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

Personal Author(s):

• Midler,Joseph L.

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.

Descriptors:

• (*DECISION THEORY
• STOCHASTIC PROCESSES)
• (*CONTROL
• OPTIMIZATION)
• (*STOCHASTIC PROCESSES
• CONTROL SYSTEMS)
• RANDOM VARIABLES
• MATHEMATICAL PROGRAMMING
• DYNAMICS
• MATHEMATICAL MODELS
• MAPPING(TRANSFORMATIONS)
• DYNAMIC PROGRAMMING
• ALGORITHMS

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE