Nonlinear Stochastic Problems

Abstract

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.