Optimal impulse control of a diffusion process with both fixed and proportional costs of control

This paper concerns the optimal control of a system where the state is modeled by a homogeneous diffusion process in R1. Each time the system is controlled a fixed cost is incurred as well as a cost which is proportional to the magnitude of the control applied. In addition to the cost of control, th...

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Bibliographic Details
Published in1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes pp. 759 - 763
Main Author Richard, Scott F.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.1976
Subjects
Control systems
Cost function
Diffusion processes
Infinite horizon
Optimal control
Proportional control
Radio control
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DOI10.1109/CDC.1976.267830

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Summary:This paper concerns the optimal control of a system where the state is modeled by a homogeneous diffusion process in R1. Each time the system is controlled a fixed cost is incurred as well as a cost which is proportional to the magnitude of the control applied. In addition to the cost of control, there are holding or carrying costs incurred which are a function of the state of the system. Sufficient conditions are found to determine the optimal control for an infinite horizon problem. The optimal policy is one of "impulse" control originally introduced by Bensoussan and Lions [2] where the system is controlled only a finite number of times in any bounded time interval and the control requires an instantaneous finite change in the state variable. The issue of the existence of such controls is not addressed.
DOI:10.1109/CDC.1976.267830