nonlinear feedback design for fixed time stabilization of linear control systems two types of nonlinear control algorithms are presented for uncertain linear plants controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions the control design procedure uses block control principles and finite time attractivity properties of polynomial feedbacks controllers of the second type are modifications of the second order sliding mode control algorithms they provide global finite time stability of the closed loop system and allow to adjust a guaranteed settling time independently on initial conditions control algorithms are presented for both single input and multi input systems theoretical results are supported by numerical simulations

a hybrid fixed time observer for state estimation of linear systems abstract this paper deals with the problem of state estimation for single output linear systems under some structural properties of the system matrices it is possible to design a hybrid observer capable of estimating the state of the system exactly and in a finite time moreover the proposed hybrid observer provides fixed time convergence of the state estimation error i e there exists a convergence time that is bounded and such a bound is independent of the initial estimation error the robustness properties of the hybrid observer are analyzed for the linear system with unknown inputs and the linear system with unknown inputs and parametric uncertainty some simulation results illustrate the effectiveness of the proposed hybrid observer

direction finding with partly calibrated uniform linear arrays a new method for direction finding with partly calibrated uniform linear arrays ulas is presented it is based on the conventional estimation of signal parameters via rotational invariance techniques esprit by modeling the imperfections of the ulas as gain and phase uncertainties for a fully calibrated array it reduces to the conventional esprit algorithm moreover the direction of arrivals doas unknown gains and phases of the uncalibrated sensors can be estimated in closed form without performing a spectral search hence it is computationally very attractive the cramer rao bounds crbs of the partly calibrated ulas are also given simulation results show that the root mean squared error rmse performance of the proposed algorithm is better than the conventional methods when the number of uncalibrated sensors is large it also achieves satisfactory performance even at low signal to noise ratios snrs

maximum likelihood direction of arrival estimation in unknown noise fields using sparse sensor arrays we address the problem of maximum likelihood ml direction of arrival doa estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays in such arrays intersubarray spacings are substantially larger than the signal wavelength and therefore sensor noises can be assumed to be uncorrelated between different subarrays this leads to a block diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying doa estimation problem a new deterministic ml doa estimator is derived for this class of sparse sensor arrays the proposed approach concentrates the ml estimation problem with respect to all nuisance parameters in contrast to the analytic concentration used in conventional ml techniques the implementation of the proposed estimator is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function the proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases it is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ml based approaches to doa estimation in spatially correlated noise

doa estimation of temporally and spatially correlated narrowband noncircular sources in spatially correlated white noise the main contribution of our work consists in developing for the first time a method of estimating the direction of arrival doa parameters assuming noncircular and temporally and spatially correlated signals this new approach based on a significant enhancement of the two sided instrumental variable signal subspace fitting iv ssf method outperforms its classical version in terms of lower bias and error variance moreover it will be shown that our new method is statistically more efficient than the mode method especially in the case of partly and fully coherent signals where only the extended and the classical two sided iv ssf methods are applicable we also derive an explicit expression for the stochastic cramer rao bound crb of the doa estimates from temporally and spatially correlated signals generated from noncircular sources the new crb is compared to those of circular temporally correlated and noncircular independent and identically distributed signals to show that the crb obtained assuming both noncircular sources and temporally correlated signals is lower than the crbs derived considering only one of these two assumptions this illustrates the potential gain that both noncircularity and temporal correlation provide when considered together it will also be proven that the difference between the three crbs increases with the number of snapshots however as the signal to noise ratio snr increases the crbs merge together and decrease linearly moreover at low snr values it will be shown that temporal correlation is more informative about the unknown doa parameters than noncircularity finally the crb derived assuming noncircular and temporally correlated signals depends on the noncircularity rate the circularity phase separation and the doa separation

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

iterative methods for subspace and doa estimation in nonuniform noise usually direction of arrival doa estimators are derived under the assumption of uniform white noise whose covariance matrix is a scaled identity matrix however in practice the noise can be nonuniform with an arbitrary unknown diagonal covariance matrix in this situation the performance of doa estimators may be deteriorated considerably if the noise nonuniformity is ignored to tackle this problem iterative approaches to subspace estimation are developed and the corresponding subspace based doa estimators are addressed in our proposed methods the signal subspace and noise covariance matrix are first determined by maximizing the log likelihood ll function or solving a least squares ls minimization problem both of which are accomplished in an iterative manner then the doas are determined from the subspace estimate and or noise covariance matrix estimate with the help of traditional doa estimators as the signal subspace and noise covariance matrix can be computed in closed form in each iteration the proposals are computationally attractive furthermore the signal subspace is directly calculated without the requirement of the exact knowledge of the array manifold enabling us to handle array uncertainties by incorporating conventional subspace based calibration algorithms simulations and experimental results are included to demonstrate the superiority of the proposed approaches

finite time observers application to secure communication in this paper control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue this paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to an output injection the finite time convergence relies on the homogeneity properties of nonlinear systems the observer is then applied to the problem of secure data transmission based on the finite time chaos synchronization and the two channel transmission method

truncation order and its effect in a class of nonlinear systems fundamental results are established for truncation order and its effect in the volterra class of nonlinear systems these results provide a significant insight into the analytical relationships among truncation order truncation error and estimation error for the output spectra of nonlinear systems and also lead to the development of novel methods for choosing the truncation order and excitation magnitudes for accurate determination of nonlinear frequency response components these results should be important in the kernel estimation and frequency domain analysis of nonlinear systems on the basis of the volterra series structure and order selection of block oriented nonlinear systems with polynomial nonlinearity the results also provide a much improved version of the multi level excitation method for system analysis and identification

homogeneous approximation recursive observer design and output feedback we introduce two new tools that can be useful in nonlinear observer and output feedback design the first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity homogeneity in the bi limit exploiting this extension we give several results concerning stability and robustness for a homogeneous in the bi limit vector field the second tool is a new recursive observer design procedure for a chain of integrator combining these two tools we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems

doa estimation and detection in colored noise using additional noise only data in a typical array processing scenario noise acting on the array can not be assumed spatially white it is in many cases necessary to use quiet periods when only noise is received to estimate the noise covariance if estimation of the signal parameters and noise covariance is performed jointly performance can be improved this is especially true when stationarity considerations limit the amount of available valid noise only data an asymptotically valid approximative maximum likelihood method aml for the estimation problem is derived in this work the resulting criterion is when concentrated with respect to the signal parameters relatively simple in numerical experiments aml shows promising small sample performance compared to earlier methods the criterion function is also well suited for numerical optimization the new criterion function allows for the development of a novel mode like non iterative estimation procedure if the array belongs to the important class of uniform linear arrays the resulting procedure retains the asymptotic properties of maximum likelihood and numerical simulations indicate superior threshold performance when compared to an optimally weighted subspace fitting wsf formulation of mode for the detection problem no method has been presented that takes the unknown noise covariance into account here a well known detection scheme for wsf is extended to work in this scenario as well the derivations of this scheme further stress the importance of using the correct weighting in wsf when the noise covariance is unknown it is also shown that the minimum value of the criterion function associated with aml can be used for the detection purpose numerical experiments indicate very promising performance for the aml detection scheme

estimation of the number of sources in unbalanced arrays via information theoretic criteria estimating the number of sources impinging on an array of sensors is a well known and well investigated problem a common approach for solving this problem is to use an information theoretic criterion such as minimum description length mdl or the akaike information criterion aic the mdl estimator is known to be a consistent estimator robust against deviations from the gaussian assumption and nonrobust against deviations from the point source and or temporally or spatially white additive noise assumptions over the years several alternative estimation algorithms have been proposed and tested usually these algorithms are shown using computer simulations to have improved performance over the mdl estimator and to be robust against deviations from the assumed spatial model nevertheless these robust algorithms have high computational complexity requiring several multidimensional searches in this paper which is motivated by real life problems a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken an mdl type estimator that is robust against deviation from assumption of equal noise level across the array is studied the consistency of this estimator even when deviations from the equal noise level assumption occur is proven a novel low complexity implementation method avoiding the need for multidimensional searches is presented as well making this estimator a favorable choice for practical applications

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

recursive design of finite time convergent observers for a class of time varying nonlinear systems this paper considers the problem of designing globally finite time convergent observers for a class of nonlinear systems with time varying and output dependent coefficients which make the existing design approaches inapplicable to solve this problem a bottom up design approach is first employed to recursively construct a finite time convergent observer with time varying coefficients for the nominal system then using the homogeneous domination approach we scale the finite time convergent observer with an appropriate choice of gain for the original nonlinear system satisfying a holder condition in addition we show that the holder condition imposed on the nonlinearities can be removed for nonlinear systems with bounded trajectories

instrumental variable approach to array processing in spatially correlated noise fields high performance signal parameter estimation from sensor array data is a problem which has received much attention a number of so called eigenvector ev techniques such as music esprit wsf and mode have been proposed in the literature the ev techniques for array processing require knowledge of the spatial noise correlation matrix that constitutes a significant drawback a novel instrumental variable iv approach to the sensor array problem is proposed the iv technique relies on the same basic geometric properties as the ev methods to obtain parameter estimates however by exploiting the temporal correlation of the source signals no knowledge of the spatial noise covariance is required the asymptotic properties of the iv estimator are examined and an optimal iv method is derived computer simulations are presented to study the properties of the iv estimators in samples of practical length the proposed algorithm is also shown to perform better than music on a full scale passive sonar experiment

maximum likelihood estimation for array processing in colored noise direction of arrival estimation of multiple sources using a uniform linear array in noise with unknown covariance is considered the noise is modeled as a spatial autoregressive process with unknown parameters both stochastic and deterministic signal models are considered for the random signal case an approximate maximum likelihood estimator of the signal and noise parameters is derived it requires numerical maximization of a compressed likelihood function over the unknown arrival angles analytical expressions for the mles of the signal covariance and the ar parameters are given similar results for the case of deterministic signals are also presented

a global high gain finite time observer a global finite time observer is designed for nonlinear systems which are uniformly observable and globally lipschitz this result is based on a high gain approach combined with recent advances on finite time stability using lyapunov function and homogeneity concepts

mapping non linear integro differential equations into the frequency domain a recursive algorithm is derived to compute the generalized frequency response functions for a large class of non linear integro differential equations applications to duffing s equation and a modified van der pol model are discussed

the parametric characteristic of frequency response functions for nonlinear systems the characteristic of the frequency response functions of nonlinear systems can be revealed and analyzed by analyzing of the parametric characteristics of these functions to achieve these objectives a new operator is defined and several fundamental and important results about the parametric characteristics of the frequency response functions of nonlinear systems are developed these theoretical results provide a significant and novel insight into the frequency domain characteristics of nonlinear systems and circumvent a large amount of complicated integral and symbolic calculations which have previously been required to perform nonlinear system frequency domain analysis several new results for the analysis and synthesis of nonlinear systems are also developed examples are included to illustrate potential applications of the new results

homogeneity approach to high order sliding mode design it is shown that a general uncertain single input single output regulation problem is solvable only by means of discontinuous control laws giving rise to the so called high order sliding modes the homogeneity properties of the corresponding controllers yield a number of practically important features in particular finite time convergence is proved and asymptotic accuracy is calculated in a very general way in the presence of input noises discrete measurements and switching delays a robust homogeneous differentiator is included in the control structure thus yielding robust output feedback controllers with finite time convergence it is demonstrated that homogeneity features significantly simplify the design and investigation of a new family of high order sliding mode controllers finally simulation results are presented

mapping from parametric characteristics to generalized frequency response functions of non linear systems based on the parametric characteristic of the nth order generalized frequency response function gfrf for non linear systems described by a non linear differential equation nde model a mapping function from the parametric characteristics to the gfrfs is established by which the nth order gfrf can be directly written into a more straightforward and meaningful form in terms of the first order gfrf i e an n degree polynomial function of the first order gfrf the new expression has no recursive relationship between different order gfrfs and demonstrates some new properties of the gfrfs which can explicitly unveil the linear and non linear factors included in the gfrfs and reveal clearly the relationship between the nth order gfrf and its parametric characteristic as well as the relationship between the nth order gfrf and the first order gfrf the new results provide a novel and useful insight into the frequency domain analysis and design of non linear systems based on the gfrfs several examples are given to illustrate the theoretical results

output frequency response function of nonlinear volterra systems an expression for the output frequency response function ofrf which defines the explicit analytical relationship between the output spectrum and the system parameters is derived for nonlinear systems which can be described by a polynomial form differential equation model an effective algorithm is developed to determine the ofrf directly from system simulation or experimental data simulation studies demonstrate the significance of the ofrf concept and verify the effectiveness of the algorithm which evaluates the ofrf numerically these new results provide an important basis for the analytical study and design of a wide class of nonlinear systems in the frequency domain

a transform based covariance differencing approach for some classes of parameter estimation problems a method of parameter estimation is presented for a class of problems in which the desired signal is embedded in colored noise with unknown covariance the proposed algorithm does not require multiple estimates of the signal covariance matrix instead it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while the signal component is transformed in some appropriate manner the noise component is then eliminated by forming the difference of the original and transformed covariance differencing methods to be applied to a wider class of problems than was previously possible this is illustrated by applying the algorithm to the problems of bearing estimation resolution of overlapping echos and transient response analysis simulation results demonstrate that the technique affords significant improvement in certain situations over conventional methods

state observation of nonlinear uncertain dynamical systems this note proposes new types of observers for nonlinear dynamical systems subjected to bounded nonlinearities or uncertainties the design of these observers utilizes techniques related to variable structure systems theory a measure for the rate at which the estimates converge to the actual states is derived

nonlinear influence in the frequency domain alternating series the nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have volterra series expansion it is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities the magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series sufficient and necessary conditions in which the output spectrum can be cast into an alternating series are studied these results reveal a novel frequency domain insight into the nonlinear influence on a system and provide a new method for the analysis and design of nonlinear systems in the frequency domain examples are given to illustrate the results

frequency response functions for nonlinear convergent systems convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time invariant systems in this note we extend frequency response functions defined for linear systems to nonlinear convergent systems such nonlinear frequency response functions for convergent systems give rise to nonlinear bode plots which serve as a graphical tool for performance analysis of nonlinear convergent systems in the frequency domain the results are illustrated with an example

array processing in correlated noise fields based on instrumental variables and subspace fitting accurate signal parameter estimation from sensor array data is a problem which has received much attention in the last decade a number of parametric estimation techniques have been proposed in the literature in general these methods require knowledge of the sensor to sensor correlation of the noise which constitutes a significant drawback this difficulty can be overcome only by introducing alternative assumptions that enable separating the signals from the noise in some applications the raw sensor outputs can be preprocessed so that the emitter signals are temporally correlated with correlation length longer than that of the noise an instrumental variable iv approach can then be used for estimating the signal parameters without knowledge of the spatial color of the noise a computationally simple iv approach has recently been proposed by the authors herein a refined technique that can give significantly better performance is derived a statistical analysis of the parameter estimates is performed enabling optimal selection of certain user specified quantities a lower bound on the attainable error variance is also presented the proposed optimal iv method is shown to attain the bound if the signals have a quasideterministic character

detection and localization in colored noise via generalized least squares a method for detection and localization of multiple signals in spatially colored noise by an arbitrary passive sensor array is presented the method also enables exploitation of prior knowledge that the signals are uncorrelated so as to improve the performance and to allow detection and localization even if the number of signals exceeds the number of sensors the estimation based on the generalized least squares criterion is both consistent and asymptotically efficient the detection is performed via the minimum description length mdl principle and is proved to be consistent simulation results confirming the theoretical results are included

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

determination of the analytical parametric relationship for output spectrum of volterra systems based on its parametric characteristics the output frequency response function ofrf of volterra systems can be described as a polynomial function of model parameters however the analytical determination of the ofrf is very computationally intensive especially for higher order ofrf to circumvent this problem a numerical method can be adopted provided that a series of simulation or experimental data for this polynomial function are given in this study it is theoretically shown that the analytical parametric relationship of ofrf up to any order can be determined accurately by using a simple least square method and every specific component of the output spectrum can also be determined explicitly based on the ofrf s parametric characteristics practical techniques to obtain a unique and accurate solution for the least square method are discussed this study provides a fundamental result for the determination of the analytical parametric relationship for this kind of system polynomial functions by using numerical methods

output frequency characteristics of nonlinear systems some interesting properties of output frequencies of volterra type nonlinear systems are particularly investigated these results provide a very novel and useful insight into the super harmonic and inter modulation phenomena in output frequency response of nonlinear systems with consideration of the effects incurred by different nonlinear components in the system the new properties theoretically demonstrate several fundamental output frequency characteristics and unveil clearly the mechanism of the interaction or coupling effects between different harmonic behaviors in system output frequency response incurred by different nonlinear components these results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities they can provide an important guidance to modeling identification control and signal processing by using the volterra series theory in practice

robust exact uniformly convergent arbitrary order differentiator an arbitrary order differentiator that in the absence of noise converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented the only assumption on a signal to be differentiated n 1 times is that its n th derivative is uniformly bounded by a known constant the proposed differentiator switches from a newly designed uniform differentiator to the classical high order sliding mode hosm differentiator the uniform part drives the differentiation error trajectories into a compact neighborhood of the origin in a time that is independent of the initial differentiation error then the hosm differentiator is used to bring the differentiation error to zero in finite time

direction estimation in partially unknown noise fields the problem of direction of arrival estimation in the presence of colored noise with unknown covariance is considered the unknown noise covariance is assumed to obey a linear parametric model using this model the maximum likelihood directions parameter estimate is derived and a large sample approximation is formed it is shown that a priori information on the source signal correlation structure is easily incorporated into this approximate ml aml estimator furthermore a closed form expression of the cramer rao bound on the direction parameter is provided a perturbation analysis with respect to a small error in the assumed noise model is carried out and an expression of the asymptotic bias due to the model mismatch is given computer simulations and an application of the proposed technique to a full scale passive sonar experiment is provided to illustrate the results

second order sliding mode observer for mechanical systems the super twisting second order sliding mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems the finite time convergence of the observer is proved thus the observer can be designed independently of the controller a discrete version of the observer is considered and the corresponding accuracy is estimated