Differential games : a concise introduction / by Jiongmin Yong, University of Central Florida, USA.

Format:

Book

Author/Creator:

Yong, J. (Jiongmin), 1958- author.

Language:

English

Subjects (All):

Differential games.

Game theory.

Physical Description:

1 online resource (337 p.)

Place of Publication:

New Jersey : World Scientific, [2015]

Language Note:

English

Summary:

This book uses a small volume to present the most basic results for deterministic two-person differential games. The presentation begins with optimization of a single function, followed by a basic theory for two-person games. For dynamic situations, the author first recalls control theory which is treated as single-person differential games. Then a systematic theory of two-person differential games is concisely presented, including evasion and pursuit problems, zero-sum problems and LQ differential games. The book is intended to be self-contained, assuming that the readers have basic knowledge of calculus, linear algebra, and elementary ordinary differential equations. The readership of the book could be junior/senior undergraduate and graduate students with majors related to applied mathematics, who are interested in differential games. Researchers in some other related areas, such as engineering, social science, etc. will also find the book useful.

Contents:

1. Introduction. 1.1. Optimization problems. 1.2. Game theory - a brief glance. 1.3. Control and differential game problems. 1.4. Some mathematical preparations. 1.5. Brief historic remarks

2. Control theory - single-player differential games. 2.1. Control systems. 2.2. Optimal control - existence theory. 2.3. Pontryagin maximum principle - a variational method. 2.4. Dynamic programming and HJB equation. 2.5. Viscosity solutions. 2.6. Autonomous systems - controllability problems. 2.7. Viability problems. 2.8. Non-uniqueness of solutions to HJ equations. 2.9. Brief historic remarks

3. Two-person zero sum differential games - a general consideration. 3.1. Strategies. 3.2. Open-loop Pareto optima and Nash equilibria. 3.3. Two-person zero-sum differential games. 3.4. Brief historic remarks

4. Differential games with unbounded controls. 4.1. Unbounded controls. 4.2. Upper and lower Hamiltonians. 4.3. Uniqueness of viscosity solution. 4.4. Upper and lower value functions. 4.5. Brief historic remarks

5. Differential games of pursuit and evasion. 5.1. Differential pursuit games. 5.2. Differential evasion games. 5.3. Brief historic remarks

6. Linear-quadratic differential games. 6.1. Linear-quadratic optimal control problems. 6.2. Differential games. 6.3. A quadratic game in a Hilbert space. 6.4. Open-loop saddle points and two-point boundary value problems. 6.5. Closed-loop saddle points and Riccati equations. 6.6. Solution to LQ differential games. 6.7. Fredholm integral equation. 6.8. Brief historic remarks

7. Differential games with switching strategies. 7.1. Optimal switching control problems. 7.2. Differential games with switching controls. 7.3. Brief historic remarks.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on print version record.

ISBN:

981-4596-23-X

OCLC:

900633240