iterative learning control for a class of nonlinear systems abstract for precise tracking control of a class of nonlinear systems over a finite time interval an iterative learning control method using the relative degree of a system is proposed the class of nonlinear systems where the iterative learning control is applied can be extended by using the proposed method a sufficient condition is derived for guaranteeing a uniform convergence of the output to the desired output the results obtained for a class of nonlinear systems are shown to be a generalization of the existing results for linear time invariant systems

comments on the cramer rao lower bounds for signals with constant amplitude and polynomial phase for original paper see ieee trans signal processing vol 39 p 749 52 march 1991 different expressions for the cramer rao lower bounds crlbs of constant amplitude polynomial phase signals embedded in white gaussian noise appear in the literature the present paper revisits the derivation of the bounds reported by peleg and porat 1991 and indicates that the resulting expressions depend on the interval over which the signal is defined the proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds

computational studies for the stochastic landau lifshitz gilbert equation the stochastic landau lifshitz gilbert equation describes the thermally induced dynamics of magnetic moments in ferromagnetic materials solutions of this highly nonlinear stochastic pde are unit vector fields and satisfy an energy estimate these are crucial properties to construct a convergent discretization in space and time we propose a convergent finite element approximation of the problem based on the midpoint rule the numerical scheme preserves the underlying properties of the continuous problem further we construct a robust and efficient newton multigrid solver for the solution of the nonlinear systems associated with the discretized problems at each time level computational studies show the optimal convergence behavior of the scheme in the case of smooth solutions long time dynamics for finite ensembles of spins evidence the ergodicity of an invariant measure of the continuum model numerical experiments in two dimensions demonstrate pathwise finite time blow up behavior of the solution w

iterative learning control synthesis based on 2 d system theory an algorithm is presented for iterative learning of the control input for a linear discrete time multivariable system necessary and sufficient conditions are stated for convergence of the proposed algorithm the algorithm synthesis and analysis are based on two dimensional 2 d system theory a numerical example is given

instantaneous frequency estimation of polynomial fm signals using the peak of the pwvd statistical performance in the presence of additive gaussian noise the peak of the polynomial wigner ville distribution pwvd has been previously proposed as an estimator of the instantaneous frequency if for a monocomponent polynomial frequency modulated fm signal in this paper we evaluate the statistical performance of this estimator in the case of additive white gaussian noise and provide an analytical expression for the variance we show that for a given pwvd order the estimator performance can be improved by a proper choice of the kernel coefficients in the pwvd a performance comparison between the pwvd based if estimator and another previously proposed one based on the high order ambiguity function haf is also provided simulation results show that for a signal to noise ratio larger than 3 db the proposed sixth order pwvd outperforms the haf in estimating the if of a third or fourth order polynomial phase signal evaluated at the central point of the observation interval

improved instantaneous frequency estimation using an adaptive short time fourier transform instantaneous frequency estimation ife arises in a variety of important applications including fm demodulation we present here a new time frequency representation tfr based approach to ife based on an adaptive short time fourier transform astft this tfr leads naturally to a type of short term ml estimator of the if to further improve the performance we apply a multistate hidden markov model hmm based post estimation tracker the end result is up to a 16 db reduction in the threshold snr over the frequency discriminator fd and an 8 db improvement over the phase locked loop pll for a rayleigh fading channel

on a discrete time stochastic learning control algorithm the learning gain for a selected learning algorithm is derived based on minimizing the trace of the input error covariance matrix for linear time varying systems it is shown that if the product of the input output coupling matrices is a full column rank then the input error covariance matrix converges uniformly to zero in the presence of uncorrelated random disturbances however the state error covariance matrix converges uniformly to zero in presence of measurement noise moreover it is shown that if a certain condition is met then the knowledge of the state coupling matrix is not needed to apply the proposed stochastic algorithm the proposed algorithm is shown to suppress a class of nonlinear and repetitive state disturbance the application of this algorithm to a class of nonlinear systems is also considered a numerical example is included to illustrate the performance of the algorithm

cramer rao bounds and maximum likelihood estimation for random amplitude phase modulated signals the problem of estimating the phase parameters of a phase modulated signal in the presence of colored multiplicative noise random amplitude modulation and additive white noise both gaussian is addressed closed form expressions for the exact and large sample cramer rao bounds crbs are derived it is shown that the crb is significantly affected by the color of the modulating process when the signal to noise ratio snr or the intrinsic snr is small maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed these estimators are shown to be equivalent to the nonlinear least squares estimators which consist of matching the squared observations with a constant amplitude phase modulated signal when the mean of the multiplicative noise is forced to zero closed form expressions are derived for the efficiency of these estimators and are verified via simulations

quantitative performance analysis of scalogram as instantaneous frequency estimator instantaneous frequency if estimation through the estimation of peak locations in the time frequency plane is an important approach for signals contaminated with additive white gaussian noise in this paper the forementioned analysis is carried out for continuous wavelet transform the analysis of the scalogram as the instantaneous frequency estimator is performed for any fm signal regardless of the mother wavelet accurate expressions for the bias and the variance of the estimator are derived and reveal that the bias and the variance are signal dependent results are statistically confirmed through the numerical analysis for several mother wavelets and among considered wavelets the morlet wavelet produces the smallest estimation error furthermore the performance of the if estimator based on the scalogram and the spectrogram were compared through analysis of mean square error these results showed that the scalogram with the morlet wavelet exhibited good performance for the sample linear fm signal and the sample hyperbolic fm signal in comparison to the spectrogram

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

asymptotic wavelet and gabor analysis extraction of instantaneous frequencies the behavior of the continuous wavelet and gabor coefficients in the asymptotic limit using stationary phase approximations are investigated in particular it is shown how under some additional assumptions these coefficients allow the extraction of some characteristics of the analyzed signal such as frequency and amplitude modulation laws applications to spectral line estimations and matched filtering are briefly discussed

the monogenic wavelet transform this paper extends the 1 d analytic wavelet transform to the 2 d monogenic wavelet transform the transformation requires care in its specification to ensure suitable transform coefficients are calculated and it is constructed so that the wavelet transform may be considered as both local and monogenic this is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform classes of monogenic wavelets are proposed with suitable local properties it is shown that the monogenic wavelet annihilates anti monogenic signals that the monogenic wavelet transform is phase shift covariant and that the transform magnitude is phase shift invariant a simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived the monogenic wavelet ridges of local plane waves are given

the achievable accuracy in estimating the instantaneous phase and frequency of a constant amplitude signal the approach is based on modeling the signal phase by a polynomial function of time on a finite interval the phase polynomial is expressed as a linear combination of the legendre basis polynomials first the cramer rao bound crb of the instantaneous phase and frequency of constant amplitude polynomial phase signals is derived then some properties of the crbs are used to estimate the order of magnitude of the bounds the analysis is extended to signals whose phase and frequency are continuous but not polynomial the crb can be achieved asymptotically if the estimation of the phase coefficients is done by maximum likelihood the maximum likelihood estimates are used to show that the achievable accuracy in phase and frequency estimation is determined by the crb of the polynomial coefficients and the deviation of true phase and frequency from the polynomial approximations

a discrete time learning control algorithm for a class of linear time invariant systems a discretized version of the d type learning control algorithm is presented for a mimo linear discrete time system a necessary and sufficient condition for uniform convergence of the proposed learning algorithm is presented then we prove that the same condition is sufficient for the global robustness of the proposed learning algorithm to state disturbances measurement noise at the output and reinitialization error are present at each iteration a numerical example is given to illustrate the results

model based iterative learning control with a quadratic criterion for time varying linear systems in this paper iterative learning control ilc based on a quadratic performance criterion is revisited and generalized for time varying linear constrained systems with deterministic stochastic disturbances and noises the main intended area of application for this generalized method is chemical process control where excessive input movements are undesirable and many process variables are subject to hard constraints it is shown that within the framework of the quadratic criterion based ilc q ilc various practical issues such as constraints disturbances measurement noises and model errors can be considered in a rigorous and systematic manner algorithms for the deterministic case the stochastic case and the case with bounded parameter uncertainties are developed and relevant properties such as the asymptotic convergence are established under some mild assumptions numerical examples are provided to demonstrate the performance of the proposed algorithms

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

generalized instantaneous parameters and window matching in the time frequency plane the concept of instantaneous parameters which has previously been associated exclusively with 1 d measures like the instantaneous frequency and the group delay are extended to the 2 d time frequency plane such generalized instantaneous parameters are associated with the short time fourier transform they may also be interpreted as local moments of certain time frequency distributions it is shown that these measures enable local signal behavior to be characterized in the time frequency plane for nonstationary deterministic signals the usefulness of the generalized instantaneous parameters is demonstrated in their application to optimal selection of windows for spectrograms this is achieved through window matching in the time frequency plane an algorithm is provided that illustrates the performance of this window matching results based on simulated and real data are presented

stochastic p type d type iterative learning control algorithms this paper presents stochastic algorithms that compute optimal and sub optimal learning gains for a p type iterative learning control algorithm ilc for a class of discrete time varying linear systems the optimal algorithm is based on minimizing the trace of the input error covariance matrix the state disturbance reinitialization errors and measurement errors are considered to be zero mean white processes it is shown that if the product of the input output coupling matrices c t 1 b t is full column rank then the input error covariance matrix converges to zero in presence of uncorrelated disturbances another sub optimal p type algorithm which does not require the knowledge of the state matrix is also presented it is shown that the convergence of the input error covariance matrices corresponding to the optimal and sub optimal p type and d type algorithms are equivalent and all converge to zero at a rate inversely proportional to the number of learning iterations a transient response pe

parameter estimation for random amplitude chirp signals we consider the problem of estimating the parameters of a chirp signal observed in multiplicative noise i e whose amplitude is randomly time varying two methods for solving this problem are presented first an unstructured nonlinear least squares approach nls is proposed it is shown that by minimizing the nls criterion with respect to all samples of the time varying amplitude the problem reduces to a two dimensional 2 d maximization problem a theoretical analysis of the nls estimator is presented and an expression for its asymptotic variance is derived it is shown that the nls estimator has a variance that is very close to the cramer rao bound the second approach combines the principles behind the high order ambiguity function hbf and the nls approach it provides a computationally simpler but suboptimum estimator a statistical analysis of the haf based estimator is also carried out and closed form expressions are derived for the asymptotic variance of the haf estimators based on the data and on the squared data numerical examples attest to the validity of the theoretical analyzes and establish a comparison between the two proposed methods

cramer rao bounds for wavelet transform based instantaneous frequency estimates we use an asymptotic integral approximation of a wavelet transform as a model for the estimation of instantaneous frequency if our approach allows the calculation of the cramer rao bound for the if variance at each time directly without the need for explicit phase parameterization this is in contrast to other approaches where the cramer rao bounds rely on a preliminary decomposition of the if with respect to a usually polynomial basis attention is confined to the morlet wavelet transform of single component signals corrupted with additive gaussian noise potential computationally and statistically efficient if extraction algorithms suggested by the analysis are also discussed

brief sampled data iterative learning control for nonlinear systems with arbitrary relative degree in this paper a sampled daata iterative learning control method is proposed for nonlinear systems without restriction on system relative degree the learning algorithm does not require numerical differentiations of any order from the tracking error a sufficient condition is derived to guarantee the convergence of the system output at each sampling instant to the desired trajectory numerical simulation is conducted to demonstrate the theoretical result

on the analytic wavelet transform an exact and general expression for the analytic wavelet transform of a real valued signal is constructed resolving the time dependent effects of nonnegligible amplitude and frequency modulation the analytic signal is first locally represented as a modulated oscillation demodulated by its own instantaneous frequency and then taylor expanded at each point in time the terms in this expansion called the instantaneous modulation functions are time varying functions which quantify at increasingly higher orders the local departures of the signal from a uniform sinusoidal oscillation closed form expressions for these functions are found in terms of bell polynomials and derivatives of the signal s instantaneous frequency and bandwidth the analytic wavelet transform is shown to depend upon the interaction between the signal s instantaneous modulation functions and frequency domain derivatives of the wavelet inducing a hierarchy of departures of the transform away from a perfect representation of the signal the form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal in which case our expressions simplify considerably one may then quantify the time varying bias associated with signal estimation via wavelet ridge analysis and choose wavelets to minimize this bias

a stochastic iterative learning control algorithm with application to an induction motor a recursive optimal algorithm based on minimizing the input error covariance matrix is derived to generate the learning gain matrix of a p type ilc for linear discrete time varying systems with arbitrary relative degree it is shown that in the case where the number of inputs is not greater than the number of outputs the input error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of uncorrelated random state disturbance reinitialization errors and measurement noise the state error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of measurement noise in the case where the number of inputs is greater than the number of outputs then the system output error converges to zero at a rate inversely proportional to the number of iterations in presence of measurement noise another suboptimal recursive algorithm is also proposed based on unknown system dynamics and unknown disturb