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Noncooperative Game TheoryAn Introduction for Engineers and Computer Scientists$
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João P. Hespanha

Print publication date: 2017

Print ISBN-13: 9780691175218

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175218.001.0001

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One-Player Differential Games

One-Player Differential Games

Chapter:
(p.190) Lecture 16 One-Player Differential Games
Source:
Noncooperative Game Theory
Author(s):

João P. Hespanha

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175218.003.0016

This chapter focuses on one-player continuous time dynamic games, that is, the optimal control of a continuous time dynamical system. It begins by considering a one-player continuous time differential game in which the (only) player wants to minimize either using an open-loop policy or a state-feedback policy. It then discusses continuous time cost-to-go, with the following conclusion: regardless of the information structure considered (open loop, state feedback, or other), it is not possible to obtain a cost lower than cost-to-go. It also explores continuous time dynamic programming, linear quadratic dynamic games, and differential games with variable termination time before concluding with a practice exercise and the corresponding solution.

Keywords:   continuous time dynamic, continuous time differential, open-loop policy, state-feedback policy, continuous time cost-to-go, information structure, continuous time dynamic programming, linear quadratic dynamic, variable termination time

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