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# Accession Number:

## AD0656696

# Title:

## OPTIMAL CONTROL OF A DISCRETE-TIME STOCHASTIC SYSTEM LINEAR IN THE STATE,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Report Date:

## 1967-08-01

# Pagination or Media Count:

##
10.0

# Abstract:

## Considered is a discrete-time stochastic control problem whose dynamic equations and loss function are linear in the state vector with random coefficients, but which may vary in a nonlinear, random manner with the control variables. The controls are constrained to lie in a given set. For this system it is shown that the optimal control or policy is independent of the value of the state. The result follows from a simple dynamic programming argument. Under suitable restrictions on the functions, the dynamic programming approach leads to efficient computational methods for obtaining the controls via a sequence of mathematical programming problems in fewer variables than the number of controls in the entire process. The result provides another instance of certainty equivalence for a sequential stochastic decision problem. The expectations of the random variables play the role of certainty equivalents in the sense that the optimal control can be found by solving a deterministic problem in which expectations replace the random quantities.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#