L. R. Nardizzi

Synthesizing optimal controls for modulated discrete-time systems†

The methods of steepest descent and gradient projection are used to solve the two-point boundary value problem associated with the optimal control of open-loop aperiodically modulated discrete-time systems. A comparison of optimal systems employing various combinations of pulse-width and pulse-amplitude modulation is presented. Numerous examples illustrate the diverse nature of the open-loop solutions for different types of modulation.

Optimally sensitive control for distributed parameter systems

The objective of this paper is the extension of optimally sensitive control techniques to distributed parameter systems. In particular, these adaptive control techniques are applied to distributed systems in which either the initial states or a vector of constant plant parameters are unknown. The result is the synthesis of a feedback control structure that adapts the nominal open-loop control in such a manner as to compensate for the errors introduced by model uncertainties. This requires defining the sensitivity matrices and deriving a set of distributed equations whose solution yields the requisite sensitivity matrices.

Noninvasive radioisotope cardiographic images with digital prefiltering and boundary detection for measuring left ventricular parameters

Abstract Noninvasive radioisotope cardiographic techniques have become a useful tool in studying left ventricular anatomy and function. The data obtainable by these techniques are often corrupted by various noise sources, and the need for image quality improvement by selective digital filtering has become evident. This investigation describes a new sequential estimating algorithm useful for several different types of radioisotope cardiographic images. In particular, the sizing of acute myocardial infarcts using technetium-99 m stannous pyrophosphate ( 99 m Tc-PYP) scintigrams and the determination of left ventricular ejection fractions using the gated blood pool method are investigated before and after the sequential estimating algorithm was applied to the original images. The results demonstrate significant improvement in myocardial infarct sizing in animals after digital filtering as well as increased accuracy in left ventricular ejection fraction determinations when compared to cineangiocardiographic measurements. The findings suggest that these nontraumatic and relatively noninvasive techniques will have improved diagnostic capability when used in conjuction with digital filtering for serial evaluation and follow-up studies of both acutely ill and nonhospitalized patients.

Two-Dimensional E-Filtering Applied to Image Processing

A generalization of the E-filter originated by Moore and Parker [10] from a one-dimensional filter to a nonlinear two-dimensional filter is presented. It is demonstrated that the response of the E-filter is almost independent of the frequency of the incoming signal under certain conditions but depends largely on the signal amplitude. Consequently, it can be used to filter out low-amplitude noise which has been superimposed additively on the signal. The performance of a one-dimensional E-filter as applied sequentially to the rows and then the columns of a digitized image is compared with the direct application of a two-dimensional E-filter. A simple two-dimensional E-filter digital realization and several filtered biomedical images are presented to demonstrate the application of this nonlinear filtering technique.

A computational technique for the control of systems described by partial difference equations

A penalty function method is applied to the determination of optimal controls for systems described by partial difference equations. The use of this penalty function method known as the ϵ-technique allows us to incorporate the dynamical constraints of the distributed parameter system into a new objective function. The conditions for the solution which minimizes the new objective function and the interrelationships between this solution and the solution which minimizes the original objective function are given. These interrelationships also suggest computational schemes for the synthesis of optimal controls for linear and non-linear distributed systems.

An optimization algorithm for pulse-frequency modulated control systems

A technique is presented for optimizing open-loop plants driven by PFM inputs. Ft. determines both the optimal amplitude and time of occurrence of the input pulses. It can be applied to linear or non-linear plants, to a large class of objective functionst to any number of input pulses, and for fixed or free end times. A step-by-step algorithm and a numerical example are given to demonstrate the technique.

Parameter estimation applied to noninvasive radiocardiographic data for determination of left ventricular ejection and valvular regurgitant fractions

Abstract Models of cardiac pump function are useful in extracting clinical information from radiocardiographic data. One type of information present in data from certain radiocardiographic studies refers to competence of the mitral and aortic valves. While quantitative and qualitative assessment of valvular competence from this type of data has been accomplished, previous methods have required invasively injecting tracer via a pulmonary wedge catheter. A noninvasive procedure should permit determination of forward ejection fraction and mitral and aortic regurgitant fractions in situations where cardiac catheterization is deemed too risky or expensive. A two-phase model of cardiac pump function has been developed for use with a general tracer input function, such as that resulting from noninvasive injection of tracer. An iterative parameter estimation algorithm using the model has been tested with “noisy” simulated data and patient data. It performs well in simulation tests and agrees with other methods in estimating ejection fractions and regurgitant fractions from patient data.

Several digital realizations of two-dimensional E-filters applied to image processing

This paper presents several digital implementations for two-dimensional E-filters. The E-filter is based on a non-linear transformation into the spatial domain. Its response is essentially independent of the frequency of the incoming signal under certain conditions, but depends largely on the digital amplitude. Several digital realizations and attendant problems are presented for E-filters applied to biomedical images obtained from an Anger scintillation camera. The associated sensitivity of the digital E-filter to changes of its parameters is examined. A two-dimensional linear filter is realized by the use of a bi-cubic spline interpolation scheme. The boundary detection of unprocessed and filtered images is also investigated using the hexagonal Golay transform. Several examples of abnormal heart and brain-scans are presented including the filtered images and bounded areas of infarcted and abnormal tissue.

A heterogeneous tissue model for measurement of regional blood perfusion in the myocardium using inert gas isotopes

Abstract Inert gas isotopes are finding increasing application in the measurement of blood perfusion in the capillary beds of muscle, especially the myocardium. When measuring blood perfusion of the myocardium, washout curves are first produced by precordial monitoring of isotope activity following intracoronary artery injection of an inert gas isotope dissolved in saline. The washout curve data are then applied to a mathematical model to yield blood perfusion rate. Present models for this purpose either ignore any diffusive effects of gas movement (Kety-Schmidt model), or diffusive effects are accounted for by weighting the calculated perfusion value (Zierlers height-over-area technique). A new model is described here for convective and diffusive movement of an inert, nonpolar gas in myocardial tissue. A digital computer simulation of the model equations is used both to simply the model and to show agreement between the model response and experimental 133 Xe washout curves from normal and infracted canine hearts. The model assumes that the tail of the washout curves (portion after roughly 1.5 minutes) is caused by a heterogeneous, diffusion-limited tissue structure. The model provides two parameters which can be adjusted to washout curve data using model-matching techniques. These are perfusion rate, and a parameter which is an index of the diffusive nature of the particular myocardial area under study.

Applications of Optimally Sensitive Control to Systems Involving Time-Varying Uncertainties

The implementation of control systems capable of identifying and adapting to time-varying unknown parameters has become increasingly important in air-traffic control and other applications. In the recent literature the control problem, in which both the initial state vector as well as a vector of constant plant parameters are unknown, has been treated utilizing sensitivity techniques referred to as optimally sensitive control. The concepts of optimally sensitive control as developed by Kokotovic, Perkins, Cruz, and others are extended to the problem in which the state dynamics contain a vector of stochastic inputs which can be represented as Martingale processes. The resulting optimally sensitive system is shown to be an effective and realistic adaptive controller for systems containing unknown time-varying parameters. A numerical example is presented to demonstrate the effectiveness of the resulting control system at identifying and adapting to the levels of the unknown time-varying inputs.