Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra

Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on... We consider the problem of constructing approximate Stackelberg solutions in a linear non-zero-sum positional differential game of two players with terminal payoffs and player controls chosen on convex polyhedra. A formalization of player strategies and motions generated by them is based on the formalization and results of the theory of zero-sum positional differential games developed by N.N. Krasovskii and his scientific school. The problem of finding a Stackelberg solution reduces to solving nonstandard optimal control problems. We propose an approach based on operations with convex polyhedra. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automation and Remote Control Springer Journals

Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Pleiades Publishing, Ltd.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Control, Robotics, Mechatronics; Mechanical Engineering; Computer-Aided Engineering (CAD, CAE) and Design
ISSN
0005-1179
eISSN
1608-3032
D.O.I.
10.1134/S0005117918030074
Publisher site
See Article on Publisher Site

Abstract

We consider the problem of constructing approximate Stackelberg solutions in a linear non-zero-sum positional differential game of two players with terminal payoffs and player controls chosen on convex polyhedra. A formalization of player strategies and motions generated by them is based on the formalization and results of the theory of zero-sum positional differential games developed by N.N. Krasovskii and his scientific school. The problem of finding a Stackelberg solution reduces to solving nonstandard optimal control problems. We propose an approach based on operations with convex polyhedra.

Journal

Automation and Remote ControlSpringer Journals

Published: Mar 12, 2018

References

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