Optimal control and differential games
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Date
2016-06-26
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Addis Ababa University
Abstract
A differential game problem is a generalized optimal control problem in cases where there are
more than one decision makers, called players. However, differential games are conceptually
far more complex than optimal control problems in the sense that it is no longer obvious
what constitutes a solution. If the number of players are two, one player chooses the control
u1(t) 2 u1 _ <mu1 and tries to maximize his cost functional J1(u1; u2), while the other
player chooses the control u2(t) 2 u2 _ <mu2 and tries to maximize his cost functional
J2(u1; u2) within a common dynamic system which is described by di_erential equation of
the form x_ (t) = f(t; x; u1; u2). Where u1(t) and u2(t) are the controls implemented by
therst and second player respectively. In this cases, solving a differential game problem
is mathematically quite tricky in order to satisfy the absolute need of the two players.
Depending on the willingness of the two players they may cooperate or may not cooperate
each other. In this project, we discussed only non cooperative di_erential game in particular
by adopting open-loop strategies and feedback(closed-loop) strategies to solve the problem
of the game. Solution procedures for two person di_erential games are also discussed
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Keywords
Optimal control, Differential