Edwin B. Stear

Kalman Filter Applications in Airborne Radar Tracking

This paper studies the application of Kalman filtering to single-target track systems in airborne radar. An angle channel Kalman filter is configured which incorporates measures of range, range rate, and on-board dynamics. Theoretical performance results are given and a discussion of methods for reducing the complexity of the Kalman gain computation is presented. A suboptimal antenna controller which operates on the outputs of the angle Kalman filter is also described. In addition, methodological improvements are shown to exist in the design of range and range-rate trackers using the Kalman filter configuration.

A New Approach to Prosthetic Control: EEG Motor Signal Tracking With an Adaptively Designed Phase-Locked Loop

The feasibility of using brain waves to control an externally powered prosthetic device for amputees was investigated. Two subjects were studied; one normal and one with a right hand disarticulation. Each subject, otherwise at rest, performed the protocol of voluntarily, repetitively opening and closing his hand. The normal accomplished this, while the amputee attempted to use her missing limb as if it were present. The time between opening and the next closing, and between closing and the next opening, was approximately 2 s. Simultaneously with this procedure, electroencephglograms (EEGs) were recorded from scalp electrodes presumably overlying the motor cortex on the left side, and an electromyogram (EMG) was taken from right forearm surface electrodes. The EEG and EMG were recorded on a polygraph and on magnetic tape. The latter recording was later sampled at 128 samples/s and quantized to 2 10 levels.

Application of control theory to endocrine regulation and control.

This paper considers some aspects of the application of control theory to endocrine regulation and control. Consideration is given to both the structural and functional aspects of various control concepts and ideas in this context. For single-input, single-output feedback control structures, emphasis is placed on loop gain and its importance in establishing the functional capability of such structures. Examples are given of both functional and nonfunctional feedback structures proposed by endocrinologists. For multi-input, multi-output structures, emphasis is placed on the concept of input and output decoupling, and the possible applicability of these concepts to hormonal control system interrelationships is illustrated. Finally, the possible application of optimal control theory to endocrine regulation and control is illustrated by means of a naive and highly simplified example involving control of the thyroid gland by the pituitary gland, and several surprising and interesting implications are shown to be implicit in the resulting control structure.

Systems Theory Aspects of Physiological Systems

Abstract The application of systems theory to the study of physiological systems during the past twenty-five years is examined with particular reference to endocrinology and metabolism. Some of the main directions which these applications have taken are outlined. Also, some of the more significant deficiencies (from a systems theory point of view) in such applications as they have appeared in the literature to date are pointed out, along with some of the reasons for these deficiencies. Several critical questions concerning the relevance of certain systems theoretic concepts and methods to the study of physiological systems are posed. Some suggestions as to how the current status of the application of systems theory to physiological systems might be improved are made. In particular, the need for, and importance of developing an effective thermodynamic theory of physiological systems based on appropriate variational principles and supported by a suitable underlying statistical mechanics, is discussed in some detail.

Automated design of space booster control systems

Abstract This paper describes a new algorithm for the automated design of compensators for space booster control systems. Use of this algorithm results in the selection of a forward-loop compensation filter (or filters, if filter switching is used), and a compatible time-dependent gain schedule which will stabilize the booster for a complete ascent stage by producing an open-loop gain versus phase response which satisfies a set of specified stability margins at critical flight times. The digital computer routine is based on minimizing a non-linear penalty function which is a function of the violations of the specified stability margins. Gradient search techniques are used to carry out the minimization of the penalty function. The results of considerable experience with the use of this programme by the authors and by several design engineers who were not involved in the development of the algorithm are summarized. These results clearly establish the substantial time and cost savings achieved by use of the ...

Near-optimal non-linear filtering using quasi-moment functions†

In previous publications (Fisher and Stear 1967 a, b), the authors dealt extensively with the general non-linear filtering problem. This paper utilizes the very desirable properties of the expansion of a probability density function in terms of its quasi-moment functions to obtain near-optimal ‘solutions’ to the general dynamical equation of the non-linear filtering problem. Specifically, stochastic differential equations are derived for the near-optimal non-linear filter using the theory of approximation of a probability density function by its lower-order quasi-moment functions. In addition, the result of approximating the conditional density function by a Gaussian density function is compared with the frequently used method of linearizing the non-linear equations about a nominal solution and applying Kalman linear filtering techniques.

Some current directions in nonlinear estimation and filtering theory

Nonlinear estimation and filtering theory began with the pioneering work of Stratonovich and Kushner. After several years of intense activity associated with applying their results (equations) to a great many applied problems of interest via various approximate solution techniques and associated with the development of more rigorous and more general approaches to the problem, several definite and distinct directions in the theory can now be identified. Some of these directions are described and discussed in this paper so as to provide a basis for assessing where the subject stands currently and where it seems to be going.

Linear Stochastic Optimal Control under Information Rate Constraints

The discrete-time, linear, stochastic optimal control problem is considered under information rate constraints on the feedback loop. The feedback loop, including sensor, is modelled as a communication channel which provides a specified amount of information (in the Shannon sense) about the state of the linear plant at each discrete-time instant given the current and past observations and past controls. No further specific structure for the sensor is assumed. The expected value of a positive definite quadratic loss function is used as the performance criterion to be minimized. This leads to a double minimization problem in which the performance criterion is minimized over the set of admissible controls and the set of conditional probability densities for the state given the observations and controls which achieve the specified information. A set of recursion relationships for the solution of this problem is derived using the techniques of calculus of variations and dynamic programming. The solution indicat...

Stochastic Optimal Control with a Constrained Feedback Information Rate

Abstract In this paper the stochastic optimal problem is considered for the case where the exact relationship between the observables and the state of the plant is unknown. Instead of assuming a known sensor structure, it is assumed that the unknown sensor is modeled as a communication channel which transmits information about the state to the controller at a fixed given information rate (in the Shannon sense). This leads to a double minimization problem over the set of admissible controls and the set of admissible conditional probability density functions describing the sensor. This problem is treated using a combination of techniques from calculus variations and dynamic programming to obtain a set of recursive equations for determining the optimal control sequence and the optimal probability density functions describing the sensor. The general results obtained are then applied to the linear plant-quadratic cost case. It is shown that, in this case, the optimal sensor is linear with additive noise and the results reduce to well-known results for the linear plant quadratic cost problem where the sensor is known to be linear and the noises are additive and Gaussian. The optimal costs obtained herein can be interpreted as lower bounds on the performance achievable using real sensors.

Discrete Stochastic Differential Games

Publisher Summary This chapter focuses on discrete stochastic differential games. The term differential games is a derivative of the mathematical theory of games. Games can have many forms depending on the number of players and the way in which winnings and losses are computed. Differential games involve only two players, where the loser pays the winner a specified amount after the play of a given game. As the algebraic sum of the winners game (positive) and losers gain (negative) is zero, this type of game is known as two-player zero sum game. Games can be presented either in extensive form as a set of rules and a succession of choices for each player or in normal form as a matrix or function, which relates the amount to the winner to the choices made by the two players. The amount, as a function of the choices, is known as the payoff of the game. An important concept in game theory is information. In games of perfect information, each player knows the exact value of the payoff and all that has occurred in the past. Differential games involve a payoff, which is in some way related to a dynamical system. The two players attempt to optimize this payoff by choosing game optimal control strategies. Differential games can be divided into classes, namely, those where observations of the state are perfect and those where they are not.