auto regressive moving average with exogenous inputs narmax model by using implicit function theorem the existence of the implicit desired feedback control idfc is proved mnns are used as the emulator of the desired feedback control projection algorithms are used to guarantee the boundedness of the neural network nn weights which removes the need of persistent exciting pe condition for parameter convergence simulation results show the effectiveness of the proposed control scheme

stochastic algorithms for robustness of control performances in recent years there has been a growing interest in developing statistical learning methods to provide approximate solutions to difficult control problems in particular randomized algorithms have become a very popular tool used for stability and performance analysis as well as for design of control systems however as randomized algorithms provide an efficient solution procedure to the intractable problems stochastic methods bring closer to understanding the properties of the real systems the topic of this paper is the use of stochastic methods in order to solve the problem of control robustness the case of parametric stochastic uncertainty is considered necessary concepts regarding stochastic control theory and stochastic differential equations are introduced then a convergence analysis is provided by means of the chernoff bounds which guarantees robustness in mean and in probability as an illustration the robustness of control performances of example control systems is computed

neural network based control design an lmi approach we address a neural network based control design for a discrete time nonlinear system our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin a linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state feedback control law for the nonlinear system based on the certainty equivalence principle the control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal further the stability of the closed loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed loop system converges finally a simple example is presented so as to illustrate our control design procedure

multiple model self tuning control for a class of nonlinear systems this study develops a novel nonlinear multiple model self tuning control method for a class of nonlinear discrete time systems an increment system model and a modified robust adaptive law are proposed to expand the application range thus eliminating the assumption that either the nonlinear term of the nonlinear system or its differential term is global bounded the nonlinear self tuning control method can address the situation wherein the nonlinear system is not subject to a globally uniformly asymptotically stable zero dynamics by incorporating the pole placement scheme a novel nonlinear control structure based on this scheme is presented to improve control precision stability and convergence can be confirmed when the proposed multiple model self tuning control method is applied furthermore simulation results demonstrate the effectiveness of the proposed method

functional reproducibility of general multivariable analytic non linear systems in this paper the functional reproducibility of a general multivariable analytic nonlinear system of the form x f x u y h x u will be discussed where the state space is a real analytic manifold a general inversion algorithm is presented for the system a sufficient and necessary condition for the functional reproducibility of the system is derived the construction of a right inverse system is also included

model free control of nonlinear stochastic systems with discrete time measurements consider the problem of developing a controller for general nonlinear and stochastic systems where the equations governing the system are unknown using discrete time measurement this paper presents an approach for estimating a controller without building or assuming a model for the system such an approach has potential advantages in accommodating complex systems with possibly time varying dynamics the controller is constructed through use of a function approximator such as a neural network or polynomial this paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements a convergence result for stochastic approximation algorithms with time varying objective functions and feedback is established it is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite difference gradient approximations

survey approximate linearization via feedback an overview fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static state feedback and coordinate transformation in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback main reason for that is the limited applicability of the rigorous methods and the complexity sensitivity and design difficulties of the exact linearizing compensators if any in the present paper the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective recent works especially in the area of data based techniques are in fact described and related whenever possible to fundamental results previously obtained by model based differential geometric methods this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to fill visible gaps in this direction

direct adaptive control for a class of mimo nonlinear systems using neural networks in this note direct adaptive neural network nn control is studied for a class of multiple input multiple output nonlinear systems based on input output discrete time model with unknown interconnections between subsystems by finding an orthogonal matrix to tune the nn weights the closed loop system is proven to be semiglobally uniformly ultimately bounded the control performance of the closed loop system is guaranteed by suitably choosing the design parameters