White Noise Disturbance Research Articles

P 358 White-noise field campimetry abnormalities and color vision disturbances in patients with central serous chorioretinopathy

P 358 White-noise field campimetry abnormalities and color vision disturbances in patients with central serous chorioretinopathy

Generating directional residuals with dynamic parity relations

It is shown how diagnostic residuals, which exhibit directional properties at all times in response to an arbitrary mix of input and output faults, can be generated using dynamic parity relations. The parity relations are applied directly to the observables of the monitored plant; the design relies on the plant's dynamic input-output model. This residual generator can be made computationally polynomial (moving average) by including the invariant zero polynomial of the fault system in the specified fault responses. The polynomial design yields moving average noise transfers as well. White noise transfer and disturbance decoupling are achieved by extending the response specification. The parity relation approach is compared with the traditional detection filter design, and is shown to be more straightforward and have milder existence conditions; if subjected to the same specification, the two approaches yield identical residual generators.

State-feedback control of systems with multiplicative noise via linear matrix inequalities

We consider LTI systems perturbed by parametric uncertainties, modeled as white noise disturbances. We show how to maximize, via state-feedback control, the smallest norm of the noise intensity vector producing instability in the mean square sense, using convex optimization over linear matrix inequalities. We also show how to maximize performance robustness, where performance is measured by expected output energy, with either bounded initial conditions and zero inputs (classical LQG cost), or zero initial conditions and deterministic inputs of bounded energy (a generalization of the H ∞ norm).

Nonlinear smoothing for random fields

Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the explicit form of nonlinear smoother is presented in the finitely additive observation noise set up.

Development of an optimal control system for maintaining minimum groundwater levels

This paper describes the development and application of an optimal control system designed to reduce the deviation of piezometric head from minimum monthly target levels. The control strategy is generated from a Box-Jenkins double input-single output transfer function (SARIMAX) model relating local piezometric head fluctuations at an ecologically vulnerable location to regional rainfall and pumping volumes. The optimal control scheme is developed to minimize head deviations from the minimum target levels while simultaneously satisfying pumping/injection constraints associated with predetermined water resource management preferences. The control action manipulates the control variable (pumping) to compensate for existing and expected deviations of the piezometric head from target levels due to both observed disturbances (i.e., rainfall) and random (i.e., white noise) disturbances. An example applied to a localized region of the Upper Floridan aquifer in northeast Florida shows that the control action reduces the number of deviations below target head levels by 79% and the magnitude of the mean deviation below target by 72%. This improvement was achieved through a 29% reduction in pumping volume. The optimal control system thus provides a useful means of managing groundwater fluctuations at ecologically vulnerable locations by restricting regional pumping to offset regional rainfall deficits.

State-space interpretation of model predictive control

A model predictive control technique based on a step response model is developed using state estimation techniques. The standard step response model is extended so that integrating systems can be treated within the same framework. Based on the modified step response model, it is shown how the state estimation techniques from stochastic optimal control can be used to construct the optimal prediction vector without introducing significant additional numerical complexity. In the case of integrated or double integrated white noise disturbances filtered through first-order dynamics and white measurement noise, the optimal filter gain is parametrized explicitly in terms of a single parameter between 0 and 1, thus removing the requirement for solving a Riccati equation and equipping the control system with useful on-line tuning parameters. Parallels are drawn to the existing MPC techniques such as Dynamic Matrix Control (DMC), Internal Model Control (IMC) and Generalized Predictive Control (GPC).

Simultaneous optimum design of structure and control systems by sensitivity analysis

An approach is proposed for simultaneous optimum design of a structure and feedback control system by sensitivity analysis, for the following two purposes. One is to decrease both the response and the control force of the system under a white noise disturbance force. The other is to modify the gain, the pole and the zero-point to the desirable values. The weighting constant of the feedback control system, and the mass, stiffness, shape, dimensions, etc. of the structure, are adopted simultaneously as the design variables. The proposed method is verified by a model simulation.

Controller Gain Selection for an Electromagnetic Suspension Under Random Excitation

This paper considers the modeling and control of a single axis electromagnetic suspension for vibration isolation. Here, the nonlinear dynamic equations for the suspension are derived using a lumped-parameter model of the system that includes factors for flux leakage, fringing and finite permeability of the materials. To study the vibration isolation characteristics a set of linearized dynamic equations are used. The feedback signals considered are the air gap size, the absolute velocity of the isolated load and the current in the coil. Stability boundary plots that illustrate the domain of controller gains that will stabilize the system are presented. It is shown that feedback stabilization can be achieved without current feedback. The paper also considers the design of state feedback controllers that (i) minimize the mean square absolute displacement response of the suspension and (ii) minimize a measure of the system energy dissipation. In both cases the suspension system is assumed to be excited by random white noise disturbances. It is shown that near optimum disturbance attenuation and energy dissipation can be achieved without current feedback. Procedures for selecting these suboptimum controller gains are suggested. The paper compares the suboptimum controller gains with the state feedback gains obtained using Linear Quadratic optimal control theory. It is shown that the disturbance attenuation characteristics of the electromagnetic suspension can be made to be superior to that of a passive isolation system. Experimental results are also presented.

Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable

The small sample bias of the least-squares coefficient estimator is examined in the dynamic multiple linear regression model with normally distributed whitenoise disturbances and an arbitrary number of regressors which are all exogenous except for the one-period lagged-dependent variable. We employ large sample (T → ∞) and small disturbance (σ → 0) asymptotic theory and derive and compare expressions to O(T−1) and to O(σ2), respectively, for the bias in the least-squares coefficient vector. In some simulations and for an empirical example, we examine the mean (squared) error of these expressions and of corrected estimation procedures that yield estimates that are unbiased to O(T−l) and to O(σ2), respectively. The large sample approach proves to be superior, easily applicable, and capable of generating more efficient and less biased estimators.

Extended optimality properties of the linear quadratic regulator and stationary Kalman filter

It is shown that the constant gain state-feedback solution to the infinite-time linear quadratic regulator problem is optimal not only for arbitrarily initial conditions or white noise disturbances, but also for worst-case L/sup 1/ disturbances. Using a similar technique, it is shown that in the stationary Kalman filter, the white disturbance and measurement noise can be replaced by unknown bounded energy signals, and that optimality still holds if the performance criterion is a time domain L/sub infinity / normal of the state estimation errors in the presence of worst-case energy signals.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust stability and performance analysis for linear dynamic systems

In a recent paper K. Zhou and P.P. Khargonekar (ibid., vol.AC-32, pp.621-623, 1987) obtained sufficient conditions for robust stability over specified sets of matrix perturbations. These results are here extended to include performance bounds. Performance is defined as the worst-case expected value of a quadratic functional involving the state variables when the system is subjected to white noise disturbances. The results are illustrated by considering the gain margin of both an LQG controller and a robustified design obtained by D.S. Bernstein and S.W. Greeley (1986) for J.C. Doyle's examples. >

Wiener theory of digital linear-quadratic control

Abstract The linear quadratic regulator problem is considered for discrete time systems with time delay. The theory forms a close parallel to that for stationary prediction and filtering. For coloured noise disturbance at the plant input it is shown that the optimal control decomposes into the solution for white noise disturbance plus a feedforward controller. For unit time delay the solution becomes equivalent to that given by the stationary Kalman theory.

Wiener theory of digital linear-quadratic control

Abstract The linear quadratic regulator problem is considered for discrete time systems with time delay. The theory forms a close parallel to that for stationary prediction and filtering. For coloured noise disturbance at the plant input it is shown that the optimal control decomposes into the solution for white noise disturbance plus a feedforward controller. For unit time delay the solution becomes equivalent to that given by the stationary Kalman theory.

On the maximum of gaussian fourier series emerging in the analysis of random vibrations

In this paper we study the maximum of Gaussian Fourier series emerging in the analysis of random vibrations of a finite string. Evaluating the distribution of the maximal displacement corresponds to the analysis of the maximum for the related Gaussian Fourier series with independent coefficients.When vibrations are triggered by an initial white noise disturbance (where the instantaneous form of the vibrating string is composed of three processes pieced together) we give upper bounds for the maximal displacement.In the last section we consider forced vibrations at special instants where the instantaneous form of the vibrating string has the structure of a Brownian bridge. This enables us to give the exact distribution of the maximum for the related sine series.

On the maximum of gaussian fourier series emerging in the analysis of random vibrations

In this paper we study the maximum of Gaussian Fourier series emerging in the analysis of random vibrations of a finite string. Evaluating the distribution of the maximal displacement corresponds to the analysis of the maximum for the related Gaussian Fourier series with independent coefficients. When vibrations are triggered by an initial white noise disturbance (where the instantaneous form of the vibrating string is composed of three processes pieced together) we give upper bounds for the maximal displacement. In the last section we consider forced vibrations at special instants where the instantaneous form of the vibrating string has the structure of a Brownian bridge. This enables us to give the exact distribution of the maximum for the related sine series.

Parameter Identification of Exponential Signals in Colored Noise Environments

An algorithmic procedure is presented for the identification of the parameters of exponential signals, measured in colored noise. Previous papers on identifying sinusoids in noise have concentrated mainly on white noise disturbances. In a practical environment however, the disturbance is usually colored; sea-clutter in a radar context, is lowpass type noise for exampleWhen least squares type estimators are used in the colored noise environment, this usually leads to an unacceptable bias in the estimates. In this paper we propose an identification method called Singu1ar Val ue Decomposition Bias Elimination (SVDBE). In this approach assumptions are made about the noise generation system being ARMA, or ARMA respectively. The parameters of this noise model are then iteratively estimated along with the exponential signal parameters, via Singular Value Decomposition (SVD) based least squares. The iteration process starts with the white noise assumption, and improves on that by allowing parameters in the noise model to vary away from the white noise case. A high order modal decomposition is found, and the best subset of the identified modes is selected. Simulations assess the merits of the proposed algorithm

Combined Filtering and Parameter Estimation for Discrete-time Systems Driven by Approximately White Gaussian Noise Disturbances

We consider a partially observable, discrete-time process{xt, θt, yt} over a finite horizon T, where the unobservable components are {xt, θt}. Conditionally on {θt}, the pair {xt}, {yt} satisfies a linear model of the form (1) below; {θt} itself evolves according to a given joint a-priori distribution p(θ0,…, θT), The purpose of the paper is to determine recursively the joint conditional distribution p(xt, θt|yt), (yt: = {y0,…,yt}), or, more specifically, E{f(xt, θt)|yt}, namely the (mean squre)optimal filter for a given When θtis constant our problem becomes that of the combined filtering and parameter estimation.The optimal filter is computed for the ideal situation of white Gaussian noises and it is shown that, when this filter is applied to a more realistic situation where the noises are only approximately (in the sense of weak convergence of measures) white Gaussian and also {θt} has only approximately the given distribution p(θ0,…,θT), then it remains almost (mean-square) optimal with respect to all alternative filters that are continuous and bounded functions of the past observations.

An approach to structure/control simultaneous optimization for largeflexible spacecraft

This paper presents an approach to the simultaneous optimal design of a structure and control system for large flexible spacecrafts based on realistic objective function and constraints. The weight or total cost of structure and control system is minimized subject to constraints on the magnitude of response to a given disturbance involving both rigid-body and elastic modes. A nested optimization technique is developed to solve the combined problem. As an example, simple beam-like spacecraft under a steady-state white-noise disturbance force is investigated and some results of optimization are presented. In the numerical examples, the stiffness distribution, location of controller, and control gains are optimized. Direct feedback control and linear quadratic optimal controls laws are used with both inertial and noninertial disturbing force. It is shown that the total cost is sensitive to the overall structural stiffness, so that simultaneous optimization of the structure and control system is indeed useful.

Asymptotically Efficient Self-Tuning Regulators

This paper studies the problem of adaptive regulation of linear systems with white-noise disturbances. The apparent dilemma between the control objective and the need of information for parameter estimation is resolved by occasional use of white-noise probing inputs and by a reparametrization of the model. Insights into the question concerning how often and when such probing inputs should be introduced are provided by the concept of “asymptotic efficiency,” which quantifies the asymptotically minimal cost due to parameter ignorance, or equivalently, due to the infeasibility of using the optimal regulator that assumes knowledge of the system parameters. Asymptotically efficient adaptive regulators are constructed by making use of certain basic properties of adaptive predictors involving recursive least squares for the reparametrized model.

Nonlinear smoothing algorithms using white noise model

Nonlinear smoothing algorithms are studied where the white noise disturbance in the observation is treated directly, instead of the usual modelling through its integrated version of Brownian motion. This framework yields results already in the robust form. Furthermore, the Ito integrals involving the observations do not appear in this approach, thereby eliminating complications arising out of considering backward Ito integrals in the smoothing problems.