1Differential 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.

Xk:

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

Uk:

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.

Ck:

is the set of constraints at epoch k.

Gk:

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

t:

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

Xt:

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

Ut:

is the set of strategies at time t.

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

Ct:

is the set of constraints at time t.

Gt:

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:

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