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# Accession Number:

## ADA019555

# Title:

## An Exact Estimator-Controller Solution to a Stochastic Optimal-Control Problem with Point Process Observations.

# Descriptive Note:

## Interim rept.,

# Corporate Author:

## WASHINGTON UNIV ST LOUIS MO DEPT OF SYSTEMS SCIENCE AND MATHEMATICS

# Report Date:

## 1975-09-01

# Pagination or Media Count:

##
7.0

# Abstract:

## The so-called dual control problem is the most general stochastic optimal-control problem and has been solved only under very restrictive conditions. Of special importance is the separation theorem which demonstrates that for a linear stochastic plant, quadratic costs, and linear observations in additive Gaussian noise, the optimal control law can be determined by solving separately and independently a causal stochastic-estimation problem and a deterministic control problem. In this paper, we give the exact solution to a dual control problem involving a linear stochastic plant, quadratic costs, and nonlinear, nongaussian observations. The observations are in the form of a point process in which each point has both a temporal and a spatial coordinate. The state of the stochastic plant influences the intensity of the observed time-space point process. We show that the solution to this dual control problem can be realized with a separated estimator-controller in which the estimator is nonlinear, mean-square optimal, and finite-dimensional, and the controller is linear.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#