W.S. Gray

Optimal data fusion of correlated local decisions in multiple sensor detection systems

Z. Chair and P.R. Varshney (1986) solved the data fusion problem for fixed binary local detectors with statistically independent decisions. Their solution is generalized by using the Bahadur-Lazarsfeld expansion of probability density functions. The optimal data fusion rule is developed for correlation local binary decisions, in terms of the conditional correlation coefficients of all orders. It is shown that when all these coefficients are zero, the rule coincides with the original Chair-Varshney design. >

Minimality and local state decompositions of a nonlinear state space realization using energy functions

In this paper a set of sufficient conditions is developed in terms of controllability and observability functions under which a given state-space realization of a formal power series is minimal. Specifically, it is shown that positivity of these functions, in addition to a stability requirement and a few technical conditions, implies minimality. Using the nonlinear analogue of the Kalman decomposition, connections are then established between minimality, singular value functions, balanced realizations, and various notions of reachability and observability for nonlinear systems.

Stability analysis of digital linear flight controllers subject to electromagnetic disturbances

High intensity electromagnetic radiation has been demonstrated to be a source of computer upsets in commercially available digital flight control systems. Such upsets can degrade the quality of the control signal ranging from a perturbation error over a few sample periods to a permanent error mode or computer failure. Under these conditions, the primary concern of the control engineer is to insure that the closed-loop system remains stable. A stochastic disturbance model and a set of associated stability assessment tools are introduced for determining stability robustness of a nominal closed-loop system subject to electromagnetic disturbances. The focus is primarily on night control applications, but the methodology is suitable for any application where highly reliable digital control is needed. The technique is demonstrated on a simple test example and on a stabilizing controller for the longitudinal dynamics of the AFTI/F-16 aircraft.

Modeling electromagnetic disturbances in closed-loop computer controlled flight systems

High intensity electromagnetic radiation has been demonstrated to be a source of computer upsets in commercially available digital flight control systems. In this paper we introduce an electromagnetic disturbance model which can be used for stability analysis and augmentation of any such digitally implemented control law. The model is composed of a Markovian exosystem supplying radiation events to a discrete-time jump linear system which models how the radiation interferes with the nominal operation of the closed-loop system. We discuss how this model can be used to characterize stability and how it can be parametrized and validated in an experimental setting.

Hankel operators and Gramians for nonlinear systems

In the theory for continuous-time linear systems, the system Hankel operator plays an important role in a number of realization problems ranging from providing an abstract notion of state to yielding tests for state space minimality and algorithms for model reduction. But in the case of continuous-time nonlinear systems, Hankel theory is considerably less developed beyond a well known Hankel mapping introduced by Fliess (1974). In this paper, a definition of a system Hankel operator is developed for causal L/sub 2/-stable input-output systems. If a generating series representation of the input-output system is given then an explicit representation of the corresponding Hankel operator is possible. If, in addition, an affine state space model is available with certain stability properties then a unique factorization of the Hankel operator can be constructed with direct connections to well known and new nonlinear Gramian extensions.

Performance Analysis of Digital Flight Control Systems With Rollback Error Recovery Subject to Simulated Neutron-Induced Upsets

This paper introduces a class of stochastic hybrid models for the analysis of closed-loop control systems implemented with NASAs Recoverable Computer System (RCS). Such systems have been proposed to ensure reliable control performance in harsh environments. The stochastic hybrid model consists of a stochastic finite-state automaton driven by a Markov input process, which in turn drives a switched linear discrete-time dynamical system. Stability and output tracking performance are analyzed using an extension of the existing theory for Markov jump-linear systems. The theory is then applied to predict the tracking error performance of a Boeing 737 at cruising altitude and in closed-loop with an RCS subject to neutron-induced single-event upsets. The results are validated using experimental data obtained from a simulated neutron environment in NASAs SAFETI Laboratory.

Nonlinear balanced realizations

Properties of sliding interval balancing for linear systems are revisited, as this notion is basic for our extension of balanced realizations to nonlinear systems. Nonlinear balancing is based upon three principles: 1) Balancing should be defined with respect to a nominal flow; 2) Only gramians defined over small time intervals should be used to preserve the accuracy of the linear perturbation model and; 3) Linearization should commute with balancing, in the sense that the linearization of a globally balanced model should correspond to the balanced linearized model in the original coordinates. Whereas it is generically possible to define a balanced framework locally, it is not possible to do so globally, and the notion of balancing was therefore relaxed, using integrating factors, to that of uncorrelatedness. As obstruction to the integrability of the (scaled) Jacobian is generic in dimensions n > 2, we focus our attention on the planar case, for which global balanced or uncorrelated realizations exist As with linear systems, the metric provided by a canonical gramian is shown to provide useful information about the dynamics of the system and the topology of the state space.In this paper a balanced realization for a smooth nonlinear system is defined. The approach is distinct from other notions of nonlinear balancing that appear in the literature and may be more computationally attractive since it avoids the need to compute the state transition matrix.

On singular value functions and Hankel operators for nonlinear systems

In linear system theory, the Hankel singular values are often computed in a state space setting using the product of Gramian matrices. They are known, however, to be intrinsically dependent only on the input-output map and not on any choice of state space coordinates. In the nonlinear case, there are well defined notions of singular value functions and a Hankel operator, but the connections between the two have not been established. We address the problem in two ways, and show that it is possible to establish an explicit connection using a method that is very reminiscent of the way singular values are usually defined for compact linear operators.

Digital linear state feedback control subject to electromagnetic disturbances

High intensity electromagnetic radiation has been demonstrated to be a source of computer upsets in commercially available digital flight control systems. In this paper we present an analysis of one consequence of an electromagnetic disturbance: the flipping of bits in a computer word. Specifically, we analyze the closed-loop stability of a digital linear state feedback control law when the electromagnetic radiation causes the gain vector to be corrupted by bit errors in its floating-point representation. As an example, we analyze a stabilizing controller for the longitudinal dynamics of the AFTI/F-16 aircraft.

Volterra series analysis and synthesis of a neural network for velocity estimation

The motion detection problem occurs frequently in many applications connected with computer vision. Researchers have studied motion detection based on naturally occurring biological circuits for over a century. In this paper, we propose and analyze a motion detection circuit which is based on nerve membrane conduction. It consists of two unidirectional neural networks connected in an opposing fashion. Volterra input-output (I-O) models are then derived for the network so that velocity estimation can be cast as a parameter estimation problem. The technique is demonstrated through simulation.