quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

correlations and variability in electrical signals related to earthquake activity abstract evaluating complex fluctuations in geoelectric time series is an important task not only for earthquake prediction but also for understanding complex processes related to earthquake preparation previous studies have reported alterations such as the emergence of correlated dynamics in geoelectric potentials prior to an important earthquake eq however the presence of correlations and its relation with variability has not been widely explored in this work we apply the detrended fluctuation analysis and the multiscale entropy methods to analyze the fluctuations of geoelectric time series monitored in two sites located in mexico we systematically calculate the correlation exponents and the sample entropy s e of geoelectric time series important differences in the scaling exponents and entropy profiles for several time scales are observed in particular a complex behavior characterized by a high entropy across several scales and crossover in the correlation exponents is observed in the vicinity of an m 7 4 eq that occurred on sept 14 1995 moreover we compare the changes in the entropy of the original data with their corresponding shuffled version to see whether correlations in the original data are related to variability

approximation based control of nonlinear mimo time delay systems approximation based control is presented for a class of multi input multi output mimo nonlinear systems in block triangular form with unknown state delays neural networks nns are utilized to approximate and compensate for unknown functions in the system dynamics including the unknown bounds of the functions of delayed states the use of a separation technique removes the need for any assumption on the function of delayed states and allows the handling of multiple delays in each function of delayed states by combining the use of lyapunov krasovskii functionals and adaptive nn backstepping the proposed control guarantees that all closed loop signals remain bounded while the outputs converge to a neighborhood of the desired trajectories simulation results demonstrate the effectiveness of the proposed scheme

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

universal neural network control of mimo uncertain nonlinear systems in this brief a continuous tracking control law is proposed for a class of high order multi input multi output uncertain nonlinear dynamic systems with external disturbance and unknown varying control direction matrix the proposed controller consists of high gain feedback nussbaum gain matrix selector online approximator ola model and a robust term the ola model is represented by a two layer neural network the continuousness of the control signal is guaranteed to relax the requirement for the actuator bandwidth and avoid the incurred chattering effect asymptotic tracking performance is achieved theoretically by standard lyapunov analysis the control feasibility is also verified in simulation environment

on minimal compensators for decoupling control abstract the general construction of minimal regular compensators for decoupling a nonlinear system is given by means of vector subspaces which are generated by differential vectors of outputs and states and the minimal dimension of a decoupling compensator is expressed in intrinsic characterization the equivalence relation of all minimal regular compensators is established though these compensators may have different dynamic behavior from each other

fitting a cm smooth function to data iii suppose we are given a finite subset e rn and a function f e r how to extend f to a cm function f rn r with cm norm of the smallest possible order of magnitude in this paper and in 20 we tackle this question from the perspective of theoretical computer science we exhibit algorithms for constructing such an extension function f and for computing the order of magnitude of its cm norm the running time of our algorithms is never more than cn log n where n is the cardinality of e and c is a constant depending only on m and n

data driven asymptotic stabilization for discrete time nonlinear systems abstract in this paper we propose a data driven feedback controller design method based on lyapunov approach which can guarantee the asymptotic stability of the closed loop and enlarge the estimate of domain of attraction doa for the closed loop first sufficient conditions for a feedback controller asymptotically stabilizing the discrete time nonlinear plant are proposed that is if a feedback controller belongs to an open set consisting of pairs of control input and state whose elements can make the difference of a control lyapunov function clf to be negative definite then the controller asymptotically stabilizes the plant then for a given clf candidate an algorithm to estimate the open set only using data is proposed with the estimate it is checked whether the candidate is or is not a clf if it is a feedback controller is designed just using data which satisfies sufficient conditions mentioned above finally the estimate of doa for closed loop is enlarged by finding an appropriate clf from a clf candidate set based on data because the controller is designed directly from data complexity in building the model and modeling error are avoided

long range correlations in the electric signals that precede rupture further investigations the correlations within the time series of the seismic electric signal ses activities have been studied in a previous paper p varotsos n sarlis and e skordas phys rev e 66 011902 2002 here we analyze the time series of successive high and low level states durations the existence of correlation between the states is investigated by means of hurst and detrended fluctuation analysis dfa the multifractal dfa mf dfa is also employed the results point to a stronger correlation and hence longer memory in the series of the high level states furthermore an analysis in the natural time domain reveals that certain power spectrum characteristics seem to distinguish ses activities from artificial man made electric noises more precisely for natural frequencies 0 f 0 5 the curves of the ses activities and artificial noises lie above and below respectively that of the uniform distribution ud a classification of these two types of electric signals ses activities artificial noises cannot be achieved on the basis of the values of the power law exponents alone if the hurst analysis dfa and mf dfa are applied to the original time series the latter two methods however seem to allow a distinction between the ses activities and artificial noises when treating them not in conventional the time frame but in the natural time domain to further test the techniques a time series produced by another system was examined we chose a signal of ion current fluctuations in membrane channels icfmcs the following conclusions among others have been obtained first the power spectrum analysis in the natural time domain shows that the icfmc curve almost coincides in the range 0 f 0 5 with that of the ud and hence icfmc lies just in the boundary between the ses activities and artificial noises second mf dfa indicates monofractality for the icfmcs with a generalized hurst exponent h 50 8460 03 in the range 7 70 ms

dynamic scaling approach to study time series fluctuations we propose an approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface growth problem in this framework the fluctuation sampling time interval plays the role of time variable whereas the physical time is treated as the analog of spatial variable in this way we found that the fluctuations of many real world time series satisfy the analog of the family viscek dynamic scaling ansatz this finding permits us to use the powerful tools of kinetic roughening theory to classify model and forecast the fluctuations of real world time series

high order unconditionally stable fc ad solvers for general smooth domains ii elliptic parabolic and hyperbolic pdes theoretical considerations a new pde solver was introduced recently in part i of this two paper sequence on the basis of two main concepts the well known alternating direction implicit adi approach on one hand and a certain fourier continuation fc method for the resolution of the gibbs phenomenon on the other unlike previous alternating direction methods of order higher than one which only deliver unconditional stability for rectangular domains the new high order fc ad fourier continuation alternating direction algorithm yields unconditional stability for general domains at an o nlog n cost per time step for an n point spatial discretization grid in the present contribution we provide an overall theoretical discussion of the fc ad approach and we extend the fc ad methodology to linear hyperbolic pdes in particular we study the convergence properties of the newly introduced fc gram fourier continuation method for both approximation of general functions and solution of the alternating direction odes we also present for parabolic pdes on general domains and thus for our associated elliptic solvers a stability criterion which when satisfied ensures unconditional stability of the fc ad algorithm use of this criterion in conjunction with numerical evaluation of a series of singular values of the alternating direction discrete one dimensional operators suggests clearly that the fifth order accurate class of parabolic and elliptic fc ad solvers we propose is indeed unconditionally stable for all smooth spatial domains and for arbitrarily fine discretizations to illustrate the fc ad methodology in the hyperbolic pde context finally we present an example concerning the wave equation demonstrating sixth order spatial and fourth order temporal accuracy as well as a complete absence of the debilitating dispersion error also known as pollution error that arises as finite difference and finite element solvers are applied to solution of wave propagation problems

robust adaptive control for a class of mimo nonlinear systems by state and output feedback in this technical note high dimensional integral lyapunov functions are introduced for a class of mimo nonlinear systems with unknown nonlinearities first adaptive state feedback control is presented based on the integral lyapunov function when only the output is measurable by using a high gain observer to estimate the derivative of the system output adaptive output feedback control is also derived the proposed control scheme provides a general approach to stabilize the mimo plant without any restrictive assumptions the control is continuous and ensures closed loop stability and convergence of the tracking error to a small residual set the size of the tracking error at steady state can be specified a priori and guaranteed by choosing the design parameters

essential orders and the non linear decoupling problem abstract the concept of essential orders has recently been introduced into linear system theory and has been shown to be useful in the solution of static and dynamic decoupling problems commauit et al 1986 de luca et al 1985 this paper presents a non trivial extension to the class of non linear affine systems of some of these definitions and results it is shown that these invariant integers give the minimal order for a regular dynamic compensator that decouples a right invertible system

fast monte carlo algorithms for matrices iii computing a compressed approximate matrix decomposition in many applications the data consist of or may be naturally formulated as an m times n matrix a which may be stored on disk but which is too large to be read into random access memory ram or to practically perform superlinear polynomial time computations on it two algorithms are presented which when given an m times n matrix a compute approximations to a which are the product of three smaller matrices c u and r each of which may be computed rapidly let a cur be the computed approximate decomposition both algorithms have provable bounds for the error matrix a a in the first algorithm c columns of a and r rows of a are randomly chosen if the m times c matrix c consists of those c columns of a after appropriate rescaling and the r times n matrix r consists of those r rows of a also after appropriate rescaling then the c times r matrix u may be calculated from c and r for any matrix x let x f and x 2 denote its frobenius norm and its spectral norm respectively it is proven that left a a right xi le min d mathrm rank d le k left a d right xi poly k 1 c left a right f holds in expectation and with high probability for both xi 2 f and for all k 1 ldots mbox rank a thus by appropriate choice of k left a a right 2 le epsilon left a right f also holds in expectation and with high probability this algorithm may be implemented without storing the matrix a in ram provided it can make two passes over the matrix stored in external memory and use o m n additional ram assuming that c and r are constants independent of the size of the input the second algorithm is similar except that it approximates the matrix c by randomly sampling a constant number of rows of c thus it has additional error but it can be implemented in three passes over the matrix using only constant additional ram to achieve an additional error beyond the best rank k approximation that is at most epsilon a f both algorithms take time which is a low degree polynomial in k 1 epsilon and 1 delta where delta 0 is a failure probability the first takes time linear in mbox max m n and the second takes time independent of m and n the proofs for the error bounds make important use of matrix perturbation theory and previous work on approximating matrix multiplication and computing low rank approximations to a matrix the probability distribution over columns and rows and the rescaling are crucial features of the algorithms and must be chosen judiciously

long range correlations in the electric signals that precede rupture the smoluchowski chapman kolmogorov functional equation is applied to the electric signals that precede rupture the results suggest a non markovian character of the analyzed data the rescaled range hurst and detrended fluctuation analyses as well as that related with the mean distance a walker spanned lead to power law exponents which are consistent with the existence of long range correlations a universality in the power spectrum characteristics of these signals emerges if an analysis is made not in the conventional time frame but in the natural time domain within this frame it seems that certain power spectrum characteristics of ion current fluctuations in membrane channels distinguish them from the electric signals preceding rupture the latter exhibit a behavior compatible with that expected from a model based on the random field ising hamiltonian at the critical point

minimality of dynamic input output decoupling for nonlinear systems in this note we study the strong dynamic input output decoupling problem for nonlinear systems using an algebraic theory for nonlinear control systems we obtain for a dynamic input output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem

multifractal cross correlation analysis in electricity spot market abstract in this paper we investigate the multiscale cross correlations between electricity price and trading volume in czech market based on a newly developed algorithm called multifractal cross correlation analysis mfcca the new algorithm is a natural multifractal generalization of the detrended cross correlation analysis dcca and is sensitive to cross correlation structure and free from limitations of other algorithms by considering the original sign of the cross covariance it allows us to properly quantify and detect the subtle characteristics of two simultaneous recorded time series first the multifractality and the long range anti persistent auto correlations of price return and trading volume variation are confirmed using multifractal detrended fluctuation analysis mf dfa furthermore we show that there exist long range anti persistent cross correlations between price return and trading volume variation by mfcca and we also identify that the cross correlations disappear on the level of relative small fluctuations in order to obtain deeper insight into the dynamics of the electricity market we analyze the relation between generalized hurst exponent and the multifractal cross correlation scaling exponent q we find that the difference between the generalized hurst exponent and the multifractal cross correlation scaling exponent is significantly different for smaller fluctuation which indicates that the multifractal character of cross correlations resembles more each other for electricity price and trading volume on the level of large fluctuations and weakens for the smaller ones

effect of nonlinear filters on detrended fluctuation analysis when investigating the dynamical properties of complex multiple component physical and physiological systems it is often the case that the measurable system s output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms instead the output signal is often a linear or nonlinear function of the quantity of interest here we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal using the detrended fluctuation analysis dfa which has been shown to accurately quantify power law correlations in nonstationary signals specifically we study the effect of three types of transforms i linear y i a x i b ii nonlinear polynomial y i a x k i and iii nonlinear logarithmic y i log x i delta filters we compare the correlation and scaling properties of signals before and after the transform we find that linear filters do not change the correlation properties while the effect of nonlinear polynomial and logarithmic filters strongly depends on a the strength of correlations in the original signal b the power k of the polynomial filter and c the offset delta in the logarithmic filter we further apply the dfa method to investigate the apparent scaling of three analytic functions i exponential exp x a ii logarithmic log x a and iii power law x a lambda which are often encountered as trends in physical and biological processes while these three functions have different characteristics we find that there is a broad range of values for parameter a common for all three functions where the slope of the dfa curves is identical we further note that the dfa results obtained for a class of other analytic functions can be reduced to these three typical cases we systematically test the performance of the dfa method when estimating long range power law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider

data driven approximate value iteration with optimality error bound analysis abstract features of the data driven approximate value iteration avi algorithm proposed in li et al 2014 for dealing with the optimal stabilization problem include that only process data is required and that the estimate of the domain of attraction for the closed loop is enlarged however the controller generated by the data driven avi algorithm is an approximate solution for the optimal control problem in this work a quantitative analysis result on the error bound between the optimal cost and the cost under the designed controller is given this error bound is determined by the approximation error of the estimation for the optimal cost and the approximation error of the controller function estimator the first one is concretely determined by the approximation error of the data driven dynamic programming dp operator to the dp operator and the approximation error of the value function estimator these three approximation errors are zeros when the data set of the plant is sufficient and infinitely complete and the number of samples in the interested state space is infinite this means that the cost under the designed controller equals to the optimal cost when the number of iterations is infinite

some applications of persistent random walks and the telegrapher s equation abstract a persistent random walk can be regarded as a multidimensional markov process the bias free telegraphers equation is 2 p t 2 1 t p t v 2 2 p it can be regarded as interpolating between the wave equation t and the diffusion equation t 0 previously it has found application in thermodynamics cf the review in rev mod phys 61 1989 41 62 1990 375 more recent applications are reviewed in the present article

decoupling with dynamic compensation for strong invertible affine non linear systems abstract in this paper we tackle for affine non linear systems the morgan problem i e the scalar input scalar output decoupling problem for square systems with dynamic compensation the result provided here theorem 3 1 generalizes that one previously given by wang 1970 for linear systems

nonuniform fast fourier transforms using min max interpolation the fast fourier transform fft is used widely in signal processing for efficient computation of the ft of finite length signals over a set of uniformly spaced frequency locations however in many applications one requires nonuniform sampling in the frequency domain i e a nonuniform ft several papers have described fast approximations for the nonuniform ft based on interpolating an oversampled fft this paper presents an interpolation method for the nonuniform ft that is optimal in the min max sense of minimizing the worst case approximation error over all signals of unit norm the proposed method easily generalizes to multidimensional signals numerical results show that the min max approach provides substantially lower approximation errors than conventional interpolation methods the min max criterion is also useful for optimizing the parameters of interpolation kernels such as the kaiser bessel function

parameter selection and numerical approximation properties of fourier extensions from fixed data fourier extensions have been shown to be an effective means for the approximation of smooth nonperiodic functions on bounded intervals given their values on an equispaced or in general scattered grid related to this method are two parameters these are the extension parameter t the ratio of the size of the extended domain to the physical domain and the oversampling ratio h the number of sampling nodes per fourier mode the purpose of this paper is to investigate how the choice of these parameters affects the accuracy and stability of the approximation our main contribution is to document the following interesting phenomenon namely if the desired condition number of the algorithm is fixed in advance then the particular choice of such parameters makes little difference to the algorithm s accuracy as a result one is free to choose t without concern that it is suboptimal in particular one may use the value t 2 which corresponds to the case where the extended domain is precisely twice the size of the physical domain for which there is known to be a fast algorithm for computing the approximation in addition we determine the resolution power points per wavelength of the approximation to be equal to email protected and address the trade off between resolution power and stability

a remark on nonlinear accessibility conditions and infinite prolongations the lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order it yields to a new lie algebraic criterion and to the consideration of first integrals which apply to nonlinear systems in quite general form the latter characterization in particular is valid without distinguishing between the system variables and is independent of time scalings weak accessibility is also considered

noninteracting control with stability for a class of nonlinear systems abstract in this paper we address the problem of noninteracting control with stability for the class of nonlinear square systems for which noninteraction can be achieved without stability by means of invertible static state feedback the use of both static state feedback and dynamic state feedback is investigated we prove that in both cases the asymptotic stabilizability of certain subsystems is necessary to achieve noninteraction and stability we use this and some recent results to state a complete set of necessary and sufficient conditions in order to solve the problem

data driven zero sum neuro optimal control for a class of continuous time unknown nonlinear systems with disturbance using adp this paper is concerned with a new data driven zero sum neuro optimal control problem for continuous time unknown nonlinear systems with disturbance according to the input output data of the nonlinear system an effective recurrent neural network is introduced to reconstruct the dynamics of the nonlinear system considering the system disturbance as a control input a two player zero sum optimal control problem is established adaptive dynamic programming adp is developed to obtain the optimal control under the worst case of the disturbance three single layer neural networks including one critic and two action networks are employed to approximate the performance index function the optimal control law and the disturbance respectively for facilitating the implementation of the adp method convergence properties of the adp method are developed to show that the system state will converge to a finite neighborhood of the equilibrium the weight matrices of the critic and the two action networks are also convergent to finite neighborhoods of their optimal ones finally the simulation results will show the effectiveness of the developed data driven adp methods

entropy in the natural time domain a surrogate data analysis is presented which is based on the fluctuations of the entropy s defined in the natural time domain phys rev e 68 031106 2003 this entropy is not a static one as for example the shannon entropy the analysis is applied to three types of time series i e seismic electric signals artificial noises and electrocardiograms and recognizes the nonmarkovianity in all these signals furthermore it differentiates the electrocardiograms of healthy

preseismic electromagnetic signals in terms of complexity there is a recent thesis in the literature that an important organization of a physical system precedes a catastrophic event in this context one can search for signatures that imply the transition from a normal state to a main catastrophic event e g earthquake experimental techniques are thus useful in corroborating theories from observed data for example recent results indicate that preseismic electromagnetic time series contain information characteristic of an ensuing earthquake event hereby we attempt to demonstrate that an easily computable complexity measure such as t complexity or approximate entropy gives evidence of state changes leading to the point of global instability the appearance of a precatastrophic state is characterized by significant lower complexity in terms of t complexity and approximate entropy the present study confirms the conclusions of previous works based on an independent linear fractal spectral analysis this convergence between nonlinear and linear analysis provides a more reliable detection concerning the emergence of the last phase of the earthquake preparation process more precisely we claim that our results suggest an important principle significant complexity decrease and accession of persistency in electromagnetic em time series can be confirmed at the tail of the preseismic em emission which could be used as diagnostic tools for the earth s impending crust failure direct laboratory and field experimental data as well as theoretical arguments support the conclusions of the present analysis 2006 the american physical society

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

spectral methods in non tensor geometry part ii single domain spectral methods have been largely restricted to tensor product bases on a tensor product grid to break the tensor barrier we studied approximation in two idealized families of domains one family is bounded by a squircle the zero isoline of b x y x 2 y 2 1 the boundary varies smoothly from a circle 1 to the square the other family is bounded by a perturbed quadrifolium the plane algebraic curve x 2 y 2 x 2 y 2 3 x 2 y 2 2 this varies smoothly from the singular self intersecting curve known as the quadrifolium to a circle as varies from zero to infinity we compared two different bivariate polynomial bases truncating by total degree zernike polynomials are natural for the disk tensor products of chebyshev polynomials are equally sensible for the square both yield an exponential rate of convergence for our non tensor neither disk nor square domains indeed the chebyshev basis worked well for the disk and the zernike polynomials were good for the square the expected differences due to numerical ill conditioning did not emerge much to our surprise the price for the nontensor domain was that hyperinterpolation was necessary that is least squares fitting with more interpolation constraints than unknowns denoting the number of interpolation points by p and the basis size by n a ratio of p n around two to three was optimum while p near one was very inacccurate a uniform grid truncated to include only those points within the squircle or other boundary curve was satisfactory even without interpolation points on the boundary although boundary points are a cost effective improvement interpolation costs were greatly reduced by exploiting the invariance of the squircle bounded and perturbed quadrifolium domains to the eight element d4 dihedral group

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

power spectrum and detrended fluctuation analysis application to daily temperatures the variability measures of fluctuation analysis fa and detrended fluctuation analysis dfa are expressed in terms of the power spectral density and of the autocovariance of a given process the diagnostic potential of these methods is tested on several model power spectral densities in particular we find that both fa and dfa reveal an algebraic singularity of the power spectral density at small frequencies corresponding to an algebraic decay of the autocovariance a scaling behavior of the power spectral density in an intermediate frequency regime is better reflected by dfa than by fa we apply fa and dfa to ambient temperature data from the 20th century with the primary goal to resolve the controversy in literature whether the low frequency behavior of the corresponding power spectral densities are better described by a power law or a stretched exponential as a third possible model we suggest a weibull distribution however it turns out that neither fa nor dfa can reliably distinguish between the proposed models

effect of extreme data loss on long range correlated and anticorrelated signals quantified by detrended fluctuation analysis detrended fluctuation analysis dfa is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations to better identify the intrinsic correlation properties of real world signals where a large amount of data is missing or removed due to artifacts we investigate how extreme data loss affects the scaling behavior of long range power law correlated and anticorrelated signals we introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long range correlations the surrogate signals we generate are characterized by four parameters i the dfa scaling exponent alpha of the original correlated signal u i ii the percentage p of the data removed from u i iii the average length mu of the removed or remaining data segments and iv the functional form p l of the distribution of the length l of the removed or remaining data segments we find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90 in contrast the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost these observations are confirmed on two examples of real world signals human gait and commodity price fluctuations we further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales we find that for anticorrelated signals even 10 of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior in contrast positively correlated signals show no observable changes in the local scaling for up to 65 of data loss while for larger percentage of data loss the local scaling shows overestimated regions with higher local exponent at small scales followed by underestimated regions with lower local exponent at large scales finally we investigate how the scaling is affected by the average length probability distribution and percentage of the remaining data segments in comparison to the removed segments we find that the average length mu r of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value interestingly the scales where the maximum deviation occurs follow a power law relationship with mu r whereas the percentage of data loss determines the extent of the deviation the results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss

numerical differentiation by a fourier extension method with super order regularization abstract based on the idea of fourier extension we develop a new method for numerical differentiation the tikhonov regularization method with a super order penalty term is presented to deal with the illposdness of the problem and the regularization parameter can be chosen by a discrepancy principle for various smooth conditions the solution process of the new method is uniform and order optimal error bounds can be obtained numerical experiments are also presented to illustrate the effectiveness of the proposed method

hybrid adaptive control laws solving a path following problem for non holonomic mobile manipulators in this paper a general solution to the path following problem for mobile manipulators with non holonomic mobile platform has been presented new proposed control algorithms for mobile manipulators with fully known dynamics or with parametric uncertainty in the dynamics take into considerations the kinematics as well as the dynamics of the non holonomic mobile manipulator the convergence of the control algorithms is proved using the lasalle s invariance principle

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

a fast algorithm for fourier continuation a new algorithm is presented which provides a fast method for the computation of recently developed fourier continuations a particular type of fourier extension method that yield superalgebraically convergent fourier series approximations of nonperiodic functions previously the coefficients of an approximating fourier series have been obtained by means of a regularized singular value decomposition svd based least squares solution to an overdetermined linear system of equations these svd methods are effective when the size of the system does not become too large but they quickly become unwieldy as the number of unknowns in the system grows we demonstrate a novel decoupling of the least squares problem which results in two systems of equations one of which may be solved quickly by means of fast fourier transforms ffts and another that is demonstrated to be well approximated by a low rank system utilizing randomized algorithms the low rank system is reduced to a significantly smaller system of equations this new system is then efficiently solved with drastically reduced computational cost and memory requirements while still benefiting from the advantages of using a regularized svd the computational cost of the new algorithm in on the order of the cost of a single fft multiplied by a slowly increasing factor that grows only logarithmically with the size of the system

on dynamic feedback linearization abstract we address the problem of transforming a nonlinear multi input system into a linear controllable one via nonsingular dynamic feedback and extended state space diffeomorphism we show that in the single input case if a system is dynamic feedback linearizable it is also static feedback linearizable we then give sufficient conditions for a class of multi input systems to be dynamic feedback linearizable all three dimensional systems with two controls and a controllable linear approximation about the origin are shown to belong to such a class

characterization of allowable perturbations for robust decoupling of affine non linear systems for affine non linear systems we study the effects of uncertainties in systems vector fields on decoupled linear input output behaviour a characterization of an allowable class of perturbations which preserve the decoupling properties of the nominal system is given an immediate consequence of this characterization indicates that decoupling position control of rigid robotic manipulators is not robust under any perturbations in robot dynamics the result is applied to simple hamiltonian control systems to characterize the allowable perturbation of total energy function

estimation of multifractality based on natural time analysis abstract recent studies have shown that results deduced on the basis of a new time domain termed natural time reveal that novel dynamical features hidden behind time series in complex systems can be uncovered here we propose a method for estimating the multifractal behavior of time series by studying the fluctuations of natural time under time reversal examples of the application of this method to fractional gaussian noises fractional brownian motions binomial multifractal series levy processes as well as interbeat intervals time series from electrocardiograms are presented

stochastic origins of the long range correlations of ionic current fluctuations in membrane channels an explicit stochastic representation of a stationary ionic current signal recorded from a single channel of a biological membrane is presented in the framework of the proposed approach we show how the dichotomous time structure of the signal leads to the non markovian character of the channel current the rescaled range hurst and detrended fluctuation analyses confirm the theoretical result to investigate the ionic current fluctuations we introduce the orey index as a statistical method providing additional information on the properties of stochastic processes in order to reveal any differences between the experimental and reconstructed signals we apply also the statistical tests to the model based simulations of the channel action

heavy tails and long range dependence in on off processes and associated fluid models on off models are common inputs for a variety of communication network models as well as storage and inventory models a stationary renewal process alternating periods of activity active transmission fluid buildup etc with periods of inactivity silence no transmission inputs off etc induces a stationary indicator process which indicates if the system is active or not heavy tails for the on periods induces a covariance function for the indicator process which decreases slowly at a rate characteristic of long range dependence this has dramatic consequences for fluid models where fluid flows in at constant rate and there is a constant rate of release

a fast algorithm for the convolution of functions with compact support using fourier extensions we present a new algorithm for computing the convolution of two compactly supported functions the algorithm approximates the functions to be convolved using fourier extensions and then uses the fast fourier transform to efficiently compute fourier extension approximations to the pieces of the result the complexity of the algorithm is mathcal o bigl n log n 2 bigr where n is the number of degrees of freedom used in each of the fourier extensions

accurate high order representation of complex three dimensional surfaces via fourier continuation analysis we present a new method for construction of high order parametrizations of surfaces starting from point clouds the method we propose can be used to produce full surface parametrizations by sets of local charts each one representing a large surface patch which typically contains thousands of the points in the original point cloud for complex surfaces of scientific and engineering relevance the proposed approach accurately renders both smooth and non smooth portions of a surface it yields super algebraically convergent fourier series approximations to a given surface up to and including all points of geometric singularity such as corners edges conical points etc in view of their c smoothness except at true geometric singularities and their properties of high order approximation the surfaces produced by this method are suitable for use in conjunction with high order numerical methods for boundary value problems in domains with complex boundaries including pde solvers integral equation solvers etc our approach is based on a very simple concept use of fourier analysis to continue smooth portions of a piecewise smooth function into new functions which defined on larger domains are both smooth and periodic the continuation functions arising from a function f converge super algebraically to f in its domain of definition as discretizations are refined we demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

local nonlinear model matching from linearity to nonlinearity the model matching problem consists of designing a compensator for a given system called the plant in such a way that the resulting input output behaviour matches that of a prespecified model in this paper a local solution of the nonlinear model matching problem is given for the case that the model is decouplable by static state feedback the main theorem states that under generic conditions on the plant the problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model the generic conditions are identified they naturally appear in the solution of the dynamic input output decoupling problem for the plant the theory is illustrated by means of two examples

correlation based tuning of decoupling multivariable controllers the iterative method labelled correlation based tuning cbt is considered in this paper for tuning linear time invariant multivariable controllers the approach allows one to tune some elements of the controller transfer function matrix to satisfy the desired closed loop performance while the other elements are tuned to mutually decouple the closed loop outputs decoupling is achieved by decorrelating a given reference with the non corresponding outputs the controller parameters are calculated either by solving a correlation equation decorrelation procedure or by minimizing a cross correlation function correlation reduction in addition the preferred way of exciting a 2x2 system for cbt is investigated via the accuracy of the estimated controller parameters it is shown that simultaneous excitation of both reference signals does not improve the accuracy of the estimated controller parameters compared to the case of sequential excitation in fact one must choose between low experimental cost simultaneous excitation and better accuracy of the estimated parameters sequential excitation the theoretical results are illustrated via three simulation studies

approximate i o feedback linearization of discrete time non linear systems via virtual input direct design the design of linearizing compensators via output feedback for discrete time non linear plants using i o measurements only is typically performed in an indirect way by identifying first a non linear model of the plant and resorting then to a suitable model based design technique in this paper we propose the use of a new method based on a virtual input direct design vid2 approach the main feature of such a method is to carry the control design into a standard non linear mapping approximation problem thus avoiding any preliminary plant identification phase as compared with the existing methods the new one requires less computational effort while taking full advantage of the non linear approximation software tools already available in this paper the new method is described and some theoretical results are given concerning the i o linearization of discrete time systems via dynamic output feedback

robust output tracking for nonlinear systems with weakly non minimum phase this paper is concerned with the problem of designing a robust output tracking controller for mimo nonlinear systems with weakly non minimum phase based on our system formulation control plants with uncertainties and or with actuator dynamics fall into the class under consideration the controller design here is divided into two phases fast feedback control and slow feedback control so that a final composite control is obtained the former is chosen to stabilize the boundary layer system whereas the latter essentially handles the mismatched uncertainties after the system is reformulated under some mild assumptions it is shown that the overall states are bounded and the tracking errors converge to a residual set whose size is a class k function of e as e 0 the residual set shrinks to the origin an interesting application to a simplified aircraft model with fast actuator dynamics which turns out to be weakly non minimum phase is given the computer simulation has verified the expected satisfac

a sufficient condition for nonlinear noninteracting control with stability via dynamic state feedback a sufficient condition is given to solve the problem of achieving local noninteracting control with asymptotic stability via dynamic state feedback for a nonlinear affine system the condition which is automatically satisfied in the case of linear systems although only sufficient is helpful in overcoming some of the geometric obstructions pointed out in the literature an example in which the author assumptions are satisfied is given clearly showing how to construct a decoupling and stabilizing dynamic state feedback and how the condition can weaken the requirement that the p dynamics be locally asymptotically stable

natural time analysis of critical phenomena a quantity exists by which one can identify the approach of a dynamical system to the state of criticality which is hard to identify otherwise this quantity is the variance of natural time where and pk is the normalized energy released during the kth event of which the natural time is defined as k k n and n stands for the total number of events then we show that 1 becomes equal to 0 070 at the critical state for a variety of dynamical systems this holds for criticality models such as 2d ising and the bak tang wiesenfeld sandpile which is the standard example of self organized criticality this condition of 1 0 070 holds for experimental results of critical phenomena such as growth of rice piles seismic electric signals and the subsequent seismicity before the associated main shock

on the resolution power of fourier extensions for oscillatory functions functions that are smooth but non periodic on a certain interval possess fourier series that lack uniform convergence and suffer from the gibbs phenomenon however they can be represented accurately by a fourier series that is periodic on a larger interval this is commonly called a fourier extension when constructed in a particular manner fourier extensions share many of the same features of a standard fourier series in particular one can compute fourier extensions which converge spectrally fast whenever the function is smooth and geometrically fast if the function is analytic much the same as the fourier series of a smooth analytic and periodic function with this in mind the purpose of this paper is to describe analyse and explain the observation that fourier extensions much like classical fourier series also have excellent resolution properties for representing oscillatory functions the resolution power or required number of degrees of freedom per wavelength depends on a user controlled parameter and as we show it varies between 2 and p the former value is optimal and is achieved by classical fourier series for periodic functions for example the latter value is the resolution power of algebraic polynomial approximations thus fourier extensions with an appropriate choice of parameter are eminently suitable for problems with moderate to high degrees of oscillation

predictability of the coherent noise model and its applications we study the threshold distribution function of the coherent noise model for the case of infinite number of agents this function is piecewise constant with a finite number of steps n the latter exhibits a 1 f behavior as a function of the order of occurrence of an avalanche and hence versus natural time an analytic expression of the expectation value mathcal e s for the size s of the next avalanche is obtained and used for the prediction of the next avalanche apart from mathcal e s the number of steps n can also serve for this purpose this enables the construction of a similar prediction scheme which can be applied to real earthquake aftershock data

discrete periodic extension using an approximate step function the discrete periodic extension is a technique for augmenting a given set of uniformly spaced samples of a smooth function with auxiliary values in an extension region if a suitable extension is constructed the interpolating trigonometric polynomial found via an fft will accurately approximate the original function in its original interval of definition the discrete periodic extension is a key construction in the algorithm fc gram fourier continuation based on gram polynomials algorithm the fc gram algorithm in turn lies at the heart of several recent efficient and high order accurate pde solvers this paper presents a new flexible discrete periodic extension procedure that performs at least as well as the fc gram method but with somewhat simpler constructions and significantly decreased setup time

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

an intrinsic sufficient condition for regular decoupling abstract this paper introduces an intrinsic regularity property namely regular invertibility which requires that a sequence of vector spaces has constant dimension after a certain order thus allowing some degeneracies in the beginning it corresponds to the system and its tangent having the same defect using the constant rank theorem this property is shown to be sufficient condition for regular decoupling

attempt to distinguish long range temporal correlations from the statistics of the increments by natural time analysis most probable value of 1 of the shuffled data is found to be approximately equal to that of the original data the difference most likely arising from temporal correlation finally it is found that the differential entropy associated with the probability p1 maximizes for around 1 6 1 7 which is comparable to the value determined experimentally in diverse phenomena e g solar flares icequakes dislocation glide in stressed single crystals of ice etc it also agrees with the b value in the gutenberg richter law of earthquakes in addition the case of multiplicative cascades is studied in the natural time domain

a new approach to the structure at infinity of nonlinear systems abstract zeros at infinity for nonlinear systems are defined by using differential algebra this approach can be viewed as a nonlinear generalization of silverman s structure algorithm the connection with the problem of inverting input output systems is briefly described

the nonlinear interactor and its application to input output decoupling the solvability of the input output decoupling problem via pure dynamic state feedback a special type of dynamic compensator without zeros at infinity is investigated a necessary and sufficient condition for the solvability of this problem is established in terms of a nonlinear interactor a new concept in the theory of nonlinear control

approximate decoupling and asymptotic tracking for mimo systems this paper presents an algorithm for approximate input output decoupling of nonlinear mimo systems that are either numerically ill posed or exhibit nearly singular behavior in the application of decoupling algorithms although the systems considered are regular so that the exact decoupling algorithms are applicable in this case they require inversion of an ill conditioned matrix and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros the approximate algorithms of this paper are numerically robust and provide solutions that do not cancel far off right half plane zeros this latter characteristic is especially valuable when some of the far off right half plane zeros are unstable the algorithms are inspired by and are generalizations of some examples in the flight control literature

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

a triangular canonical form for a class of 0 flat nonlinear systems this article proposes a triangular canonical form for a class of 0 flat nonlinear systems necessary and sufficient geometrical conditions are given in order to guarantee the existence of a local diffeomorphism to transform the studied nonlinear systems into the proposed 0 flat canonical form which enables us to compute the flat output as well

a canonical dynamic extension for noninteraction with stability for affine nonlinear square systems we study the problem of noninteracting control with stability via dynamic feedback for continuous affine nonlinear square systems given a system which may not be decouplable via static state feedback but is decouplable via dynamic feedback a canonical dynamic extension is constructed we show that every dynamic extension contains this canonical one hence the mix dynamics as defined by wagner of the canonical extension is contained in every other dynamic extension following wagner s result the stability of this mix dynamics is necessary for noninteraction with internal stability the results in this paper show that under some regularity assumptions in the investigation of noninteraction with stability one can assume without loss of generality that the system is decouplable via static state feedback

data driven model free adaptive control for a class of mimo nonlinear discrete time systems in this paper a data driven model free adaptive control mfac approach is proposed based on a new dynamic linearization technique dlt with a novel concept called pseudo partial derivative for a class of general multiple input and multiple output nonlinear discrete time systems the dlt includes compact form dynamic linearization partial form dynamic linearization and full form dynamic linearization the main feature of the approach is that the controller design depends only on the measured input output data of the controlled plant analysis and extensive simulations have shown that mfac guarantees the bounded input bounded output stability and the tracking error convergence

nonextensivity and natural time the case of seismicity nonextensive statistical mechanics pioneered by tsallis has recently achieved a generalization of the gutenberg richter law for earthquakes this remarkable generalization is combined here with natural time analysis which enables the distinction of two origins of self similarity i e the process memory and the process increments infinite variance by using also detrended fluctuation analysis for the detection of long range temporal correlations we demonstrate the existence of both temporal and magnitude correlations in real seismic data of california and japan natural time analysis reveals that the nonextensivity parameter q in contrast to some published claims cannot be considered as a measure of temporal organization but the tsallis formulation does achieve a satisfactory description of real seismic data for japan for q 1 66 when supplemented by long range temporal correlations