On the variational process in optimal control theory
type: Item
instance of: scholarly article
title: On the variational process in optimal control theory
zbMATH Open document ID: 0697.49016
DOI: 10.1007/BF00939644
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: The variational process is established and applied to the development of the second variation for the free-final-time optimal control problem. First, it is shown that, given a change in the control (the independent variable), the change in the state (the dependent variable) consists of all orders of the change in the control. Hence, the change in the state is a total change. This implies that variations of dependent variations exist. Next, the variational relationship between time-constant and time- free variations is developed, and the formula for taking the variation of an integral is presented. These results are used to derive the second variation following three different approaches: taking the variation of the first variation after performing the integration by parts; taking the variation of the first variation before performing the integration by parts; and using the Taylor series approach. The ability to get the same result requires the existence of the total change in the state or of the variation of the state variation. Finally, if the nominal path is not an extremal, this process gives extra terms in the second variation.
Mathematics Subject Classification ID: 49K05
zbMATH DE Number: 4142877
zbMATH Keywords: variational process
zbMATH Keywords: second variation
zbMATH Keywords: free-final-time optimal control problem
author: David G. Hull
MaRDI profile type: Publication
cites work: On the variational process in parameter optimization
cites work: Second-Order Optimality Conditions for Variable End Time Terminal Control Problems
full work available at URL: https://doi.org/10.1007/bf00939644
OpenAlex ID: W2038732362
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description: scientific article; zbMATH DE number 4142877