Accession Number : ADA194272
Title : Analytical Methods in Stochastic Control and Nonlinear Filtering.
Descriptive Note : Final rept. 1 Jun 86-30 Aug 87,
Corporate Author : SYSTEMS ENGINEERING INC GREENBELT MD
Personal Author(s) : Baras, J S ; Blankenship, G L
PDF Url : ADA194272
Report Date : 31 Dec 1987
Pagination or Media Count : 120
Abstract : The focus of this report is on advanced tools for the analysis of nonlinear stochastic control and filtering systems. In Sections 1 and 2, we present a series of results on the analysis of certain classes of nonlinear filtering problems using comparatively simple bounding techniques. We consider both problems with small noise (large signal to noise ratios) and weakly nonlinear systems. We show that the optimal nonlinear filters can be well approximated by linear filters which are very easy to implement. Moreover, we provide sharp estimates of the degree of suboptimality involved in using the linear approximating filters. In Section 3, we consider the problem of managing the estimation of (nonlinear) diffusion process by a system employing several sensors. The essential problem is to schedule the use of the sensor to optimize the estimate of a function of the state of the diffusion process. The solution is obtained in terms of a system of quasi-variational inequalities in the space of solutions of certain Zakai equations. In Section 4, we provide a new proof of the minimum principle in stochastic optimal control theory for systems of partially observed diffusions. In Section 5, we provide a concise analysis of the conditional adjoint process arising in the stochastic minimum principle for partially observed diffusion processes.
Descriptors : *LINEAR FILTERING, *NONLINEAR ANALYSIS, *STOCHASTIC CONTROL, BOUNDARIES, CONTROL THEORY, DETECTORS, DIFFUSION, EQUATIONS, ESTIMATES, FILTERS, MATHEMATICAL FILTERS, NOISE, NONLINEAR SYSTEMS, OPTIMIZATION, SHARPNESS, SIGNAL TO NOISE RATIO, SIGNALS, TOOLS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE