optimal controllers for finite wordlength implementation when a controller is implemented by a digital computer with a d and d a conversion numerical errors can severely affect the performance of the control system there exist realizations of a given controller transfer function exhibiting arbitrarily large effects from computational errors assuming sufficient excitation of the system the problem of designing an optimal controller in the presence of both external disturbances and internal roundoff errors is solved the results reduce to the standard lqg controller when infinite precision computation is used for finite precision however the separation principle does not hold a penalty is also added to the cost function to penalize the sum of the wordlengths used to compute the fractional part of each state variable of the controller this sum can be used to represent the lower bound on computer memory needed for controller synthesis it measures controller complexity and is minimized penalized here

identification with stochastic sampling time jitter this work investigates how stochastic sampling jitter noise affects the result of system identification and proposes a modification of known approaches to mitigate the effects of sampling jitter when the jitter is unknown and not directly measurable by just assuming conventional additive measurement noise the analysis shows that the identified model will get a bias in the transfer function amplitude that increases for higher frequencies a frequency domain approach with a continuous time model allows an analysis framework for sampling jitter noise the bias and covariance in the frequency domain model are derived these are used in bias compensated weighted least squares algorithms and by asymptotic arguments this leads to a maximum likelihood algorithm continuous time output error models are used for numerical illustrations

symplectic methods for the nonlinear schrodinger equation abstract in this paper we show that the spatial discretization of the nonlinear schrodinger equation leads to a hamiltonian system which can be simulated with symplectic numerical schemes in particular we apply two symplectic integrators to the nonlinear schrodinger equation and we demonstrate that they are able to produce accurate results and to preserve very well the invariants of the original system such as the energy and charge

comments on robust fragile or optimal with reply the issue of fragile controllers produced by using popular robust and optimal control synthesis methods was raised by keel bhattacharyya in the above mentioned paper ibid vol 42 1997 the commenter points out that the controller fragility problem described in the paper is 1 well known in the literature 2 due to the poor choice of examples 3 can easily be fixed by changing the optimization criteria and 4 can be fixed by changing the implementation in reply keel bhattacharyya disagree with him on all counts and explain their argument

noise reduction strategies for digital filters error spectrum shaping versus the optimal linear state space formulation the noise reduction performance of error spectrum shaping ess structures and of the optimal linear state space lss structure are compared for second order digital filter sections it is shown that optimal direct form 1 and direct form 2 ess realizations have a higher signal to noise ratio than the optimal lss structure in practice suboptimal ess structures with simple hardware implementations are of greater interest several of these implementations are considered and optimal values for the ess coefficients in these structures are derived for filters with zeros at z 1 it is shown that some of the simple ess structures can outperform the optimal lss structure for elliptic filters it is shown that several of the suboptimal ess structures perform poorly but that others still perform well

symplectic integrator for nonlinear high order schrodinger equation with a trapped term in the manuscript we discuss the symplectic integrator for the numerical solution of a kind of high order schrodinger equation with trapped terms the hamiltonian formulism is discovered for it we first discretize the hamiltonian system in space to reduce it to a finite dimensional one then the symplectic midpoint scheme is applied to the temporal discretization the symplectic scheme we devise is of second order accuracy in time and 2lth order accuracy in space it is proved that it preserves the charge of the original equation veraciously the energy is not preserved explicitly for the exception of the linear case however after some computation the energy transit formula in the temporal direction is obtained in the numerical part we compare our scheme with some existing schemes including the leap frog scheme and the energy preserving scheme from the numerical evidence we find that our numerical schemes are efficient and available the numerical results are consistent with the theoretical analysis

tracking in clutter with strongest neighbor measurements i theoretical analysis when tracking a target in clutter a measurement may have originated from either the target clutter or some other source the measurement with the strongest intensity amplitude in the neighborhood of the predicted target measurement is known as the strongest neighbor sn measurement a simple and commonly used method for tracking in clutter is the so called strongest neighbor filter snf which uses the sn measurement at each time as if it were the true one the paper deals with tracking in clutter with the sn measurements it presents analytic results along with useful comments for the sn measurement and the snf including the a priori and a posteriori probabilities of data association events the conditional probability density functions and the covariance matrices of the sn measurement and various mean square error matrices of state prediction and state update these results provide valuable insight into the problem of tracking in clutter and theoretical foundation for the development of improved tracking algorithms for performance analysis prediction and comparison of tracking with the sn measurements and for solving some important detection tracking problems such as the optimal determination of the detection threshold and gate size

difference schemes for solving the generalized nonlinear schrodinger equation this paper studies finite difference schemes for solving the generalized nonlinear schrodinger gnls equationiut uxx q u 2 u f x t u a new linearlized crank nicolson type scheme is presented by applying an extrapolation technique to the real coefficient of the nonlinear term in the gnls equation several schemes including crank nicolson type schemes hopscotch type schemes split step fourier scheme and pseudospectral scheme are adopted for solving three model problems of gnls equation which arise from many physical problems withq s s2 q s ln 1 s andq s 4s 1 s respectively the numerical results demonstrate that the linearized crank nicolson scheme is efficient and robust

reconstruction from projections based on detection and estimation of objects parts i and ii performance analysis and robustness analysis the problem of reconstructing a multidimensional field from noisy limited projection measurements is approached using an object based stochastic field model objects within a cross section are characterized by a finite dimensional set of parameters which are estimated directly from limited noisy projection measurements using maximum likelihood estimation in part i the computational structure and performance of the ml estimation procedure are investigated for the problem of locating a single object in a deterministic background simulations are also presented in part ii the issue of robustness to modeling errors is addressed

balanced realizations via gradient flow techniques abstract the task of finding a class of balanced minimal realizations is shown to be equivalent to finding limiting solutions of certain gradient flow differential equations by viewing such algebraic tasks in the context of calculus they are amenable to analog computational solutions or parallel processing machines perhaps even neural networks the convergence rates of the differential equations is exponential and consequentially convergence is rapid and numerical stability properties are attractive

low roundoff noise and normal realizations of fixed point iir digital filters explicit design and performance equations are given in terms of the parameters of the desired transfer function h z for two classes of realizations these realizations offer the digital circuit designer an alternative to the usual designs based on direct forms in addition to low roundoff noise these new realizations offer other desirable properties such as low coefficient sensitivities and freedom from overflow oscillations numerical results are presented which detail the design process and verify the theory

floating point arithmetic and digital filters the roundoff noise properties of floating point digital filters are examined to make the analysis tractable a high level model to deal with the errors in the inner product operation is developed this model establishes a broad connection between coefficient sensitivity and roundoff noise along with the model an efficient procedure to keep track of the addition scheme used in the inner product and to compute the statistics of the errors is introduced a systematic procedure based on the model is then developed to derive general expressions for the roundoff noise of fir direct form iir and state space filters the expressions in the context of state space filters are explored in some detail optimality issues are considered and it is shown that when double precision accumulation is used the optimal filters are similar in nature to those derived in the context of fixed point arithmetic with the essential difference that they also do depend on the spectrum of the input signal optimality with respect to addition schemes and second order filters are also examined in some detail

internal model control in the shift and delta domains we construct multivariable internal model controllers in the shift and delta domains to do so we develop a linear algebraic approach to the multivariable command following and disturbance rejection problem that facilitates a unified treatment of the differential shift and delta domains

when does randomness come from randomness a result of shen says that if f 2 n 2 n is an almost everywhere computable measure preserving transformation and y 2 n is martin lof random then there is a martin lof random x 2 n such that f x y answering a question of bienvenu and porter we show that this property holds for computable randomness but not schnorr randomness these results combined with other known results imply that the set of martin lof randoms is the largest subset of 2 n satisfying this property and also satisfying randomness conservation if f 2 n 2 n is an almost everywhere computable measure preserving map and if x 2 n is random then f x is random

the descriptive complexity of brownian motion abstract a continuous function x on the unit interval is a generic brownian motion when every probabilistic event which holds almost surely with respect to the wiener measure is reflected in x provided that the event has a suitably effective description we show that a generic one dimensional brownian motion can be computed from an infinite binary string which is complex in the sense of kolmogorov chaitin conversely one can construct a kolmogorov chaitin random string from the values at the rational numbers of a generic brownian motion in this way we construct a recursive isomorphism between encoded versions of generic brownian motions and kolmogorov chaitin random reals

optimal realizations of floating point implemented digital controllers with finite word length considerations the closed loop stability issue of finite precision realizations is investigated for digital controllers implemented in floating point arithmetic unlike the existing methods which only address the effect of the mantissa bits in floating point implementation to the sensitivity of closed loop stability the sensitivity of closed loop stability is analyzed with respect to both the mantissa and exponent bits of floating point implementation a computationally tractable fwl closed loop stability measure is then defined and the method of computing the value of this measure is given the optimal controller realization problem is posed as searching for a floating point realization that maximizes the proposed fwl closed loop stability measure and a numerical optimization technique is adopted to solve for the resulting optimization problem simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced fwl closed loop stability performance

symplectic and multi symplectic methods for the nonlinear schrodinger equation the hamiltonian and the multi symplectic formulations of the nonlinear schrodinger equation are considered for the multi symplectic formulation a new six point difference scheme which is equivalent to the multi symplectic preissman integrator is derived numerical experiments are also reported c 2002 elsevier science ltd all rights reserved

conserved quantities of some hamiltonian wave equations after full discretization hamiltonian pdes have some invariant quantities which would be good to conserve with the numerical integration in this paper we concentrate on the nonlinear wave and schrodinger equations under hypotheses of regularity and periodicity we study how a symmetric space discretization makes that the space discretized system also has some invariants or nearly invariants which well approximate the continuous ones we conjecture some facts which would explain the good numerical approximation of them after time integration when using symplectic runge kutta methods or symmetric linear multistep methods for second order systems

principal components algorithms for arma spectrum estimation principal components algorithms are presented for the problem of fitting an arma model to a given segment of a sample sequence of a discrete time stochastic process and the model is used to estimate the process power spectrum to reduce the effects of finite wordlength errors balanced state pace parameterization of the arma model is used instead of the more popular difference equation parameterization model identification is formulated as a problem of selecting a partial state to span approximately an apparently large dimensional information interface between the past and the future of the process different criteria are used to measure the quality of the approximation which leads to principal components algorithms for the problem that are based on singular value decomposition

analysis of coefficient quantization errors in state space digital filters in this paper we examine the sensitivity of state space digital filters to coefficient quantization errors a cost function using an l p norm criteria is used to measure the deviation in frequency response of the filter the cost function is used to indicate the connection between roundoff noise and filter sensitivity to coefficient quantization errors then based on this cost function it is shown that low roundoff noise state space digital filters filters in balanced coordinates and filters based on polynomials orthogonal on the unit circle have low sensitivity to coefficient quantization errors furthermore the sensitivity of the filters is shown to depend on the second order modes thereby exhibiting certain robustness and immunity to filter bandwidth

finite wordlength controller realisations using the specialised implicit form a specialised implicit state space representation is introduced to deal with finite wordlength effects in controller implementations this specialised implicit form provides a macroscopic description of the algorithm to be implemented so it constitutes a unifying framework allowing to encompass various implementation forms such as the operator the direct form ii transposed observer based and many other realisations usually considered separately in the literature different measures quantifying the finite wordlength effects on the overall closed loop behaviour are defined in this new context they concern both stability and performance the gap with the infinite precision case is evaluated classically through the coefficient sensitivity and roundoff noise analysis the problem of determining a realisation with minimum finite wordlength effects can subsequently be solved using appropriate numerical methods the approach is illustrated with an example

structure preserving algorithms for the two dimensional sine gordon equation with neumann boundary conditions abstract this paper presents two kinds of strategies to construct structure preserving algorithms with homogeneous neumann boundary conditions for the sine gordon equation while most existing structure preserving algorithms are only valid for zero or periodic boundary conditions the first strategy is based on the conventional second order central difference quotient but with a cell centered grid while the other is established on the regular grid but incorporated with summation by parts sbp operators both the methodologies can provide conservative semi discretizations with different forms of hamiltonian structures and the discrete energy however utilizing the existing sbp formulas schemes obtained by the second strategy can directly achieve higher order accuracy while it is not obvious for schemes based on the cell centered grid to make accuracy improved easily further combining the implicit midpoint method and the scalar auxiliary variable sav approach we construct symplectic integrators and linearly implicit energy preserving schemes for the two dimensional sine gordon equation respectively extensive numerical experiments demonstrate their effectiveness with the homogeneous neumann boundary conditions

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

improved l sub 2 sensitivity for state space digital system an improved l sub 2 sensitivity measure for linear state space digital systems is presented it gives a more precise evaluation of the transfer function deviation spl delta h z between the infinite wordlength system and the finite wordlength system when the structure matrices a b c contain 0 and spl plusmn 1 coefficients this measure can be applied in the system optimization resulting in a computationally efficient and very low l sub 2 sensitivity structure the theoretical result is verified by a numerical example

multi symplectic runge kutta nystrom methods for nonlinear schrodinger equations with variable coefficients in this paper we consider runge kutta nystrom rkn methods applied to nonlinear schrodinger equations with variable coefficients nlsevc concatenating symplectic nystrom methods in spatial direction and symplectic runge kutta methods in temporal direction for nlsevc leads to multi symplectic integrators i e to numerical methods which preserve the multi symplectic conservation law mscl we present the corresponding discrete version of mscl it is shown that the multi symplectic rkn methods preserve not only the global symplectic structure in time but also local and global discrete charge conservation laws under periodic boundary conditions we present a 4 order multi symplectic rkn method and use it in numerical simulation of quasi periodically solitary waves for nlsevc and we compare the multi symplectic rkn method with a non multi symplectic rkn method on the errors of numerical solutions the numerical errors of discrete energy discrete momentum and discrete charge the precise conservation of discrete charge under the multi symplectic rkn discretizations is attested numerically some numerical superiorities of the multi symplectic rkn methods are revealed

on the preservation of phase space structure under multisymplectic discretization in this paper we explore the local and global properties of multisymplectic discretizations based on finite differences and fourier spectral approximations multisymplectic ms schemes are developed for two benchmark nonlinear wave equations the sine gordon and nonlinear schrodinger equations we examine the implications of preserving the ms structure under discretization on the numerical scheme s ability to preserve phase space structure as measured by the nonlinear spectrum of the governing equation we find that the benefits of multisymplectic integrators include improved resolution of the local conservation laws dynamical invariants and complicated phase space structures

the effect of identifier structure on parameter convergence the effects of a chosen system structure on the identification of its parameters are considered in particular convergence rates are compared for the parameters of three state space structures direct form ii parallel and dual generalized hessenberg representation structures it is shown that the chosen structure does influence identification algorithms and that this influence is measured by examining the information contained in the structural parameters a conjecture about the relative convergence of the parameters is offered and evidence in its support is provided an important result is that identification of the usually identified direct from ii parameters the standard arma parameters does not necessarily yield the fastest parameter convergence for the system being identified

reduction of controller fragility by pole sensitivity minimization presents a method for the reduction of controller fragility the method is based on the sensitivity of closed loop poles to perturbations in the controller parameters by means of a state space parameterization of the controller the closed loop pole sensitivity can be reduced a controller fragility measure based on the closed loop pole sensitivity is proposed conditions for the optimal state space realization of the controller are presented along with a numerical method for obtaining the solution

an inclusion principle for dynamic systems the purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems which is a suitable mathematical framework for comparing systems with different dimensions the framework offers immediate results in reduced order modeling and the overlapping decentralized control of complex systems the presentation which is limited to linear constant systems relies on both the matrix algebra computations and the geometric elements structure to provide a balanced view of the issues involved in the concept of inclusion the framework is quite broad and has been used to consider nonlinear and time varying systems as well as systems with hereditary and stochastic effects

small roundoff noise realization of fixed point digital filters and controllers a method for finding digital realizations of discrete time transfer functions by fixed point arithmetic is presented the obtained realizations attain very small roundoff noise intensity this intensity is significantly smaller than the intensities that have been achieved so far the method applies many 0 1 coefficients in the realization it therefore requires a small number of multiplications and additions and it is significantly faster than many other realization methods a detailed comparison is made between this method and other existing methods for digital realization two different cases are investigated a butterworth filtering realization and the realization of an lqg linear quadratic gaussian optimal controller

optimizing stability bounds of finite precision pid controller structures this paper investigates a recently derived lower bound stability measure for sampled data controller structures subject to finite wordlength fwl constraints the optimal realization of the digital pid controller with fwl considerations is formulated as a nonlinear optimization problem and an efficient strategy based on adaptive simulated annealing asa is adopted to solve this complex optimization problem a numerical example of optimizing the finite precision pid controller structure for a simulated steel rolling mill system is presented to illustrate the effectiveness of the proposed strategy

brief paper an efficient controller structure with minimum roundoff noise gain based on a polynomial operator approach a new sparse controller structure is derived which is actually an improved version of the recently proposed structure li g 2004 a polynomial operator based dfiit structure for iir filters ieee transactions on circuits and systems ii 51 147 151 the performance of the proposed structure is analyzed by deriving the corresponding expression of roundoff noise gain and the problem of finding optimized sparse structures is solved efficiently with a genetic algorithm ga a numerical example is given which shows that the newly developed structure can achieve much better performance than some well known structures and particularly outperforms the traditional optimal fully parametrized realization greatly in terms of reducing roundoff noise and implementation complexity

multi symplectic runge kutta methods for nonlinear dirac equations in this paper we consider the multi symplectic runge kutta msrk methods applied to the nonlinear dirac equation in relativistic quantum physics based on a discovery of the multi symplecticity of the equation in particular the conservation of energy momentum and charge under msrk discretizations is investigated by means of numerical experiments and numerical comparisons with non msrk methods numerical experiments presented reveal that msrk methods applied to the nonlinear dirac equation preserve exactly conservation laws of charge and momentum and conserve the energy conservation in the corresponding numerical accuracy to the method utilized it is verified numerically that msrk methods are stable and convergent with respect to the conservation laws of energy momentum and charge and msrk methods preserve not only the inner geometric structure of the equation but also some crucial conservative properties in quantum physics a remarkable advantage of msrk methods applied to the nonlinear dirac equation is the precise preservation of charge conservation law

generalised modal realisation as a practical and efficient tool for fwl implementation finite word length fwl effects have been a critical issue in digital filter implementation for almost four decades although some optimisations may be attempted to get an optimal realisation with regards to a particular effect for instance the parametric sensitivity or the round off noise gain the purpose of this article is to propose an effective one i e taking into account all the aspects based on the specialised implicit form a new effective and sparse structure named modal realisation is proposed this realisation meets simultaneously accuracy low sensitivity round off noise gain and overflow risk few and flexible computational efforts with a good readability thanks to sparsity and simplicity no tricky optimisation is required to obtain it as well two numerical examples are included to illustrate the modal realisation s interest

symplectic structure preserving integrators for the two dimensional gross pitaevskii equation for bec a b s t r a c t symplectic integrators have been developed for solving the two dimensional gross pitaevskii equation the equation is transformed into a hamiltonian form with symplectic structure then symplectic integrators including the midpoint rule and a splitting symplectic scheme are developed for treating this equation it is shown that the proposed codes fulfill the discrete charge conservation law furthermore the global error of the numerical solution is theoretically estimated the theoretical analysis is supported by some numerical simulations

numerical methods for the simulation of trapped nonlinear schrodinger systems we propose analyze and compare the efficiency and accuracy of different numerical schemes for the solution of the nonlinear schrodinger equation with a trapping potential in particular we study schemes of finite difference pseudospectral and spectral types for the space discretization together with explicit symplectic multistep split step and standard variable step integrators to solve the time evolution all of these schemes are evaluated comparatively and some recommendations based on their accuracy and computational efficiency are made

roundoff noise analysis of two efficient digital filter structures in this correspondence two efficient structures are analyzed for the implementation scheme of rounding before multiplication rbm the first one is the direct form ii transposed structure in spl rho operator spl rho dfiit recently proposed in the expression of roundoff noise gain is derived based on which a revised spl rho dfiit structure denoted as spl rho rdfiit is obtained it is shown that the spl rho rdfiit structure having the same implementation complexity yields a smaller roundoff noise gain than the spl rho dfiit the roundoff noise gain for the spl rho rdfiit structure with error feedbacks is also derived each structure can be optimized with regard to the free parameters it possesses with a genetic algorithm numerical examples are presented which show that the optimized structures are very competitive because they can even outperform the traditional optimal state space realization in terms of the roundoff noise performance as well as the implementation simplicity

roundoff noise minimization using delta operator realizations digital filters the authors examine the advantages of using delta operator state space realizations rather than shift operator realizations of transfer functions in terms of minimizing roundoff noise gain they give several conditions under which the optimal roundoff noise gain for delta operator realizations is smaller than the optimal gain for shift operator realizations they then illustrate that even sparse and hence nonoptimal delta operator realizations can have smaller roundoff noise gain than the optimal shift operator realizations

perturbation analysis of an svd based linear prediction method for estimating the frequencies of multiple sinusoids a linear prediction approach is studied for estimating the frequencies of sinusoids in white noise it is shown that in the first step the continuity of the generalized inverse and the concept of angle between subspaces play an important role the continuity concept helps explain the need for a low rank approximation and the quality of the approximation is appraised by using the notion of angle between subspaces for the second step the sensitivity of the zeros of the predictor polynomial becomes an important consideration and is examined it is shown that increasing the order of the predictor polynomial and computing the minimum norm solution provides a mechanism to reduce parameter sensitivity

optimum realizations of sampled data controllers for fwl sensitivity minimization the problem of an optimal finite word length state space realization of a digital controller is investigated the closed loop to be considered consists of a continuous time plant a discrete time controller a sampler a zero order hold and an antialiasing filter an effective algorithm is proposed to find the optimal sampled data controller realization minimizing the sensitivity of the closed loop performance with respect to coefficient errors in the state variable matrices of the controller realization in order to get a tractable problem a two step procedure is to be used very fast sampling at a multiple of the sampling frequency followed by blocking or lifting to obtain a single rate system the procedure allows consideration of the system s intersample behaviour

dynamics of a generic brownian motion recursive aspects we study the local fluctuations of brownian motions which are represented by infinite binary strings which are random in the sense of kolmogorov chaitin we show how the dynamical properties of such a brownian motion at a point depend on its recursive properties

an improved closed loop stability related measure for finite precision digital controller realizations the pole sensitivity approach is employed to investigate the stability issue of the discrete time control system where a digital controller implemented with finite word length fwl is used a stability related measure is derived which is more accurate in estimating the closed loop stability robustness of an fwl implemented controller than some existing measures for the pole sensitivity analysis this improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output feedback and observer based controllers a numerical example is used to verify the theoretical analysis and to illustrate the design procedure

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

brief paper robust high order repetitive control optimal performance trade offs high order repetitive control has previously been introduced to either improve the robustness for period time uncertainty or reduce the sensitivity for non periodic inputs of standard repetitive control schemes this paper presents a systematic semidefinite programming based approach to compute high order repetitive controllers that yield an optimal trade off between these two performance criteria the methodology is numerically illustrated through trade off curves for various controller orders and levels of period time uncertainty moreover existing high order repetitive control approaches are shown to correspond to specific points on these curves

local path fitting a new approach to variational integrators a new approach for constructing variational integrators is presented in the general case the estimation of the action integral in a time interval t k t k 1 is used to construct a symplectic map q k q k 1 q k 1 q k 2 the basic idea is that only the partial derivatives of the estimated action integral of the lagrangian are needed in the general theory the analytic calculation of these derivatives gives rise to a new integral that depends on the euler lagrange vector itself which in the continuous and exact case vanishes and not on the lagrangian since this new integral can only be computed through a numerical method based on some internal grid points we can locally fit the exact curve by demanding the euler lagrange vector to vanish at these grid points thus the integral vanishes and the process dramatically simplifies the calculation of high order approximations the new technique is tested in high order solutions of the two body problem with high eccentricity up to 0 99 and of the outer planets of the solar system

brief paper insensitive h filter design for continuous time systems with respect to filter coefficient variations this paper is concerned with the problem of designing insensitive h filters for linear continuous time systems coefficient sensitivity functions of transfer functions with respect to filter additive multiplicative coefficient variations are defined and the h norms of the sensitivity functions are used to measure the sensitivity of the transfer functions with respect to additive filter coefficient variations in addition in order to deal with the filter design problem for the multiplicative filter coefficient variation case new measures based on the average of the sensitivity functions are also defined consequently the insensitive h filter design problem is reduced to a multi objective filter design problem which minimizes the coefficient s sensitivity and meets the prescribed h norm constraint simultaneously first a novel method for designing insensitive h filters subjected to additive filter coefficient variations is given in terms of the linear matrix inequality lmi optimization techniques furthermore based on the new sensitivity measures the obtained results are extended to the multiplicative coefficient variation case in addition an indirect method for solving the multiplicative variations is also proposed finally two numerical examples are provided to demonstrate the effectiveness of the proposed method

local energy preserving algorithms for nonlinear fourth order schrdinger equation with trapped term based on the rule that numerical algorithms should preserve the intrinsic properties of the original problem as many as possible we propose two local energy preserving algorithms for the nonlinear fourth order schrdinger equation with a trapped term the local energy conservation law is preserved on any local time space region with appropriate boundary conditions the first algorithm will be both globally charge and energy preserving and the second one will be energy preserving numerical experiments show that the proposed algorithms provide more accurate solution than many existing methods and also exhibit excellent performance in preserving conservation laws

effective dimension of points visited by brownian motion we consider the individual points on a martin lof random path of brownian motion we show that 1 khintchine s law of the iterated logarithm holds at almost all points and 2 there exist points besides the trivial example of the origin having effective dimension 1 the proof of 1 shows that for almost all times t the path f is martin lof random relative to t and so the effective dimension of t f t is 2

a new approach to the discretization of continuous time controllers a new method for discretizing continuous time controllers is derived using principles of controller approximation it focuses on the closed loop use of the discrete time controller the resulting approximation criterion is a measure for stability of the control system provides an upper bound on the sampling time for which stability can be guaranteed and because it is based on continuous time controller approximation it indicates the cost of discretization in terms of performance degradation the discrete time controller is obtained through minimization of this criterion which can be performed with standard software used in h sub infinity controller design

optimal finite wordlength linear quadratic regulation the authors consider the design of an lqg regulator implemented in fixed point arithmetic which is optimized with respect to its state wordlength and structure the approach extends previous design methods so that arithmetic errors are directly included the optimal finite controller gains are computed as a function of the arithmetic wordlength subject to an l sub 2 scaling constant on the controller states the design method used permits the cost for the near optimal structure to be developed so that this can then be used as a basis for comparison to other less complex structures

generation of a time series having a specified power spectrum with minimum roundoff noise the problem of determining a shaping filter which minimized the output roundoff noise variance is discussed it is shown that in the family of shaping filters of an identical mcmillan degree having an identical power spectrum the shaping filter of minimum phase attains a minimum output roundoff noise variance in either the case of optimal word lengths or the case of equal word lengths it is shown out by examples that this is not valid in the family of shaping filters having an identical power spectrum and different mcmillan degrees

on the structure of digital controllers with finite word length consideration it is well known that a stable discrete time control system may become unstable when the digital controller is actually implemented with a digital control processor due to the finite word length effects and that the stability behavior of the system depends on the structure of the digital controller due to the difficulties in adopting the existing stability robustness measures a new measure is derived which is tractable and hence enables us to handle the digital controller structure problem easily the optimal controller structure problem is formulated by maximizing this measure an analytical solution is presented an algorithm is developed for finding sparser structures

low roundoff noise augmented realizations of iir filters the scaling factor in a direct form ii infinite impulse response iir digital filter depends on only the system poles not its zeros adding pole zero cancellation pairs changes the scaling factor and the associated roundoff noise without affecting the transfer function it is shown that with l sub 2 scaling the upper bound of the noise reduction for direct form ii iir digital filters using k pole zero cancellation pairs is about 6k db the authors consider parallel form 3p to be the basic structure in which each subfilter is augmented with one or two pole zero cancellation pairs and realized in direct form ii they seek an iterative optimization process for each subfilter to find the optimal pole zero cancellation pairs that minimize the roundoff noise experimental results indicate the global optimal solution for these augmented subfilters can be obtained by using simple criteria to determine the starting points of the iterative processes alternative structures illustrative examples and overflow limit cycles are examined

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

semi implicit operator splitting pade method for higher order nonlinear schrodinger equations abstract we propose a semi implicit finite difference operator splitting pade ospd method for solving the higher order nonlinear schrodinger equation which describes the optical soliton wave propagation in fibers the method achieves fourth order of accuracy in space and has been proven to be stable by linear stability analysis numerical experiments and comparisons are investigated to show the advantages and effectivity of the ospd method and some interesting collision behaviors are also observed

a search algorithm for a class of optimal finite precision controller realization problems with saddle points with game theory we review the optimal digital controller realization problems that maximize a finite word length fwl closed loop stability measure for a large class of these optimal fwl controller realization problems which have saddle points a minimax based search algorithm is derived for finding a global optimal solution the algorithm consists of two stages in the first stage the closed form of a transformation set is constructed which contains global optimal solutions in the second stage a subgradient approach searches this transformation set to obtain a global optimal solution this algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these fwl realization problems furthermore for a small class of optimal fwl controller realization problems which have no saddle point the proposed algorithm also provides useful information to help solve them

digital methods for conversion between arbitrary sampling frequencies the paper presents filtering methods for interfacing time discrete systems with different sampling frequencies the methods are applicable for sampling rate conversion between any two sampling frequencies the conversion ratio may even be irrational or slowly time varying interpolation by irrational factors requires digital filters with nonperiodically varying coefficients this is dealt with in two ways 1 all possible coefficient values are precalculated this is in a sense possible because of the finite resolution needed or 2 the coefficients can be updated in real time using either fir or iir filters the first solution requires a huge coefficient memory the second scheme on the other hand is computationally intensive while discussing both of these solutions more practical intermediate schemes incorporating both fir and iir type filters are suggested the suggested practical implementations are either based on analog reconstruction filters where the derived digital filter coefficients are functions of the distances between current input and output samples or digital interpolators combined with simple analog interpolation schemes for finding the desired values in between the uniform output samples from the digital interpolator

low sensitivity h filter design for linear delta operator systems with sampling time jitter this article is concerned with the problem of designing h filters for a class of linear discrete time systems with low sensitivity to sampling time jitter via delta operator approach delta domain model is used to avoid the inherent numerical ill condition resulting from the use of the standard shift domain model at high sampling rates based on projection lemma in combination with the descriptor system approach often used to solve problems related to delay a novel bounded real lemma with three slack variables for delta operator systems is presented a sensitivity approach based on this novel lemma is proposed to mitigate the effects of sampling time jitter on system performance then the problem of designing a low sensitivity filter can be reduced to a convex optimisation problem an important consideration in the design of correlation filters is the optimal trade off between the standard h criterion and the sensitivity of the transfer function with respect to sampling time jitter finally a numer

a µ based optimal finite word length controller design a novel optimal finite word length fwl controller design is proposed in the framework of m theory a computationally tractable close loop stability measure with fwl implementation considerations of the controller is derived based on the m theory and the optimal fwl controller realizations are obtained by solving the resulting optimal fwl realization problem using linear matrix inequality techniques

a unified closed loop stability measure for finite precision digital controller realizations implemented in different representation schemes a computationally tractable unified finite word length closed loop stability measure is derived which is applicable to fixed point floating point and block floating point representation schemes both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure for each arithmetic scheme the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes