robust observer design under measurement noise with gain adaptation and saturated estimates abstract we use incremental homogeneity gain adaptation and incremental observability for proving new results on robust observer design for systems with noisy measurement and bounded trajectories a state observer is designed by dominating the incrementally homogeneous nonlinearities of the observation error system with its linear approximation while gain adaptation and incremental observability guarantee an asymptotic upper bound for the estimation error depending on the limsup of the norm of the measurement noise a characteristic and innovative feature of this observer is the mixed low high gain structure in combination with saturated state estimates and dynamically tuned gains and saturation levels the gain adaptation is implemented as the output of a stable filter using the squared norm of the measured output estimation error and the mismatch between each estimate and its saturated value

simulation of scattered fields some guidelines for the equivalent source method abstract three different approaches of the equivalent source method for simulating scattered fields are compared two of them deal with monopole sets the other with multipole expansions in the first monopole approach the sources have fixed positions given by specific rules while in the second one esga the optimal positions are determined via a genetic algorithm the pros and cons of each of these approaches are discussed with the aim of providing practical guidelines for the user it is shown that while both monopole techniques furnish quite good pressure field reconstructions with simple source arrangements esga requires a number of monopoles significantly smaller and with equal number of sources yields a better precision as for the multipole technique the main advantage is that in principle any precision can be reached provided the source order is sufficiently high on the other hand the results point out that the lack of rules for determining the proper multipole order necessary for a desired precision may constitute a handicap for the user

sound field reconstruction using compressed modal equivalent point source method the accuracy resolution and economic cost of near field acoustic holography nah are highly dependent on the number of spatial sampling points generally higher accuracy and resolution require more spatial sampling points which may increase the workload of measurement or the hardware cost compressive sensing cs is able to solve the underdetermined problems by utilizing the sparsity of signals and thus it can be applied to nah to reduce the number of spatial sampling points but at the same time provide a high resolution reconstruction image based on the cs theory this paper proposes a compressed modal equivalent point source method cmesm in the method a sparse basis that is obtained from the eigen decomposition of the power resistance matrix is introduced to compress the equivalent point source strengths and the l1 norm minimization is used to promote sparse solutions both numerical simulation and experimental results demonstrate the validity of the proposed cmesm and show its advantage over the existing methods when the number of spatial sampling points is reduced

on the holographic reconstruction of vibroacoustic fields using equivalent sources and inverse boundary element method in using the near field acoustical holography based on the inverse boundary element method bem for the reconstruction of vibroacoustic source parameters an enormous number of measurements required in practice have limited the extended application of this method to obtain the sufficient field data with a small number of actual measured data the regeneration method of the radiated field using the multipoint equivalent sources is attempted in this paper in using the equivalent source method a vibrating source can be represented by distributed spherical sources inside the actual source surface in this paper the radiated field is expressed with a series of spherical hankel functions and spherical harmonics for suppressing the adverse effect of high order spherical functions spatial filtering of coefficients and wave vector components by a regularization scheme is adopted restored field data appended with actual measured data can be used as input for the inverse bem to reconstruct the source field

robust design of nonlinear internal models without adaptation we propose a solution to the problem of semiglobal output regulation for nonlinear minimum phase systems driven by uncertain exosystems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals rather the proposed approach relies upon regression like arguments used to derive a nonlinear internal model able to offset the presence of an unknown number of harmonic exogenous inputs of uncertain amplitude phase and frequency the design methodology guarantees asymptotic regulation if the dimension of the regulator exceeds a lower bound determined by the actual number of harmonic components of the exogenous input if this is not the case a bounded steady state regulation error is ensured whose amplitude though can be arbitrarily decreased by acting on a design parameter of the regulator

on sets of eigenvalues of matrices with prescribed row sums and prescribed graph abstract motivated by a work of boros brualdi crama and hoffman we consider the sets of i possible perron roots of nonnegative matrices with prescribed row sums and associated graph and ii possible eigenvalues of complex matrices with prescribed associated graph and row sums of the moduli of their entries to characterize the set of perron roots or possible eigenvalues of matrices in these classes we introduce following an idea of al pin elsner and van den driessche the concept of row uniform matrix which is a nonnegative matrix where all nonzero entries in every row are equal furthermore we completely characterize the sets of possible perron roots of the class of nonnegative matrices and the set of possible eigenvalues of the class of complex matrices under study extending known results to the reducible case we derive new sharp bounds on the set of eigenvalues or perron roots of matrices when the only information available is the graph of the matrix and the row sums of the moduli of its entries in the last section of the paper a new constructive proof of the camion hoffman theorem is given

the observer follower filter a new approach to nonlinear suboptimal filtering this paper investigates the state estimation problem for a class of stochastic nonlinear differential systems a novel algorithm is proposed denoted as observer follower filter off based on a two steps mixed approach the first step makes use of a high gain observer based estimator for nonlinear systems applied to the system equations in order to provide the trajectory around which a n degree carleman approximation of the stochastic differential system is achieved second step in principle any other high gain estimator can be used but in this note we prove that the one here proposed provides a bounded mean square error numerical simulations show the effectiveness of the proposed methodology and the improvements of the off with respect to the standard extended kalman bucy filter ekbf obtained by increasing the order of the carleman approximation

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

time varying increasing gain observers for nonlinear systems a full order state observer for a class of nonlinear continuous time systems is presented as generalization of the high gain observer for having a time varying gain that is let to be small in the first time instants increases over time up to its maximum and then is kept constant the global stability of the resulting estimation error is proved by means of a lyapunov functional via a change of coordinate the design of such an observer is obtained by solving a nonlinear programming problem and using series expansions to set the time varying gain

brief paper an adaptive high gain observer for nonlinear systems in this paper the authors provide a solution to the noise sensitivity of high gain observers the resulting nonlinear observer possesses simultaneously 1 extended kalman filter s good noise filtering properties and 2 the reactivity of the high gain extended kalman filter with respect to large perturbations the authors introduce innovation as the quantity that drives the gain adaptation they prove a general convergence result propose guidelines to practical implementation and show simulation results for an example

acoustic source property prediction based on near field measurements in planar coordinate abstract near field acoustical holography nah can be used to predict the acoustical properties of noise sources by starting from measurements of near field pressures in particular the sound pressure particle velocity and intensity can all be estimated on a source plane in the present work an equation relating acoustical source properties and the pressure radiated from a source is derived from the kirchoff helmholtz integral equation and is here referred to as the inverse rayleigh method the inverse rayleigh method reduces to the rayleigh integral when the source is located on an infinite rigid baffle however the same equation can also be used to predict the acoustic properties of a source in a more general environment i e without assuming the presence of an infinite rigid baffle in this article the inverse rayleigh method is described and then its relative accuracy is compared with other procedures that can be used to predict source particle velocity from near field pressure measurements on a planar hologram by comparing the accuracy of the present nah method with other procedures in the case of a large hologram it was found that the inverse rayleigh method is accurate and computationally efficient for predicting the source particle velocity from near field pressure measurements both with and without a rigid baffle

increasing gain observers for nonlinear systems for the purpose to estimate the state of nonlinear continuous time systems we focus on the increasing gain observer regarded as generalization of the well known high gain observer as compared with the previous results on increasing gain observers the assumptions under which the global asymptotic stability of the estimation error is proved are relaxed the stability analysis is drawn by using a more general type of lyapunov functional where design parameters can be tuned to set the time varying gain a new design method based on such a lyapunov functional is proposed to construct the observer simulation results affirm the effectiveness of the increasing gain approach as compared with the high gain observer

the wave superposition method as a robust technique for computing acoustic fields the wave superposition method has recently been advocated koopmann et al a method for computing acoustic fields based on the principle of wave superposition j acoust soc am 86 2433 2438 1989 as a reliable and accurate technique for computing the acoustic fields generated by arbitrary shaped radiators this study examines in depth the robustness and numerical stability of the method the implementation of the method requires the placement of a finite number of point sources on a surface interior to the body of the radiator the magnitude of these point sources can be evaluated in terms of the prescribed velocity distribution on the surface of the radiator once calculated the magnitude of these point sources allow the pressure distribution exterior to the radiator to be evaluated the first improvement made to the robustness of the method is the use of a hybrid combination of monopole and dipole sources this modification allows the inherent problem of nonuniqueness of the method at certa

frequency domain analysis and tuning of the algebraic differentiators abstractthe algebraic differentiators introduced by mboup join and fliessare studied in the frequency domain the study complements the time domain developments of the previous reference where a least squares interpretation has allowed to explain the main properties of the method and also to devise efficient differentiators the frequency domain analysis gives answers to the central question of the choice of the algebraic differentiator parameters also an interpretation of the algebraic differentiators in terms of wavelet decomposition is given

state and unknown input observers for nonlinear systems with bounded exogenous inputs a systematic design methodology for state observers for a large class of nonlinear systems with bounded exogenous inputs disturbance inputs and sensor noise is proposed the nonlinearities under consideration are characterized by an incremental quadratic constraint parameterized by a set of multiplier matrices linear matrix inequalities are developed to construct observer gains which ensure that a performance output based on the state estimation error satisfies a prescribed degree of accuracy furthermore conditions guaranteeing estimation of the unknown inputs to arbitrary degrees of accuracy are provided the proposed scheme is illustrated with a numerical example which does not satisfy the so called matching conditions

universal integral control an approach based on mollifiers the universal integral control introduced by h k khalil universal integral controllers for minimum phase nonlinear systems ieee trans autom control vol 45 no 3 is revisited by employing mollifiers instead of a high gain observer for the differentiation of the output signal the closed loop system is a classical functional differential equation with distributed delays on which standard lyapunov arguments are applied to study the stability low pass filtering capability of mollifiers is demonstrated for a high amplitude and rapidly oscillating noise the controller is supported by numerical simulations

on a nonlinear multivariable servomechanism problem abstract multivariable nonlinear plants with both measured and unmeasured vector disturbance signals are considered output feedback dynamic control laws are designed for the problem of tracking a constant or slowly varying reference input while rejecting constant or slowly varying disturbances

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

on the spectral radius of 0 1 matrices we determine the maximum spectral radius for 0 1 matrices with k2 andk2 1 1 s respectively and for symmetric 0 1 matrices with zero trace and e k21 s graphs with e edges in all cases equality is characterized

cubic spline interpolation based time domain equivalent source method for modeling transient acoustic radiation abstract transient acoustic radiation from an arbitrarily shaped source is modeled using a cubic spline interpolation based time domain equivalent source method in the method the cubic spline interpolation function is introduced to approximate the equivalent source strengths in the time domain for establishing the relationships between the acoustic quantities in the field the normal acceleration on the source surface and the equivalent sources and the least squares solution of the equivalent source strengths at each time step is determined by an iterative solving process with the singular value decomposition technique the proposed method has the abilities of calculating the acoustic quantities directly in the time domain and applying to arbitrarily shaped sources numerical examples of calculating the transient acoustic fields from a baffled planar piston and an impulsively accelerating sphere demonstrate that the proposed method can model the transient acoustic radiation very well the experimental results also further verify the validity of the proposed method

derivatives and perturbations of eigenvectors for a matrix bf a z whose entries are complex valued functions of a complex variable z results are presented concerning derivatives of an eigenvector bf x z of bf a z associated with a simple eigenvalue lambda z when bf x z is restricted to satisfy a constraint of the form sigma bf x z 1 where sigma is a rather arbitrary scaling function the differentiation formulas lead to a new approach for analyzing the sensitivity of an eigenvector under small perturbations in the underlying matrix finally an application is given which concerns the analysis of a finite markov chain subject to perturbations in the transition probabilities

the greedy strategy for optimizing the perron eigenvalue we address the problems of minimizing and of maximizing the spectral radius over a compact family of non negative matrices those problems being hard in general can be efficiently solved for some special families we consider the so called product families where each matrix is composed of rows chosen independently from given sets a recently introduced greedy method works very fast however it is applicable mostly for strictly positive matrices for sparse matrices it often diverges and gives a wrong answer we present the selective greedy method that works equally well for all non negative product families including sparse ones for this method we prove a quadratic rate of convergence and demonstrate its efficiency in numerical examples the numerical examples are realised for two cases finite uncertainty sets and polyhedral uncertainty sets given by systems of linear inequalities in dimensions up to 2000 the matrices with minimal maximal spectral radii in product families are found within a few iterations applications to dynamical systems and to the graph theory are considered

a numerical solution for the general radiation problem based on the combined methods of superposition and singular value decomposition in the method of wave superposition the acoustic field due to a complex radiator is expressed in terms of a fredholm integral equation of the first kind called the superposition integral equation in general fredholm integral equations of the first kind are ill posed and therefore difficult to solve numerically in this paper it will be shown that a simple collocation procedure when combined with the singular value decomposition can yield accurate results for the numerical solution of the superposition integral as an example of the application of the method the acoustic radiation from a circular cylinder will be analyzed using this numerical procedure and compared to the exact solution it is shown that for this problem the accuracy of the numerical solution can be judged by evaluating how well the superposition solution approximates the specified boundary condition on the surface of the radiator an example is also given of a problem which has no exact solution in this situation it is suggested without proof that the accuracy of the numerical solution can be judged in a similar manner by evaluating the error in the superposition solution s satisfaction of the boundary condition

universal integral controllers for minimum phase nonlinear systems we consider a single input single output siso nonlinear system that has a well defined normal form with asymptotically stable zero dynamics using only knowledge of the relative degree and the sign of the high frequency gain we design an output feedback integral controller that asymptotically regulates the output to a bounded time varying reference signal with a constant limit we give regional as well as semi global results we also show that for relative degree one and two systems the proposed integral controller reduces to the classical pi and pid controllers respectively

maximal graphs and graphs with maximal spectral radius abstract a maximal graph is a connected graph with degree sequence not majorized by the degree sequence of any other graph relationships between three different sequences of integers that describe maximal graphs are given recursive and explicit forms of the characteristic polynomial of the adjacency matrix of a maximal graph are derived a correspondence between maximal graphs and connected graphs with stepwise adjacency matrices shows that among all connected graphs with n vertices and e edges the graph with maximal spectral radius is a maximal graph such maximal graphs are identified for certain values of n and e

a high gain nonlinear observer with limited gain power in this note we deal with a new observer for nonlinear systems of dimension n in canonical observability form we follow the standard high gain paradigm but instead of having an observer of dimension n with a gain that grows up to power n we design an observer of dimension 2n 2 with a gain that grows up only to power 2

high gain observers in the presence of measurement noise a switched gain approach this paper considers output feedback control using high gain observers in the presence of measurement noise for a class of nonlinear systems we study stability in the presence of measurement noise and illustrate the tradeoff when selecting the observer gain between state reconstruction speed and robustness to model uncertainty on the one hand versus amplification of noise on the other based on this tradeoff we propose a high gain observer that switches between two gain values this scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error we argue boundedness and ultimate boundedness of the closed loop system under switched gain output feedback

efficient algorithms for deciding the type of growth of products of integer matrices for a given finite set sigma of matrices with nonnegative integer entries we study the growth with t of max parallel to a 1 a t parallel to a i epsilon sigma we show how to determine in polynomial time whether this growth is bounded polynomial or exponential and we characterize all possible behaviors c 2007 elsevier inc all rights reserved

acoustic analysis of a rectangular cavity with general impedance boundary conditions a fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls the sound pressure is expressed as the combination of a three dimensional fourier cosine series and six supplementary two dimensional expansions introduced to ensure accelerate the uniform and absolute convergence rate of the series representation in the cavity including the boundary surfaces the expansion coefficients are determined using the rayleigh ritz method since the pressure field is constructed adequately smooth throughout the entire solution domain the rayleigh ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions to unify the treatments of arbitrary nonuniform impedance boundary conditions the impedance distribution function on each specified surface is invariantly expressed as a double fourier series expansion so that all the relevant integrals can be calculated analytically the modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions including nonuniform impedance distributions

a remark on the problem of semiglobal nonlinear output regulation this paper shows how the method for semiglobal stabilization by output feedback based on high gain observer and saturation and the method for structurally stable regulation based on system immersion can be effectively coupled in order to solve problems of robust output regulation in the presence of parameter uncertainties ranging over compact sets

a nonlinear high gain observer for systems with measurement noise in a feedback control framework we address the problem of state estimation for a class of nonlinear systems with measurement noise in the context of feedback control it is well known that high gain observers are robust against model uncertainty and disturbances but sensitive to measurement noise when implemented in a feedback loop this work presents the benefits of a nonlinear gain structure in the innovation process of the high gain observer in order to overcome the tradeoff between fast state reconstruction and measurement noise attenuation the goal is to generate a larger observer gain during the transient response than in the steady state response thus by reducing the observer gain after achieving satisfactory state estimates the effect of noise on the steady state performance is reduced moreover the nonlinear gain observer presented in this paper is shown to surpass the system performance achieved when using comparable linear gain observers the proof argues boundedness and ultimate boundedness of the closed loop system under the proposed output feedback

a high gain observer with updated gain for a class of mimo non triangular systems a high gain like observer with updated gain is proposed for a class of cascade nonlinear and non triangular systems that are observable for any input the objective of the gain adaptation is to perform an admissible tradeoff between state reconstruction dynamics on the one hand versus noise amplification on the other hand to this end the gain of the proposed observer is tuned through a single scalar time varying parameter governed by an adequate differential riccati equation the involved adaptation process is mainly driven by the power of the output observation error norm computed on a moving horizon window simulation results are given to show the effectiveness of the proposed observer namely its exponential convergence and its insensitivity with respect to noise measurements

lyapunov functions for persistently excited cascaded time varying systems application to consensus we present some results on stability of linear time varying systems with particular structures such systems appear in diverse problems which include the analysis of adaptive systems persistently excited observers and consensus of systems interconnected through time varying links the originality of our statements rely in the fact that we provide smooth strict lyapunov functions hence our proofs are constructive and direct moreover we establish uniform global exponential stability with explicit stability and decay estimates for illustration we address a brief but representative case study of consensus of lagrangian systems interconnected through unreliable links

a maximum principle for the stability analysis of positive bilinear control systems with applications to positive linear switched systems we consider a continuous time bilinear control system bcs with metzler matrices each entry in the transition matrix of such a system is nonnegative making the positive orthant an invariant set of the dynamics motivated by the stability analysis of positive linear switched systems plsss we define a control as optimal if for a fixed final time it maximizes the spectral radius of the transition matrix our main result is a first order necessary condition for optimality in the form of a maximum principle mp the proof of this mp combines the standard needle variation with a basic result from the perron frobenius theory of nonnegative matrices we describe several applications of this mp to the stability analysis of plsss under arbitrary switching

observer design for nonlinear triangular systems with unobservable linearisation the article deals with the observer design problem for a wide class of triangular time varying nonlinear systems with unobservable linearisation sufficient conditions are derived for the existence of a luenberger type observer when it is a priori known that the initial state of the system belongs to a given nonempty bounded subset of the state space for the general case the state estimation is exhibited by means of a switching sequence of time varying dynamics

hourglass alternative and the finiteness conjecture for the spectral characteristics of sets of non negative matrices abstract recently blondel nesterov and protasov proved 1 2 that the finiteness conjecture holds for the generalized and the lower spectral radii of the sets of non negative matrices with independent row column uncertainty we show that this result can be obtained as a simple consequence of the so called hourglass alternative used in 3 by the author and his companions to analyze the minimax relations between the spectral radii of matrix products axiomatization of the statements that constitute the hourglass alternative makes it possible to define a new class of sets of positive matrices having the finiteness property which includes the sets of non negative matrices with independent row uncertainty this class of matrices supplemented by the zero and identity matrices forms a semiring with the minkowski operations of addition and multiplication of matrix sets which gives means to construct new sets of non negative matrices possessing the finiteness property for the generalized and the lower spectral radii

spectral simplex method we develop an iterative optimization method for finding the maximal and minimal spectral radius of a matrix over a compact set of nonnegative matrices we consider matrix sets with product structure i e all rows are chosen independently from given compact sets row uncertainty sets if all the uncertainty sets are finite or polyhedral the algorithm finds the matrix with maximal minimal spectral radius within a few iterations it is proved that the algorithm avoids cycling and terminates within finite time the proofs are based on spectral properties of rank one corrections of nonnegative matrices the practical efficiency is demonstrated in numerical examples and statistics in dimensions up to 500 some generalizations to non polyhedral uncertainty sets including euclidean balls are derived finally we consider applications to spectral graph theory mathematical economics dynamical systems and difference equations

robust control for a nonlinear servomechanism problem this paper deals with the design of output feedback control to achieve asymptotic tracking and disturbance rejection for a class of nonlinear systems when the exogenous signals are generated by a known linear exosystem the system under consideration is single input single output input output linearizable minimum phase and modelled by an input output model of the form of an nth order differential equation we assume that at steady state the nonlinearities of the system can only introduce a finite number of harmonics of the original exosystem modes this assumption enables us to identify a linear servo compensator which is augmented with the original system moreover we augment a series of m integrators at the input side where m is the highest derivative of the input and then represent the augmented system by a state model the augmented system is stabilized via a separation approach in which a robust state feedback controller is designed first to ensure boundedness of all state variables and track

distributed moving horizon state estimation of two time scale nonlinear systems abstract in this paper we focus on distributed moving horizon estimation dmhe for a class of two time scale nonlinear systems described in the framework of singularly perturbed systems by taking advantage of the time scale separation property a two time scale system is first decomposed into a reduced order fast system and a reduced order slow system the slow system is further decomposed into several interconnected slow subsystems in the proposed distributed state estimation scheme a local estimator is designed for each slow subsystem and for the reduced order fast system the slow subsystem estimators communicate with each other to exchange information and they are only required to send information to the fast system one directionally the fast system estimator does not send out any information the local estimators are designed as observer enhanced moving horizon estimators sufficient conditions on the convergence of the estimation error of the dmhe are derived the application of the proposed dmhe to a chemical process example demonstrates its applicability and effectiveness

fast wideband acoustical holography patch near field acoustical holography methods like statistically optimized near field acoustical holography and equivalent source method are limited to relatively low frequencies where the average array element spacing is less than half of the acoustic wavelength while beamforming provides useful resolution only at medium to high frequencies with adequate array design both methods can be used with the same array but for holography to provide good low frequency resolution a small measurement distance is needed whereas beamforming requires a larger distance to limit sidelobe issues the wideband holography method of the present paper was developed to overcome that practical conflict only a single measurement is needed at a relatively short distance and a single result is obtained covering the full frequency range the method uses the principles of compressed sensing a sparse sound field representation is assumed with a chosen set of basis functions a measurement is taken with an irregular array and the inverse problem is solved with a method that enforces sparsity in the coefficient vector instead of using regularization based on the 1 norm of the coefficient vector an iterative solution procedure is used that promotes sparsity the iterative method is shown to provide very similar results in most cases and to be computationally much more efficient

active control of the acoustic radiation of a vibrating structure using a superposition formulation a new computational approach provides a methodology for specifying how the acoustic power radiated from a complex three dimensional vibrating structure may be controlled the method uses a superposition principle to transform the surface of a vibrating structure into a discrete distribution of acoustic sources interior to the boundary surface of the structure the transformation is carried out by requiring that the interior sources produce the same or nearly the same normal velocities as those prescribed on the surface of the vibrating structure based on this transformation the total time averaged acoustic power output from the vibrating structure can be expressed in terms of the strengths of the equivalent sources to control the radiated acoustic power one or more secondary point sources is then placed on or near the surface of the vibrating structure by using the total power radiated from the vibrating structure and the secondary sources as an objective function for an optimization operation th

numerical errors associated with the method of superposition for computing acoustic fields the method of wave superposition is based on the idea that an acoustic radiator can be approximately represented by the sum of the fields due to a finite number of interior point sources the accuracy of this representation depends upon how well the velocity boundary condition on the surface of the body is approximated the ultimate objective of this study then is to provide some guidelines for improving the accuracy of the surface velocity reconstruction and consequently the accuracy of the superposition solutions in general this is dependent upon the particular surface velocity distribution to be reconstructed as well as other formulation factors such as the acoustic wave number the number and locations of the surface nodes and the number and locations of the point sources velocity interpolation functions are introduced as a means of quantifying the dependence of reconstruction errors on the acoustic wave number and the placement of the surface nodes and point sources numerical experiments

the maximal eigenvalue of 0 1 matrices with prescribed number of ones abstract we determine the maximum spectral radius for 0 1 matrices with m 2 l ones for l 2 m 2 m 3 for all m and for a fixed l and m m l similar results are obtained for symmetric 0 1 matrix with zero diagonal in all cases equality is characterized

an equivalent source technique for calculating the sound field inside an enclosure containing scattering objects the equivalent source method has previously been used to calculate the exterior sound field radiated or scattered from bodies in the free field in this paper the method is used to calculate the internal pressure field for an enclosure which can have arbitrary boundary conditions and may include internal objects which scatter the sound some of the equivalent source positions are chosen to be the same as the first order images of the source inside the enclosure some are positioned within the scattering objects and the remainder are positioned on a spherical surface some distance outside the enclosure the normal velocity on the surfaces of the scattering objects and the enclosure walls is evaluated at a larger number of positions than there are equivalent sources the sum of the squared difference between this velocity and that expected because of the admittance of the boundary is minimized by adjusting the strengths of the equivalent sources the convergence of the method is checked by evaluating the velocity at a larger number of monitoring positions example results are presented for the sound field and frequency response inside a damped rectangular enclosure which compare very well with the conventional modal model the effect of having rigid spheres inside the enclosure are then investigated and it is found that the effect is significant even some distance from the spheres and at frequencies for which the size of the sphere is small compared to a wavelength finally the effect of a nonlocally reacting boundary condition is illustrated by assuming that one of the walls of the enclosure is an elastic plate

convergence acceleration for observers by gain commutation increasing convergence rates of observers and differentiators for a class of nonli near systems in the output canonical form under presence of bounded matched disturbances lipschitz uncertainties and measurement noises is investigated a supervisory algorithm is designed that switches among different values of observer gains to accelerate the estimation in the noise free case the presented switched gain observer ensures global uniform time of convergence of the estimation error to the origin in the presence of noise the goals of overshoot reducing for the initial phase acceleration of convergence and improvement of asymptotic precision of estimation are achieved efficiency of the proposed switching gain observer is demonstrated by numerical comparison with a sliding mode and linear high gain observers

a method for computing acoustic fields based on the principle of wave superposition a method for computing the acoustic fields of arbitrarily shaped radiators is described that uses the principle of wave superposition the superposition integral which is shown to be equivalent to the helmholtz integral is based on the idea that the combined fields of an array of sources interior to a radiator can be made to reproduce a velocity prescribed on the surface of the radiator the strengths of the sources that produce this condition can in turn be used to compute the corresponding surface pressures the results of several numerical experiments are presented that demonstrate the simplicity of the method also the advantages that the superposition method has over the more commonly used boundary element methods are discussed these include simplicity of generating the matrix elements used in the numerical formulation and improved accuracy and speed the latter two being due to the avoidance of uniqueness and singularity problems inherent in the boundary element formulation

sound field separation technique based on equivalent source method and its application in nearfield acoustic holography a technique for separating sound fields using two closely spaced parallel measurement surfaces and based on equivalent source method is proposed the method can separate wave components crossing two measurement surfaces in opposite directions which makes nearfield acoustic holography nah applications in a field where there exist sources on the two sides of the hologram surface in a reverberant field or in a scattered field possible the method is flexible in applications simple in computation and very easy to implement the measurement surfaces can be arbitrarily shaped and they are not restricted to be regular as in the traditional field separation technique and because the method performs field separation calculations directly in the spatial domain not in the wave number domain it avoids the errors and limitations the window effects etc associated with the traditional field separation technique based on the spatial fourier transform method in the paper a theoretical description is first

stabilization on zero error manifolds and the nonlinear servomechanism problem the extended linearization methodology is applied to the nonlinear servomechanism problem for the case of time varying exogenous signals this yields a novel approach to establishing exponential manifold known as the zero error manifold advantages of the approach are that the underlying theory is relatively simple and that a requirement of small derivatives for the exogenous signals is used rather than a requirement that the exogenous signals remain small thus certain cases of unbounded exogenous signals can be treated a transmission zero condition for existence of the requisite zero error manifold is given

a mapping relationship based near field acoustic holography with spherical fundamental solutions for helmholtz equation abstract in the procedure of the near field acoustic holography nah based on the fundamental solutions for helmholtz equation fs the number of fs and the measurement setup to obtain their coefficients are two crucial issues to the successful reconstruction the current work is motivated to develop a framework for the nah which supplies a guideline to the determination of the number of fs as well as an optimized measurement setup a mapping relationship between modes on surfaces of boundary and hologram is analytically derived by adopting the modes as fs in spherical coordinates thus reconstruction is converted to obtain the coefficients of participant modes on holograms in addition an integral identity is firstly to be derived for the modes on convex surfaces which is useful in determining the inefficient or evanescent modes for acoustic radiation in free space to determine the number of fs adopted in the mapping relationship based nah mrs based nah two approaches are proposed to supply reasonable estimations with criteria of point wise pressure and energy respectively a technique to approximate a specific degree of mode on patches by a set of locally orthogonal patterns is explored for three widely used holograms such as planar cylindrical and spherical holograms which results in an automatic determinations of the number and position of experimental setup for a given tolerance numerical examples are set up to validate the theory and techniques in the mrs based nah reconstructions of a cubic model demonstrate the potential of the proposed method for regular models even with corners and shapers worse results for the elongated cylinder with two spherical caps reveal the deficiency of the mrs based nah for irregular models which is largely due to the adopted modes are fs in spherical coordinates the nah framework pursued in the current work provides a new insight to the reconstruction procedure based on the fs in spherical coordinates

the state observer as a tool for the estimation of gene expression abstract in this paper a mathematical tool is presented to estimate unknown variables of transcription networks according to a set of measurements of the transcriptional activity of promoters the approach is based on the use of the mathematical model of the network under investigation and on the state reconstruction technique known as state observer borrowed from the control theory to this aim besides the general case the network motif of the multi output feed forward loop mo ffl will be investigated in details simulations show the effectiveness of the proposed approach in a wide range of possible critical frameworks such as only one target gene measurements non smooth input perturbations noisy measurements and model parameter uncertainties

continuously implemented sliding mode adaptive unknown input observers under noisy measurements we propose an estimator for nonlinear systems with unmatched unknown inputs and under measurement noise the estimator design is based on the combination of observer design for descriptor systems sliding modes theory and adaptive control the estimation of the measurement noise is achieved thanks to the transformation of the original system into a singular form where the measurement noise makes part of the augmented state two adaptive parameters are updated online one to compensate for the unknown bounds on the states the unknown inputs and the measurement noise and a second one to compensate for the effect of the nonlinearities to join robust state estimation and unknown inputs reconstruction our approach borrows inspiration from sliding mode theory however all signals are continuously implemented we demonstrate that both state and unknown inputs estimation are achieved up to arbitrarily small tolerance the utility of our theoretical results is illustrated through simulation case studies

robust disturbance attenuation of nonlinear systems using output feedback and state dependent scaling this paper presents an approach to output feedback stabilization with l 2 disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties a new formulation of state dependent scaling is introduced into the output feedback design which unifies treatment of nonlinear and linear gains the effect of disturbance on the controlled output which is allowed to be any function of output measurements can be always attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of triangular systems whose uncertainties do not necessarily have finite linear gains the uncertain dynamics is not limited to input to state stable systems either the approach is not only a natural extension of popular approaches in robust linear control but also advantageous to numerical computation which is applicable to non triangular systems as well as triangular systems

robust moving horizon estimation based output feedback economic model predictive control abstract in this work we develop an economic model predictive control scheme for a class of nonlinear systems with bounded process and measurement noise in order to achieve fast convergence of the state estimates to the actual system state as well as the robustness of the observer to measurement and process noise a deterministic high gain observer is first applied for a small time period with continuous output measurements to drive the estimation error to a small value after this initial small time period a robust moving horizon estimation scheme is used on line to provide more accurate and smoother state estimates in the design of the robust moving horizon estimation scheme the deterministic observer is used to calculate reference estimates and confidence regions that contain the actual system state within the confidence regions the moving horizon estimation scheme is allowed to optimize its estimates the output feedback economic model predictive controller is designed via lyapunov techniques based on state estimates provided by the deterministic observer and the moving horizon estimation scheme the stability of the closed loop system is analyzed rigorously and conditions that ensure the closed loop stability are derived extensive simulations based on a chemical process example illustrate the effectiveness of the proposed approach

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

a finite time convergent observer with robustness to piecewise constant measurement noise motivated by the design of observers with good performance and robustness to measurement noise the problem of estimating the state of a linear time invariant system in finite time and robustly with respect to measurement noise is considered using a hybrid systems framework a hybrid observer producing an estimate that converges to the plant state in finite time even under unknown piecewise constant noise is presented the stability and robustness properties of the observer are shown analytically and validated numerically

robust event triggered state estimation a risk sensitive approach in this work we investigate a robust event triggered remote state estimation problem for linear gaussian systems with a stochastic event triggering condition the reference measure approach is used to obtain a robust event triggered estimate that minimizes the so called risk sensitive criterion which refers to the expectation of the exponential of the sum of the squared estimation error we introduce the reference measure under which the measurements are identically independently distributed i i d and independent of the states and propose a map to link the real world measure to the reference measure so that the recursions of the information states under the reference measure can be obtained based on these results the risk sensitive criteria are reformulated under the reference measure and closed form expressions of the risk sensitive event triggered posterior and prior estimates are presented which are shown to evolve in simple recursive kalman like structures moreover two sufficient stability conditions for the proposed estimators are given where the first requires the solution of a time varying riccati equation to be positive definite and satisfy a specific inequality which can be further extended to the scenario when the weighting matrix in the risk sensitive criterion is time variant the second gives the range of values of the risk sensitive parameter and covariance of the initial state for which the proposed estimators are stable comparative simulation results demonstrate that the proposed risk sensitive event triggered estimator is more robust to model uncertainties compared with a typical minimum mean squared error mmse estimator with stochastic event triggered sensor scheduling

proportional integral controllers for minimum phase nonaffine in control systems we show that stabilizing tracking proportional integral pi controllers can be constructed for minimum phase nonaffine in control systems the constructed pi controller is an equivalent realization of an approximate dynamic inversion controller this equivalence holds only for the time response when applied to the unperturbed system even when restricted to unperturbed minimum phase linear time invariant systems their closed loop robustness properties differ this shows that in general properties that do not define the equivalence relation for systems controllers are not preserved under such equivalence transformations

sound field reconstruction within an entire cavity by plane wave expansions using a spherical microphone array a spherical microphone array has proved effective in reconstructing an enclosed sound field by a superposition of spherical wave functions in fourier domain it allows successful reconstructions surrounding the array but the accuracy will be degraded at a distance in order to extend the effective reconstruction to the entire cavity a plane wave basis in space domain is used owing to its non decaying propagating characteristic and compared with the conventional spherical wave function method in a low frequency sound field within a cylindrical cavity the sensitivity to measurement noise the effects of the numbers of plane waves and measurement positions are discussed simulations show that under the same measurement conditions the plane wave function method is superior in terms of reconstruction accuracy and data processing efficiency that is the entire sound field imaging can be achieved by only one time calculation instead of translations of local sets of coefficients with respect to every measur

peaking free output feedback adaptive neural control under a nonseparation principle high gain observers have been extensively applied to construct output feedback adaptive neural control anc for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle yet due to static gain and linear properties high gain observers are usually subject to peaking responses and noise sensitivity existing adaptive neural network nn observers cannot effectively relax the limitations of high gain observers this paper presents an output feedback indirect anc strategy under a nonseparation principle where a hybrid estimation scheme that integrates an adaptive nn observer with state variable filters is proposed to estimate plant states by applying a single lyapunov function candidate to the entire system it is proved that the closed loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability simulation results have shown effectiveness and superiority of this approach

method of superposition applied to patch near field acoustic holography the method of superposition may be applied to reconstruct the field on a partial surface on a radiating structure from measurements made on a nearby limited surface unlike conformal near field holography where the measurement surface surrounds the entire structure in patch holography the measurement surface need only be approximately as large as the patch on the structure surface where the reconstruction is required using the method of superposition the field on and near the measurement surface may be approximated by the field produced by a source distribution placed on a surface inside the structure the source strengths are evaluated by applying boundary conditions on the measurement surface the algorithm requires the inversion of the green s function matrix which may be ill conditioned truncated singular value decomposition is used to invert it the field on the structure surface is then approximated by the field produced by the source distribution the algorithm is easier to implement than the

high gain observers with limited gain power for systems with observability canonical form we consider the problem of state observation for systems having a well defined observability canonical form gauthier and kupka 2004 by means of high gain observers the main goal is to show that for this class of systems observers can be designed with the high gain parameter powered just up to the order 2 regardless the dimension of the state system in this way we substantially overtake the main limitations of standard design procedures in which the high gain parameter is powered up to the order of the system the observer structure which generalizes the ideas presented in astolfi and marconi 2015 can be used in all those contexts where fast state observation is required such as in the design of output feedback stabilizers by means of the nonlinear separation principle that is also specifically addressed in the paper