Nonlinear Stochastic Problems

This volume corresponds to the invited lectures and advanced research papers presented at the NATD Advanced Study Institute on Nonlinear Stochastic Problems with emphasis on Identification, Signal Processing, Control and Nonlinear Filtering held in Algarve (Portugal), on May 1982. The book is a blend of theoretical issues, algorithmic implementation aspects, and application examples. In many areas of science and engineering, there are problems which are intrinsically nonlinear 3nd stochastic in nature. Clear examples arise in identification and mOdeling, signal processing, nonlinear filtering, stochastic and adaptive conLrol. The meeting was organized because it was felt that there is a need for discussion of the methods and philosophy underlying these different areas, and in order to communicate those approaches that have proven to be effective. As the computational technology progresses, more general approaches to a number of problems which have been treated previously by linearization and perturbation methods become feasible and rewarding.

I - Introduction.- Overview of the ASI on Nonlinear Stochastic Problems.- II - Spectral Estimation.- Estimation of structured covariance matrices: A generalization of the Burg technique.- Classification of radar clutter using the maximum-entropy method.- A simple approach to high-resolution spectral analysis.- III - Identification.- Estimation of stochastic parameters for ARMA models by fast filtering algorithms.- Convergence study of two real-time parameter estimation schemes for nonlinear system.- Approximation by a sum of complex exponentials utilizing the pencil of function method.- Minimax estimation of ARMA systems.- IV - System Theory.- On the structure of minimal Markovian representations.- A brief tutorial on calculus on manifolds, with emphasis on applications to identification and control.- Role of multiplicative non-white noise in a nonlinear surface catalytic reaction.- V - Adaptive / Stochastic Control.- Geometric aspects of the convergence analysis of identification algorithms.- Multivariable adaptive regulators based on multistep quadratic cost functionals.- Overparametrization, positive realness and multistep minimum variance adaptive regulators.- Adaptive receding horizon controllers for discrete stochastic systems.- An explicit solution to a problem in nonlinear stochastic control involving the Wiener process.- VI - Optimal Control.- On optimal control for a class of partially-observed systems.- Optimal stochastic control of linear systems with state and control dependent noise: efficient computational algorithms.- VII - Nonlinear Filtering.- Joint information and demodulation.- Generalized finite-dimensional filters in discrete time.- Nonlinear filtering equation for Hilbert space valued processes.- Optimal orthogonal expansion for estimation I: signal in white Gaussian noise.- Optimal orthogonal expansion for estimation II: signal in counting observations.- Approximations for nonlinear filtering.- Phase demodulation: a nonlinear filtering approach.- Volterra series and finite dimensional nonlinear filtering.- VIII - Stochastic Processes.- Causal invertibility: an approach to the innovations problem.- Spectral analysis of nonlinear semi-Markov processes.- Differential calculus for Gaussian random measures.- Finite dimensional causal functionals of Brownian motion.- Transience, recurrence and invariant measures for diffusions.- Eigenfunction expansion for the nonlinear time dependent Brownian motion.- Point process differentials with evolving intensities.- Transformation properties of stochastic differential equations.- Some Applications of stochastic calculus on the nuclear spaces to the nonlinear problems.- IX - Applications.- Reconstruction and compression of two dimensional fields from sampled data by pseudo-potential functions.- Optimum perturbation signal that makes nonlinear systems approach to linear systems.- Stochastic filtering problems in multiradar tracking.- Population extinction probabilities and methods of estimation for population stochastic Differential Equation Models.- Dynamic ship positioning control systems design including nonlinear thrusters and dynamics.- Joint optimization of transmitter and receiver for cyclostationary random signal processes.- Fundamental properties and performance of nonlinear estimators for bearings-only target tracking.- List of Participants.- Index of Subjects.- Index of Authors.