minimum norm mutual coupling compensation with applications in direction of arrival estimation this paper introduces a new mutual coupling compensation method based on the minimum norm solution to an underdetermined system of equations the crucial advantage over previous techniques is that the formulation is valid independent of the type of antenna element and provides good results in situations where signal strengths vary considerably in using the matrix pencil algorithm to estimate the directions of arrival the examples show that the proposed method results in significantly lower bias than the traditional open circuit method the analysis of mutual coupling is also applied in the context of a code division multiple access communication system

on d type and p type ilc designs and anticipatory approach many schemes of iterative learning control ilc have been developed for continuous time non linear dynamic systems to improve tracking performance two schemes d type and p type have been the bases for many ilc designs recently the anticipatory ilc scheme has been introduced on the basis of a different approach wang 1998a 1999 in this paper these basic schemes are compared from both analysis and implementation view points the anticipatory ilc scheme is designed on the basis of a causal pair of the action taken and its resulting state variables this approach has the anticipatory characteristics of the d type ilc and the simplicity for implementation of p type ilcs a sampled data ilc scheme is presented as another form of this anticipatory ilc scheme furthermore control device saturation is taken into account and tracking error convergence results are established with proofs the convergence results are also provided in the presence of uncertainties disturbances and measurement noises ex

a deterministic least squares approach to space time adaptive processing stap a direct data domain d sup 3 least squares space time adaptive processing stap approach is presented for adaptively enhancing signals in a nonhomogeneous environment the nonhomogeneous environment may consist of nonstationary clutter and could include blinking jammers the d sup 3 approach is applied to data collected by an antenna array utilizing space and in time doppler diversity conventional stap generally utilizes statistical methodologies based on estimating a covariance matrix of the interference using data from secondary range cells as the results are derived from ensemble averages one filter optimum in a probabilistic sense is obtained for the operational environment assumed to be wide sense stationary however for highly transient and inhomogeneous environments the conventional statistical methodology is difficult to apply hence the d sup 3 method is presented as it analyzes the data in space and time over each range cell separately the d sup 3 method is deterministic in approach from an operational standpoint an optimum method could be a combination of these two diverse methodologies this paper represents several new d sup 3 approaches one is based on the computation of a generalized eigenvalue for the signal strength and the others are based on the solution of a set of block hankel matrix equations since the matrix of the system of equations to be solved has a block hankel structure the conjugate gradient method and the fast fourier transform fft can be utilized for efficient solution of the adaptive problem illustrative examples presented in this paper use measured data from the multichannel airborne radar measurements mcarm database to detect a sabreliner in the presence of urban land and sea clutter an added advantage for the d sup 3 method in solving real life problems is that simultaneously many realizations can be obtained for the same solution for the signal of interest soi the degree of variability amongst the different results can provide a confidence level of the processed results the d sup 3 method may also be used for mobile communications

an extension of the concept of gradient semigroups which is stable under perturbation abstract in this article we introduce the concept of a gradient like nonlinear semigroup as an intermediate concept between a gradient nonlinear semigroup those possessing a lyapunov function see j k hale asymptotic behavior of dissipative systems math surveys monogr vol 25 amer math soc 1989 and a nonlinear semigroup possessing a gradient like attractor we prove that a perturbation of a gradient like nonlinear semigroup remains a gradient like nonlinear semigroup moreover for non autonomous dynamical systems we introduce the concept of a gradient like evolution process and prove that a non autonomous perturbation of a gradient like nonlinear semigroup is a gradient like evolution process for gradient like nonlinear semigroups and evolution processes we prove continuity characterization and pullback and forwards exponential attraction of their attractors under perturbation extending the results of a n carvalho j a langa j c robinson a suarez characterization of non autonomous attractors of a perturbed gradient system j differential equations 236 2007 570 603 on characterization and of a v babin m i vishik attractors in evolutionary equations stud math appl vol 25 north holland amsterdam 1992 on exponential attraction

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

impulsive state feedback control of a predator prey model the dynamics of a predator prey model with impulsive state feedback control which is described by an autonomous system with impulses is studied the sufficient conditions of existence and stability of semi trivial solution and positive period 1 solution are obtained by using the poincare map and analogue of the poincare criterion the qualitative analysis shows that the positive period 1 solution bifurcates from the semi trivial solution through a fold bifurcation the bifurcation diagrams of periodic solutions are obtained by using the poincare map and it is shown that a chaotic solution is generated via a cascade of period doubling bifurcations

an adaptive nulling system for a narrow band signal with a look direction constraint utilizing the conjugate gradient method the problem of iterative adjustments of the weights of a phased array with a look direction constraint in the presence of jammers is presented the technique described uses the adaptive conjugate method instead of the popularly used method of steepest descent to eliminate the jammer components thus minimizing the error between the received signal and the actual one this iterative method minimized the l sub 2 norm the mean square error and is guaranteed to converge in a finite number of steps which is not available for the present techniques utilized to solve this problem improvement in rate of convergence is thus achieved at the expense of algorithmic complexity

invariant probability measures and non wandering sets for impulsive semiflows we consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows we establish sufficient conditions for the existence of probability measures which are invariant under such impulsive semiflows under these conditions we also deduce the forward invariance of their non wandering sets except the discontinuity points

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

characterization of non autonomous attractors of a perturbed infinite dimensional gradient system in this paper we determine the exact structure of the pullback attractors in non autonomous problems that are perturbations of autonomous gradient systems with attractors that are the union of the unstable manifolds of a finite set of hyperbolic equilibria we show that the pullback attractors of the perturbed systems inherit this structure and are given as the union of the unstable manifolds of a set of hyperbolic global solutions which are the non autonomous analogues of the hyperbolic equilibria we also prove again parallel to the autonomous case that all solutions converge as t infinity to one of these hyperbolic global solutions we then show how to apply these results to systems that are asymptotically autonomous as t infinity and as t infinity and use these relatively simple test cases to illustrate a discussion of possible definitions of a forwards attractor in the non autonomous case c 2007 elsevier inc all rights reserved

semicontinuity of attractors for impulsive dynamical systems abstract in this paper we introduce the concept of collective tube conditions which assures a suitable behaviour for a family of dynamical systems close to impulsive sets using the collective tube conditions we develop the theory of upper and lower semicontinuity of global attractors for a family of impulsive dynamical systems

sufficient and necessary criteria for existence of pullback attractors for non compact random dynamical systems abstract we study pullback attractors of non autonomous non compact dynamical systems generated by differential equations with non autonomous deterministic as well as stochastic forcing terms we first introduce the concepts of pullback attractors and asymptotic compactness for such systems we then prove a sufficient and necessary condition for existence of pullback attractors we also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors for random systems containing periodic deterministic forcing terms we show the pullback attractors are also periodic under certain conditions as an application of the abstract theory we prove the existence of a unique pullback attractor for reaction diffusion equations on r n with both deterministic and random external terms since sobolev embeddings are not compact on unbounded domains the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions

computation of the exact information matrix of gaussian time series with stationary random components the paper presents an algorithm for efficient recursive computation of the fisher information matrix of gaussian time series whose random components are stationary and whose means and covariances are functions of a parameter vector the algorithm is first developed in a general framework and then specialized to the case of autoregressive moving average processes with possible additive white noise the asymptotic behavior of the algorithm is explored and a termination criterion is derived finally the algorithm is used to demonstrate the behavior of the exact cramer rao bound for unbiased estimates for some arma processes as a function of the number of data points it is shown that for processes with zeros near the unit circle and short data records the exact cramer rao bound differs dramatically from its common approximation based on asymptotic theory

an iterative learning control theory for a class of nonlinear dynamic systems abstract an iterative learning control scheme is presented for a class of nonlinear dynamic systems which includes holonomic systems as its subset the control scheme is composed of two types of control methodology a linear feedback mechanism and a feedforward learning strategy at each iteration the linear feedback provides stability of the system and keeps its state errors within uniform bounds the iterative learning rule on the other hand tracks the entire span of a reference input over a sequence of iterations the proposed learning control scheme takes into account the dominant system dynamics in its update algorithm in the form of scaled feedback errors in contrast to many other learning control techniques the proposed learning algorithm neither uses derivative terms of feedback errors nor assumes external input perturbations as a prerequisite the convergence proof of the proposed learning scheme is given under minor conditions on the system parameters

reconfigurable adaptive array beamforming by antenna selection traditional adaptive array beamforming with a fixed array configuration can lead to significant inefficiencies and performance loss under different scenarios as antennas become smaller and cheaper relative to front ends it becomes important to devise a reconfigurable adaptive antenna array raaa strategy to yield high signal to noise and interference ratio using fewer antennas this is achieved by selecting k from n antennas to minimize the spatial correlation coefficient scc between the desired signal and the interference the lower bound of optimum scc is formulated with two relaxation methods to give information about the suitable number of selected antennas k a correlation measurement cm method is proposed to select the optimum subarray with k antennas thereby reducing complexity we carry out performance analysis and show that a 1 k2 suboptimum solution can be guaranteed with arbitrary shaped arrays furthermore a difference of convex sets dcs method is proposed to select the optimum subarray with controlled quiescent pattern in order to reduce the effect of interference during the reconfiguration time the utility of the proposed array reconfiguration for performance improvement without increasing the cost is demonstrated using both simulated and experimental data

an iterative learning control law for dynamical systems abstract this paper is concerned with an iterative learning control law which enables us to find a control input that generates the desired output exactly over a finite time interval through the repetition of trials we derive a sufficient condition for nonlinear systems to achieve the desired output by the iterative learning control based on this result we show that the direct transmission term of the plant plays a crucial role in the error convergence of the learning process further we identify the class of plants to which the learning control law is applicable

a modified music algorithm for direction of arrival estimation in the presence of antenna array manifold mismatch we introduce a modified multiple signal classification music algorithm to estimate the directions of arrival doas of multiple radio frequency signals we specifically consider an antenna array with an imperfectly calibrated array response the modified music algorithm estimates the doa of each signal individually after attempting to null the other signals that are present we compare the new approach to the conventional music algorithm in simulations and show that the new approach leads to improved performance the new approach converges quickly and produces doa estimates with smaller mean error and standard deviation than music over a range of incident signal separations we recommend our approach for systems with challenging antenna placements a time varying host platform and limited processing capabilities

optimal output feedback by minimizing k f 2 consider lqp with output feedback f initial condition x 0 and integral quadratic cost value given by x 0 k f x 0 choice of f to minimize parallel k f parallel 2 instead of the levine athans cost trace k f is considered an algorithm is presented

a variational principle for impulsive semiflows abstract we deduce a variational principle for impulsive semiflows defined on compact metric spaces in particular we generalize the classical notion of topological entropy to our setting of discontinuous semiflows

lasalle s theorems in impulsive semidynamical systems abstract we consider a semidynamical system subject to variable impulses and we obtain the lasalle invariance principle and the asymptotic stability theorem for this semidynamical system

extrapolation of time domain responses from three dimensional conducting objects utilizing the matrix pencil technique in this paper we use the matrix pencil approach to extrapolate time domain responses from three dimensional 3 d conducting objects that arise in the numerical solution of electromagnetic field problems by modeling the time functions as a sum of complex exponentials we can eliminate some of the instabilities that arise in late times for the electric field integral equation in the time domain however this method can also be utilized for extending the responses obtained using a finite difference time domain fdtd formulation

skew product semiflows and morse decomposition abstract this paper is devoted to the investigation of the dynamics of non autonomous differential equations the description of the asymptotic dynamics of non autonomous equations lies on dynamical structures of some associated limiting non autonomous and autonomous differential equations one for each global solution in the attractor of the driving semigroup of the associated skew product semiflow in some cases we have infinitely many limiting problems in contrast with the autonomous or asymptotically autonomous case for which we have only one limiting problem that is the semigroup itself we concentrate our attention in the study of the morse decomposition of attractors for these non autonomous limiting problems as a mean to understand some of the asymptotics of our non autonomous differential equations in particular we derive a morse decomposition for the global attractors of skew product semiflows and thus for pullback attractors of non autonomous differential equations from a morse decomposition of the attractor for the associated driving semigroup our theory is well suited to describe the asymptotic dynamics of non autonomous differential equations defined on the whole line or just for positive times or for differential equations driven by a general semigroup

non autonomous morse decomposition and lyapunov functions for gradient like processes we define time dependent morse decompositions for non autonomous evolution processes non autonomous dynamical systems and prove that a non autonomous gradient like evolution process possesses a morsedecomposition on the associated pullback attractor we also prove the existence of an associated lyapunov function which describes the gradient behavior of the system finally we apply these abstract results to non autonomous perturbations of autonomous gradient like evolution processes semigroups or autonomous dynamical systems

global attractors for impulsive dynamical systems a precompact approach abstract in this work we give the definition of a global attractor of an impulsive dynamical system and obtain several important properties for this class of attractors we prove the theorem on existence of such attractors and apply it to chosen ordinary and partial differential equations with impulsive functions

a tree structure one dimensional based algorithm for estimating the two dimensional direction of arrivals and its performance analysis a tree structure algorithm using one dimensional 1d multiple signal classification music algorithm is proposed to estimate the two dimensional direction of arrivals 2d doas of coherent signals impinging on a uniform rectangular array the basic idea of the proposed algorithm is to successively apply several times of the 1d spatial smoothing music algorithm in tree structure to estimate the azimuth and the elevation angles independently to optimally separate the receive signal constrained spatial beamformers with adjustable null width are exploited in conjunction with the 1d spatial smoothing music algorithm to decompose the received signal into several signals each lead by its own 2d doa performance analysis is provided to investigate the estimation bias caused by the residue signal propagating in the tree structure

negative trajectories in impulsive semidynamical systems abstract the theory of negative semisolutions is well defined in continuous dynamical systems in this paper we present a method to construct negative semisolutions for impulsive semidynamical systems we study topological properties of the negative limit set and the first negative prolongational set we also present a result about weak minimal sets

state steering by learning for a class of nonlinear control systems abstract the problem of steering the state of nonlinearly perturbed linear systems by learning is investigated a family of algorithms which compute the steering control by means of successive trials on the real plant is presented convergence in the face of a class of nonlinear plant perturbations is proven state feedback linearizable systems are shown to be addressable by the presented algorithms two examples illustrate the applicability of algorithms

convergence for non autonomous semidynamical systems with impulses abstract the present paper deals with impulsive non autonomous systems with convergence we show that the structure of the levinson center of a compact dissipative system is preserved under homomorphism in impulsive convergent systems also we present some criteria of convergence using lyapunov functions

robust optimal design and convergence properties analysis of iterative learning control approaches in this paper we address four major issues in the field of iterative learning control ilc theory and design the first issue is concerned with ilc design in the presence of system interval uncertainties targeting at time optimal fastest convergence and robustness properties concurrently we formulate the ilc design into a min max optimization problem and provide a systematic solution for linear type ilc consisting of the first order and higher order ilc schemes inherently relating to the first issue the second issue is concerned with the performance evaluation of various ilc schemes convergence speed is one of the most important factors in ilc a learning performance index q factor is introduced which provides a rigorous and quantified evaluation criterion for comparing the convergence speed of various ilc schemes we further explore a key issue how does the system dynamics affect the learning performance by associating the time weighted norm with the supreme norm we disclose the dynamics impact in ilc which can be assessed by global uniform bound and monotonicity in iteration domain finally we address a rather controversial issue in ilc can the higher order ilc outperform the lower order ilc in terms of convergence speed and robustness by applying the min max design which is robust and optimal and conducting rigorous analysis we reach the conclusion that the q factor of ilc sequences of lower order ilc is lower than that of higher order ilc in terms of the time weighted norm

brief adaptive robust iterative learning control with dead zone scheme an adaptive robust iterative learning control method based on a new dead zone scheme is presented for the control of nonlinear uncertain systems the new dead zone scheme ceases both learning and adaptation whenever the previous iteration error enters a pre specified error bound in the sequel enhances the robustness of the control system and meanwhile achieves arbitrary tracking accuracy for guaranteed stability it is indicated that the system will converge to the error bound within finite iterations and stay inside it and that the boundedness of the system signals for any iteration is ensured no finite escape time iterative learning control ilc and adaptive robust control are synthesized to achieve a new control paradigm the iterative learning control strategy is applied directly to deal with structured system uncertainties unknown time functions which are invariant over iterations the adaptive robust control strategy is used to handle non periodic system uncertainties associated with partially known bounding functions where the unknown parameters in the upper bounding functions are estimated with adaptation by integrating learning adaptation robust control and the new dead zone scheme using lyapunov s direct method the proposed scheme is able to handle fairly broad classes of nonlinear uncertain systems

attractors for impulsive non autonomous dynamical systems and their relations in this work we deal with several different notions of attractors that may appear in the impulsive non autonomous framework and we explore their relationships to obtain properties regarding the different scenarios of asymptotic dynamics such as the cocycle attractor the uniform attractor and the global attractor for the impulsive skew product semiflow lastly we illustrate our theory by exhibiting an example of a non classical non autonomous parabolic equation with subcritical nonlinearity and impulses

convergence of iterative learning control for siso nonrepetitive systems subject to iteration dependent uncertainties abstract this paper studies the robust convergence properties of iterative learning control ilc for single input single output siso nonrepetitive systems subject to iteration dependent uncertainties that arise in not only initial states and external disturbances but also plant models given an extended relative degree condition it is possible to propose necessary and sufficient nas conditions for robust ilc convergence the tracking error bound is shown to depend continuously on the bounds of the iteration dependent uncertainties when the iteration dependent uncertainties are bounded nas conditions exist to guarantee bounded system trajectories and output tracking error if the iteration dependent uncertainties converge then nas conditions ensure bounded system trajectories and zero output tracking error the results are also extended to a class of affine nonlinear systems satisfying a lipschitz condition simulation tests on a representative batch process demonstrate the validity of the obtained robust ilc convergence results

on impulsive semidynamical systems ii recursive properties it is now realized that the theory of impulsive differential equations is an important area of investigation in a recent book l the theory of such equations is studied in detail in 4 isolating the ideas underlying the theory of impulsive differential equations we initiated the study of impulsive semidynamical systems a study on similar lines except that the underlying structure is a dynamical system has also been conducted by rozhko 5 61 in 4 we studied periodicity properties of an impulsive semidynamical system in this paper we study what may be called recursive properties we also introduce here a discrete semidynamical system naturally associated with a given impulsive semidynamical system and study the relationship between the dynamical properties of the two systems this yields among other results a new characterization of weakly almost periodic points of a semidynamical system defined in 6 in terms of what we call strong almost periodicity of the associated semidynamical system

weak almost periodic motions minimality and stability in impulsive semidynamical systems abstract in this paper we study topological properties of semidynamical systems whose continuous dynamics are interrupted by abrupt changes of state first we establish results which relate various concepts as stability of lyapunov weakly almost periodic motions recurrence and minimality in the sequel we study the stability of zhukovskij for impulsive systems and we obtain some results about uniform attractors

internal model based design of repetitive and iterative learning controllers for linear multivariable systems repetitive and iterative learning control are two modern control strategies for tracking systems in which the signals are periodic in nature this paper discusses repetitive and iterative learning control from an internal model principle point of view this allows the formulation of existence conditions for multivariable implementations of repetitive and learning control it is shown that repetitive control can be realized by an implementation of a robust servomechanism controller that uses the appropriate internal model for periodic distrubances the design of such controllers is discussed next it is shown that iterative learning control can be implemented in the format of a disturbance observer compensator it is shown that the resulting control structure is dual to the repetitive controller and that both constitute an implementation of the internal model principle consequently the analysis and design of repetitive and iterative learning control can be generalized to the powerful analysis and design

equilibrium states for impulsive semiflows abstract we consider impulsive semiflows defined on compact metric spaces and give sufficient conditions both on the semiflows and the potential functions for the existence and uniqueness of equilibrium states we also generalize the classical notion of topological pressure to our setting of discontinuous semiflows and prove a variational principle

iterative learning control using optimal feedback and feedforward actions an algorithm for iterative learning control is developed on the basis of an optimization principle which has been used previously to derive gradient type algorithms the new algorithm has numerous benefits which include realization in terms of riccati feedback and feedforward components this realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters the algorithm is expressed as a very general norm optimization problem in a hilbert space setting and hence in principle can be used for both continuous and discrete time systems a basic relationship with almost singular optimal control is outlined the theoretical results are illustrated by simulation studies which highlight the dependence of the speed of convergence on parameters chosen to represent the norm of the signals appearing in the optimization problem

invariance and stability of global attractors for multi valued impulsive dynamical systems abstract in this paper we consider infinite dimensional impulsive dynamical systems generated by evolution problems with impulses at the moments of intersection of trajectories with given subset of the phase space uniqueness of the corresponding cauchy problem is not assumed so we use multi valued semiflows to describe the long time dynamics of such systems considering global attractor as a compact minimal uniformly attracting set of the corresponding multi valued semiflow we propose a criterion of existence of such a set under additional mild assumptions we prove the invariance of the global attractor despite the fact that our approach does not require the invariance property of the set in the definition of the global attractor moreover we prove that the obtained global attractor is stable under perturbation of the right hand part of the evolution problem we also provide examples which show that in general the global attractor is not preserved under perturbation of impulsive parameters

monotonic newton method based ilc with parameter optimization for non linear systems despite the significant progress on iterative learning control ilc in the past decade ilc algorithms for non linear systems are still under development monotonic convergence is one of the desirable properties of non linear ilc in this paper by introducing a relaxation index a newton method based ilc is shown to converge monotonically simulations verify the effectiveness of the new algorithm potential improvements are discussed for future work

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

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

newton method based iterative learning control for discrete non linear systems significant progress has been achieved in terms of both theory and industrial applications of iterative learning control ilc in the past decade however the techniques of solving non linear ilc problems are still under development the main result of this paper is a novel non linear ilc algorithm that utilizes the capability of the newton method by setting up links between non linear ilc problems and non linear multivariable equations the newton method is introduced into the ilc framework the implementation of the new algorithm allows one to decompose a nonlinear ilc problem into a sequence of linear time varying ilc problems simulations on a discrete non linear system and a manipulator model display its advantages conditions for its semi local convergence are analysed links of ilc with existing non linear topics are pointed out as ways to construct new non linear ilc schemes potential improvements are discussed for future work

robust control of nonlinear uncertain systems without generalized matching conditions a novel procedure called recursive interlacing procedure is proposed for designing globally stabilizing robust control the procedure introduces new interlacing steps and combines them with the existing recursive or backstepping design it is shown by examining all possible third order vector systems that the procedure is applicable to systems not satisfying any of the existing structural conditions that is to systems in which uncertainties are potentially anywhere and of any bounding function by its nature the procedure is not limited to systems of any specific order it either produces stabilizing control or reveals certain measure of unstabilizability and it includes recursive design as a special case

flows of characteristic 0 in impulsive semidynamical systems abstract in this paper as in e m bonotto m federson topological conjugation and asymptotic stability in impulsive semidynamical systems j math anal appl 2006 doi 10 1016 j jmaa 2006 03 042 we continue to study the dynamics of flows defined in impulsive semidynamical systems x m i where x is a metric space x is a semidynamical system m denotes an impulsive set and i is an impulsive operator we generalize some results of non impulsive flows of characteristic 0 ch 0 for systems with impulses in particular we state conditions so that the limit set of an impulsive system of ch 0 is either a periodic orbit or a single rest point we also give conditions for a subset h in x m i to be globally asymptotically stable in the impulsive system provided the flow is of ch 0

a note on the cramer rao bound for 2 d direction finding based on 2 d array the authors present explicit expressions for the cramer rao bound crb for estimating the two dimensional 2 d direction of a single source based on 2 d arrays of identical omnidirectional sensors two commonly used models random wave and unknown wave are compared it is shown that the crbs for the two models have the same dependency on the array structure a specialization of the crb to two orthogonal uniform linear arrays ulas is discussed it is found that the joint crbs of the direction angles based on the two orthogonal ulas can be as low as one quarter for a random waveform model with a large number of snapshots and low snr or one half for both models with high snr of the crbs based on each ula

topological conjugation and asymptotic stability in impulsive semidynamical systems we prove several results concerning topological conjugation of two impulsive semidynamical systems in particular we prove that the homeomorphism which defines the topological conjugation takes impulsive points to impulsive points it also preserves limit sets prolongational limit sets and properties as the minimality of positive impulsive orbits as well as stability and invariance with respect to the impulsive system we also present the concepts of attraction and asymptotic stability in this setting and prove some related results

phase only adaptive processing based on a direct data domain least squares approach using the conjugate gradient method generally adaptive antenna arrays operate by changing the complex adaptive weights consisting of both magnitudes and phases applied at each of the antenna elements however it is easier to require the adaptive weights have only phase variation with a fixed magnitude at each of the antenna elements hence this work addresses the phase only adaptive systems whose weights have a fixed magnitude through a new phase only adaptive method based on a direct data domain least squares approach d sup 3 ls which utilize only a single snapshot of the data for adaptive processing

repositioning control of a two link flexible arm by learning a finite dimensional algorithm is presented which by trial searches for a control law is able to move a two link flexible arm between two given equilibrium configurations in a finite time interval using a singular perturbation analysis the possibility of considering the system as a linear perturbed one is shown allowing the use of a linear learning algorithm which is able to reject all the nonlinear disturbances the effectiveness of this algorithm is proven by theoretical arguments and experimental results robustness with respect to unmodeled high frequency dynamics is also addressed

optimum ambiguity free directional and omnidirectional planar antenna arrays for doa estimation this paper studies the antenna array geometry impact on both direction of arrival doa estimation accuracy and array rank ambiguity some restrictions are imposed on the array geometry that guarantee first order ambiguity free arrays and at the same time reduce the cost of a global systematic optimization the subsequently derived cramer rao bound crb on the doa estimates shows to be attractive for numerical evaluation depending on whether the doa estimation accuracy is desired to be uniform in all possible directions or is to be enhanced in a given aperture around some privileged direction two optimization problems are formulated and solved by exhaustive search to compute the optimal array geometries the obtained optimal arrays significantly outperform their circular counterparts and tend to have a form close to the v shape we study in details v shaped arrays and derive asymptotic performance measures that apply for large sized arrays where exhaustive search is unaffordable

discontinuous local semiflows for kurzweil equations leading to lasalle s invariance principle for differential systems with impulses at variable times abstract in this paper we consider an initial value problem for a class of generalized odes also known as kurzweil equations and we prove the existence of a local semidynamical system there under certain perturbation conditions we also show that this class of generalized odes admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system as a consequence we obtain lasalle s invariance principle for such a class of generalized odes due to the importance of lasalle s invariance principle in studying stability of differential systems we include an application to autonomous ordinary differential systems with impulse action at variable times

brief paper noise tolerant iterative learning control for a class of continuous time systems the paper proposes a noise tolerant iterative learning control ilc for a class of linear continuous time systems which achieves high precision tracking for uncertain plants by iteration of trials in the presence of heavy measurement noise the robustness against measurement noise is achieved through i projection of continuous time i o signals onto a finite dimensional parameter space ii using error data of all past iterations via an integral operation in the learning law and iii noise reduction by h 2 optimization subject to a specified convergence speed of the ilc

topological entropy for discontinuous semiflows abstract we study two variations of bowen s definitions of topological entropy based on separated and spanning sets which can be applied to the study of discontinuous semiflows on compact metric spaces we prove that these definitions reduce to bowen s ones in the case of continuous semiflows as a second result we prove that our entropies give a lower bound for the entropy defined by alves carvalho and vasquez 2015 finally we prove that for impulsive semiflows satisfying certain regularity condition there exists a continuous semiflow defined on another compact metric space which is related to the first one by a semiconjugation and whose topological entropy equals our extended notion of topological entropy by using separated sets for the original semiflow

cramer rao bounds for antenna array design we study the impact of the geometry of the planar antenna array on the accuracy of the estimated direction s of arrivals of an emitting source we develop explicit cramer rao bounds crbs of the azimuth and elevation angles that show a simple structure in particular for a fixed elevation angle the crbs are cosine functions of the source azimuth and so regardless of the array geometry the amplitude and extremes of these functions depend on the array geometry hence the array configuration can be chosen in order to ensure a desired an isotropic behavior to do so we propose a pragmatic methodology that also takes into account the array ambiguity problem the array design problem is simplified by limiting the array search within a family of v shaped arrays that are advantageously characterized by a single parameter the angle between the two branches a performance measure is proposed then analytically expressed to assess the array directivity and gain with respect to the more standardly used uniform circular array

on jack hale s problem for impulsive systems abstract an interesting problem of jack hale deals with the existence of a maximal compact invariant set in discrete dynamical systems a solution for this problem is known for locally bounded dynamical systems following this line of research we consider in this paper a class of systems whose continuous dynamics are interrupted by abrupt changes of state and we present sufficient conditions to obtain the existence of a maximal compact invariant set for a system in this class we use the theory of asymptotic compactness to get the results

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

limit sets and the poincare bendixson theorem in impulsive semidynamical systems we consider semidynamical systems with impulse effects at variable times and we discuss some properties of the limit sets of orbits of these systems such as invariancy compactness and connectedness as a consequence we obtain a version of the poincare bendixson theorem for impulsive semidynamical systems

a note on convergence property of iterative learning controller with respect to sup norm we discuss some undesirable phenomena associated with the norm that is used in the proof of convergence of the iterative learning controller ilc specifically we first report that huge overshoot may be observed in the output trajectory error even though the applied learning algorithm has been proved to be exponentially convergent with respect to the norm this is because of the way in which the norm converges differs from that of the sup norm we then investigate the relation between the norm and the sup norm finally we present a simple method to remedy the undesirable feature of the conventional ilc

adaptive learning control of nonlinear systems by output error feedback this paper addresses the problem of designing an output error feedback control for single input single output nonlinear systems with uncertain smooth output dependent nonlinearities whose local lipschitz constants are known the considered systems are required to be observable minimum phase with known relative degree and known high frequency gain sign linear systems are included the reference output signal is assumed to be smooth and periodic with known period by developing in fourier series expansion a suitable periodic input reference signal an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its fourier coefficients bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the fourier series expansion is finite while arbitrary small tracking errors are exponentially achieved otherwise the resulting control is not model based is independent of the system order and depends only on the relative degree the reference signal period and the high frequency gain sign

correspondence comments on robust optimal design and convergence properties analysis of iterative learning control approaches and on the p type and newton type ilc schemes for dynamic systems with non affine input factors the papers by xu and tan robust optimal design and convergence properties analysis of iterative learning control approaches automatica 38 2002 1867 1880 and xu and tan on the p type and newton type ilc schemes for dynamic systems with non affine input factors automatica 38 2002 1237 1242 give a convergence analysis for several iterative learning control approaches unfortunately these papers contains several mathematical errors that render the proofs of the claimed results invalid as there are no obvious ways to correct these errors the results presented in these papers are questionable

decoupled 2d direction of arrival estimation using compact uniform circular arrays in the presence of elevation dependent mutual coupling based on the rank reduction theory rare a decoupled method for 2d direction of arrival doa estimation in the presence of elevation dependent mutual coupling is proposed for compact uniform circular arrays ucas using a new formulation of the beamspace array manifold in the presence of mutual coupling the azimuth estimates are decoupled from the elevation estimates and obtained with no need for the exact knowledge of mutual coupling for the elevation estimation a 1d parameter search in the elevation space for every azimuth estimate is performed with the elevation dependent mutual coupling effect compensated efficiently though the computational load for the elevation estimation is increased compared to that of the original uca rare algorithm the 1d parameter search in our method overcomes most of the inherent shortcomings of the uca rare algorithm this enables unambiguous and paired 2d doa estimation with the elevation dependent mutual coupling effect being compensated for effectively numerical examples are presented to demonstrate the effectiveness of the proposed method

optimal iterative learning control design for multi agent systems consensus tracking abstract under a repeatable operation environment this paper proposes an iterative learning control scheme that can be applied to multi agent systems to perform consensus tracking under the fixed communication topology the agent dynamics are modeled by time varying nonlinear equations which satisfy the global lipschitz continuous condition in addition the desired consensus trajectory is only accessible to a subset of the followers by using the concept of the graph dependent matrix norm the convergence conditions can be specified at the agent level which depend on a set of eigenvalues that are associated with the communication topology the results are first derived for homogeneous agent systems and then extended to heterogeneous systems next optimal controller gain design methods are proposed in the sense that the norm of tracking error converges at the fastest rate which imposes a tightest bounding function for the actual tracking error in the norm analysis framework in the end an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods

discrete time inverse model based iterative learning control stability monotonicity and robustness this paper considers the robustness of an inverse iterative learning control algorithm a simple learning gain results in robust convergence that is monotonic in the least squares sense provided that the multiplicative plant uncertainty satisfies a matrix positivity requirement the results are extended to the frequency domain using a simple graphical nyquist test the analysis extends naturally to a parameter optimal control setting non monotone convergence is considered by using a simple weighted norm based on exponential weighting of time series

on impulsive semidynamical systems it is now realized that the theory of impulsive differential equations is an important area of investigation moreover the theory of such equations is much richer than the corresponding theory of differential equations 1 21 in this paper we isolate the ideas involved in the theory of impulsive differential equations and initiate the study of impulsive semidynamical systems for allied results on discontinuous dynamical systems see 3 4

analysis of a high order iterative learning control algorithm for uncertain nonlinear systems with state delays key words iterative learning control nonlinear systems convergence analysis high order scheme delay tracking abstract for a better learning transient along the iteration number direction a pid type iterative learning control algo rithm is proposed for a class of delayed uncertain nonlinear systems which perform a given task repeatedly the convergence conditions for the proposed high order learning control have been established the tracking error bound is proven to be a class k function of the bounds of reinitialization errors uncer tainties and disturbances to the systems it is also indicated that the time delays in the system states do not play a significant role in the ilc convergence property the e ectiveness of the high order ilc algorithm is demonstrated by simulation examples 1998 elsevier science ltd all rights reserved

lyapunov stability for impulsive control affine systems abstract this article studies several notions of lyapunov stability for impulsive control affine systems in the setting of nonautonomous dynamical systems it presents some relations between the stability of an impulsive control affine system and the stability of its adjacent control system stability of compact sets and their components are specially investigated lyapunov functionals are employed to characterize each type of stability of closed sets

poisson stability for impulsive semidynamical systems abstract in this paper the concept of poisson stability is investigated for impulsive semidynamical systems recursive properties are also investigated

brief nonlinear learning control for a class of nonlinear systems based on the lyapunov s direct method a new learning control design is proposed the proposed technique can be applied in two ways it is either the standard backward recursive design or its extension in the first case the design yields a class of learning control with a difference learning law under which the class of nonlinear systems is guaranteed to be asymptotically stable with respect to the number of trials in performing repeated tasks however implementation of the difference learning control requires derivative measurement of the state for guaranteed stability and performance as required by most of the existing linear learning control laws to overcome this difficulty the proposed design extends the recursive design by employing a new state transformation and a new lyapunov function and it yields a class of learning control with a difference differential learning law compared with the existing design methods most of which are based on linear analysis and design the extension not only guarantees global stability and good performance but also removes such limitations as derivative measurement lipschitz condition and resetting of initial conditions in addition the proposed design does not rely on the property of a system under consideration such as the input output passivity

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

stability of learning control with disturbances and uncertain initial conditions the authors investigate the effects of state disturbances output noise and errors in initial conditions on a class of learning control algorithms they present a simple learning algorithm and exhibit via a concise proof bounds on the asymptotic trajectory errors for the learned input and the corresponding state and output trajectories furthermore these bounds are continuous functions of the bounds on the initial condition errors state disturbances and output noise and the bounds are zero in the absence of these disturbances

asymptotic performance of optimal gain and phase estimators of sensor arrays for estimating angles of arrival there are three well known algorithms weighted noise subspace fitting wnsf unconditional maximum likelihood uml and conditional maximum likelihood cml these algorithms can also be used for estimating calibrating the gains and phases of sensor arrays assuming the angles of arrival are known we show that the wnsf algorithm with an optimal weight has the same statistical efficiency as the uml algorithm but more efficient than the cml algorithm this conclusion was known for angles of arrival estimation and is now confirmed for gains and phases calibration computationally the wnsf algorithm is shown to be more attractive than the other two as it can be implemented via a quadratic minimization procedure for arbitrarily shaped arrays

brief paper stability analysis of discrete time iterative learning control systems with interval uncertainty this paper presents a stability analysis of the iterative learning control ilc problem for discrete time systems when the plant markov parameters are subject to interval uncertainty using the so called super vector approach to ilc vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ilc process it is shown that the stability of such interval ilc systems can be determined by checking the stability of the system using only the vertex points of the interval markov parameters

a unified adaptive iterative learning control framework for uncertain nonlinear systems in this note we propose a unified framework for adaptive iterative learning control design for uncertain nonlinear systems it is shown that if a lyapunov based adaptive control law is available for the system under consideration and the lyapunov function satisfies certain conditions it is straightforward to extend the adaptive controller to handle repetitive systems operating over a finite time interval according to the value of a certain parameter the parametric adaptation law can be a pure time domain adaptation a pure iteration domain adaptation or a combination of both a pure iteration domain adaptation is described by a difference equation a pure time domain adaptation is described by a differential equation and a combination of both is described by a differential difference equation the advantages and disadvantages of the three possible adaptation types are discussed and some illustrative examples are given

brief on the p type and newton type ilc schemes for dynamic systems with non affine in input factors in this paper p type learning scheme and newton type learning scheme are proposed for quite general nonlinear dynamic systems with non affine in input factors using the contraction mapping method it is shown that both schemes can achieve asymptotic convergence along learning repetition horizon in order to quantify and evaluate the learning performance new indices q factor and q order are introduced in particular to evaluate the learning convergence speed it is shown that the p type iterative learning scheme has a linear convergence order with limited learning convergence speed under system uncertainties on the other hand if more of system information such as the input jacobian is available newton type iterative learning scheme which is originated from numerical analysis can greatly speed up the learning convergence speed the effectiveness of the two learning control methods are demonstrated through a switched reluctance motor system

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

a discussion about some of the principles practices of wireless communication under a maxwellian framework there has been a plethora of papers dealing with wireless communication that use techniques which when viewed from the perspective of a maxwellian framework raise more questions than they answer by maxwellian framework we imply not only the relevance of electromagnetics in studying communication systems but also the proper interpretation of an ensemble processing in mathematical physics which was first introduced by maxwell to study the behavior of an aggregate of molecules rather than the property of individuals initially most of the modern signal processing techniques was developed for scalar acoustic problems however with the advent of wireless these same techniques are being applied to the vector electromagnetics problem which is fundamentally different in concept with respect to the scalar acoustic problem the objective is to discuss some of these concerns associated with some of the current modeling methodologies particularly related to propagation modeling and antenna diversity a goal is to initiate a dialog about the scientific merits of these new applications one of the points to be made is that an incorrect use of probability theory can often lead to erroneous conclusions that directly contradict the principles of physics a few examples are presented to initiate this dialog mainly the applicability of scalar techniques to the vector wireless problem including a proper interpretation of the shannon channel capacity theorem a methodology is also presented to illustrate how a simple multiple input multiple output system can be based on the principles of reciprocity integration of the electromagnetic principles in some of the current methodologies of signal processing and communications theory may lead to a better system

exponential convergence of a learning controller for robot manipulators the proof for the exponential convergence of a class of learning and repetitive control algorithms for robot manipulators is given the learning process involves the identification of the robot inverse dynamics function by having the robot execute a set of tasks repeatedly using the concepts of functional persistence of excitation and functional uniform complete observability it is shown that when a training task is selected for the robot which is persistently exciting the learning controllers are globally exponentially stable repetitive controllers are always exponentially stable

structure of attractors for skew product semiflows in this work we study the continuity and structural stability of the uniform attractor associated with non autonomous perturbations of differential equations by a careful study of the different definitions of attractor in the non autonomous framework we introduce the notion of lifted invariance on the uniform attractor which becomes compatible with the dynamics in the global attractor of the associated skew product semiflow and allows us to describe the internal dynamics and the characterization of the uniform attractors the associated pullback attractors and their structural stability under perturbations will play a crucial role