R. Isaacs. Differential Games--A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. John Wiley and Sons, Inc., 1965.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem without obstacles can be formulated in quite a general way. 2.1.1 The General Case In the worst case the guide will try to evade the follower. If the guide kinematics and dynamics are modeled similarly to the robot, the motion coordination problem can be formulated as a differential game [3] between the guide and the follower. The state variables of the game are given by the state A of the robot (the pursuer) and the state Be of the guide (the evader) The control variables are the same as in the respective kinematic equations, that is for example ar and at for the robot. The time t ....

R. Isaacs. Differential Games--A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. John Wiley and Sons, Inc., 1965.

....of verification, will the system behave correctly in the face of all behaviors of the environment can be rephrased as asking whether a particular given strategy is winning. Similarly, many problems in control can be viewed as simple instances of finding winning strategies in differential games [I65] For finite state discrete systems, all variants of these problems are algorithmically solvable, and we survey various attempts to extend such results to deal with continuous and hybrid dynamics. These works can be classified according to the following inter dependent criteria: 1. What is the ....

R. Isaacs, Differential Games : A Mathematical Theory With Applications to Warfare and Pursuit, Control and Optimization, Wiley, 1965. 22

....provide exemplars to MBR. The class of RL problems studied here has also been studied in the field of differential game theory. Differential game theory is an extension of traditional game theory in which a game follows a sequence of actions through a continuous state space to achieve some payoff (Isaacs 1963). This sequence can be modeled with a set of differential equations which are analyzed to determine optimal play by the players. We can also interpret differential games to be an extension of optimal control theory in which players positions develop continuously in time, and where the goal is to ....

R. Isaacs. Differential games: A mathematical theory with applications to warfare and other topics. Technical Report Research Contribution No. 1, Center for Naval Analysis, Washington, DC, 1963.

.... of strategies has been studied extensively for discrete games, both for two person games such as the Prisoner s Dilemma [Lindgren, 1991, Lindgren Nordahl, 1994a, Lindgren Nordahl, 1994b] and multi person games (e.g. Akiyama Kaneko, 1995] Continuous strategies for differential games [Isaacs, 1965], such as pursuitevasion, require more elaborate strategy representations, and have so far been less investigated. A large number of interesting problems can be formulated as games with continuous actions. Pursuit evasion problems with multiple players can address both the evolution of flocking ....

Isaacs, R., Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, (John Wiley, 1965).

....for the eventual payoff. The class of RL problems studied here has also been studied in the field of differential game theory. Differential game theory is an extension of traditional game theory in which a game follows a sequence of actions through a continuous state space to achieve some payoff [Isa63]. This sequence can be modeled with a set of differential equations which are analyzed to determine optimal play by the players. We can also interpret differential games to be an extension of optimal control theory in which players positions develop continuously in time, and where the goal is to ....

....also interpret differential games to be an extension of optimal control theory in which players positions develop continuously in time, and where the goal is to optimize competing control laws for the players [Fri71] 3. 1 Differential games Differential game theory originated in the early 1960s [Isa63] in response to the need for a more formal analysis of war games. In a differential game, the dynamics of the game (i.e. the behaviors of the players) are modeled with a system of first order differential equations of the form dk t j dt = h t j (k t ; a t ) j = 1; n where a t = ....

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R. Isaacs. Differential games: A mathematical theory with applications to warfare and other topics. Technical Report Research Contribution No. 1, Center for Naval Analysis, Washington, DC, 1963.

....simulations. Nevertheless, the different types of dynamics and neural architectures obtained in evolutionary simulations can hopefully shed some light on the basic features of proteanism. Pursuit evasion behavior has previously been studied in several different contexts: differential game theory (Isaacs, 1965), behavioral ecology and neuroethology, and robotics. A nice review which argues convincingly for the importance of pursuit evasion problems can be found in Miller and Cliff (1994) Coevolutionary simulations of pursuit evasion have been performed, e.g. by Cliff and Miller (1996) and the problem ....

Isaacs, R. (1965). Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, John Wiley.

....to Markovian problems. The class of RL problems studied here has also been studied in the field of differential game theory. Differential game theory is an extension of traditional game theory in which a game follows a sequence of actions through a continuous state space to achieve some payoff (Isaacs, 1963). This sequence can be modeled with a set of differential equations which are analyzed to determine optimal play by the players. We can also interpret differential games to be a version of optimal control theory in which players positions develop continuously in time, and where the goal is to ....

....games to be a version of optimal control theory in which players positions develop continuously in time, and where the goal is to optimize competing control laws for the players (Friedman, 1971) 3. 1 DIFFERENTIAL GAMES AND PURSUIT GAMES Differential game theory originated in the early 1960s (Isaacs, 1963) as a framework for a more formal analysis of competitive games. In a differential game, the dynamics of the game (i.e. the behaviors of the players) are modeled with a system of first order differential equations of the form dk t j dt = h t j (k t ; a t ) j = 1; n (1) where a t ....

[Article contains additional citation context not shown here]

Isaacs, R. (1963). Differential games: A mathematical theory with applications to warfare and other topics. Tech. rep. Research Contribution No. 1, Center for Naval Analysis, Washington, D.C.

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