Infinitesimal methods in control theory: deterministic and stochastic
type: Item
instance of: scholarly article
title: Infinitesimal methods in control theory: deterministic and stochastic
zbMATH Open document ID: 0585.49005
DOI: 10.1007/BF00046584
author: Nigel J. Cutland
published in: Acta Applicandae Mathematicae
publication date: 1986-01-01T00:00:00Z
review text: The entire work has been devided into two parts. The methods of nonstandard analysis are applied to deterministic control theory extending earlier work by the author, in Part I. Compactness of relaxed controls, continuity of solution and cost as functions of the controls, and existence of optimal controls are included in the established results. The methods are extended to obtain similar results for partially observed stochastic control in Part II. The feedback control involved in the systems considered depends on information from a digital read-out of the observation process. The noise in the state equation is controlled along with the drift. Similar methods are applied to a Markov system in the final section of the paper. The presentation of the contents is nice.
reviewed by: Seshadri Sridhar
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 03H05
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 26E35
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 3937907
zbMATH Keywords: Loeb spaces
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: deterministic control
zbMATH Keywords: relaxed controls
zbMATH Keywords: partially observed stochastic control
zbMATH Keywords: digital read-out
MaRDI profile type: Publication
cites work: Q3742397
cites work: A non-standard representation for Brownian motion and Ito integration
cites work: Star-Finite Representations of Measure Spaces
cites work: On the existence of solutions to stochastic differential equations on Loeb spaces
cites work: Optimal controls for partially observed stochastic systems: an infinitesimal approach
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cites work: SOME ESTIMATES OF THE PROBABILITY DENSITY OF A STOCHASTIC INTEGRAL
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cites work: Weak Limits of Measures and the Standard Part Map
full work available at URL: https://doi.org/10.1007/bf00046584
OpenAlex ID: W2035331885
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description: scientific article; zbMATH DE number 3937907