Differential Game Theory with Applications to Missiles and Autonomous Systems Guidance

Farhan A. Faruqi

• Publisher: Wiley
• Year: 2017
• Print ISBN: 9781119168478
• eBook ISBN: 9781119168492
• Edition: 1
• Topic: Technik & Maschinenbau
• Subtopic: Luft- & Raumfahrttechnik

Differential Game Theory with Applications to Missiles and Autonomous Systems explains the use of differential game theory in autonomous guidance and control systems.

The book begins with an introduction to the basic principles before considering optimum control and game theory. Two-party and multi-party game theory and guidance are then covered and, finally, the theory is demonstrated through simulation examples and models and the simulation results are discussed. Recent developments in the area of guidance and autonomous systems are also presented.

Key features:

• Presents new developments and how they relate to established control systems knowledge.
• Demonstrates the theory through simulation examples and models.
• Covers two-party and multi-party game theory and guidance.
• Accompanied by a website hosting MATLAB® code.

The book is essential reading for researchers and practitioners in the aerospace and defence industries as well as graduate students in aerospace engineering.

1
Differential Game Theory and Applications to Missile Guidance

Nomenclature

k:

is the epoch (in a discrete time game).

P:

is the set of players in a game.

U:

is the set of strategies available to all the players.

Uⁱ:

is the set of strategies available to player i.

is the objective function for players i and j.

X_k:

is the set of current state of a game at epoch k.

U_k:

is the set of strategies available to a player at epoch k.

is the strategy vector (input vector) available to player i against player j atepoch k.

C_k:

is the set of constraints at epoch k.

G_k:

is the set of elements of a discrete-time game.

t:

is the time in a continuous time (differential) game.

X_t:

is the set of states of a game at time t.

U_t:

is the set of strategies at time t.

is the strategy vector (input vector) available to player i against player j attime t.

C_t:

is the set of constraints at time t.

G_t:

is the set of elements of a continuous time (differential) game.

is the relative state vector of player i w.r.t. player j at time t.

is the strategy vector (input vector) of player i.

F:

is the state coefficient matrix.

G:

is the input coefficient matrix.

Q:

is the PI weightings matrix on the current relative states.

S:

is the PI weightings matrix on the final relative states.

are PI weightings matrices on inputs.

Abbreviations

APN:

augmented PN

CF:

cost function

LQPI:

linear system quadratic performance index

OF:

objective function

PI:

performance index

PN:

proportional navigation

UF:

utility function

4-DOF:

four degrees of freedom

w.r.t.:

with respect to

1.1 Introduction

Over the last few decades a great deal of material has been published covering some of the major aspects of game theory. The well-known publications in this field include “Games and Economic Behaviour” by John von Neumann and Oskar Morgenstern.^[1] Since then there has been a significant growth in publication on both the theoretical results and applications. A total of eight Nobel Prizes were given in Economic Sciences for work primarily in game theory, including the one given in 1994 to John Harsanyi, John Nash, and Reinhard Selten for their pioneering work in the analysis of non-cooperative games. In 2005, the Nobel Prizes in game theory went to Robert Aumann and Thomas Schelling for their work on conflict and cooperation through game-theory analysis. In 2007, Leonid Hurwicz, Eric Maskin, and Roger Myerson were awarded the Nobel Prize for having laid the foundations of mechanism design theory. These and other notable works on game theory are given in the references.^[2–7]

Cooperative game theory application to autonomous systems with applications to surveillance and reconnaissance of potential threats, and persistent area denial have been studied by a number of authors; useful references on this and allied topics are given at the end of this chapter.^[8–15] Usually, the (potential) targets and threats in a battlefield are intelligent and mobile, and they employ counter-strategies to avoid being detected, tracked, or destroyed. These action and counteraction behaviors can be formulated in a game setting, or more specifically, by pursuit/evasion differential games (with multiple players). It is noteworthy that application of differential games to combat systems can be considered to have been started by Rufus P. Isaacs when he investigated pursuit/evasion games.^[8] However, most of the theor...

Table of contents

• Cover
• Aerospace Series
• Titlepage
• Copyright
• Dedication
• Preface
• Acknowledgments
• About the Companion Website
• 1: Differential Game Theory and Applications to Missile Guidance
• 2: Optimum Control and Differential Game Theory
• 3: Differential Game Theory Applied to Two-Party Missile Guidance Problem
• 4: Three-Party Differential Game Theory Applied to Missile Guidance Problem
• 5: Four Degrees-of-Freedom (DOF) Simulation Model for Missile Guidance and Control Systems
• 6: Three-Party Differential Game Missile Guidance Simulation Study
• Index
• EULA