The largest class of games that can be used in the game control of dynamic transport processes and among them controlling the movement of ships, planes, and cars represent
differential games, described by state and output equations, and state and control constraints [20-24].
Petrosyan, "Stable solutions of
differential games with many participants," vol.
This type of inequalities also arises in zero sum stochastic
differential games of mixed type where each player uses both continuous control and stopping times.
The author covers stochastic differential equations, backward stochastic differential equations, stochastic control, continuous time stochastic optimization and control, probabilistic approaches to stochastic control, stochastic
differential games, and a wide variety of other related subjects.
Petrosyan, Cooperative Stochastic
Differential Games, New York: Springer, 2005.
Isaacs,
Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, Wiley, New York Press, 1965.
Differential games of capitalism were first explored by Lancaster (1973), (3) who adopted a two player non-cooperative
differential game where the workers control the share of their consumption in total output while the capitalists control the share of investment in the surplus.
Other areas covered include dynamic programming, optimal control for polynomial systems, multi-variable frequency-domain techniques, and
differential games. Background in the state-variable representation of systems is assumed; an appendix offers a review of matrix algebra.
Chapters cover general optimal control problems, finite-dimensional optimization, optimization of dynamic systems with general performance criteria, terminal equality constraints, the linear quadratic control problem, and linear quadratic
differential games. Detailed proofs and chapter problems are included.
The first is based on the mathematical theory of
differential games. The second one, called "the elastic bands", was developed by Quinlan and Khatib and relies on repulsive potential field generation.