scholarly journals Optimality principles of dynamic programming in differential games

1989 ◽  
Vol 138 (1) ◽  
pp. 43-51
Author(s):  
Leszek S Zaremba
Keyword(s):  
Dynamic Programming ◽  
Differential Games ◽  
Optimality Principles

scholarly journals Cooperative optimality principals in differential games on networks

2020 ◽  
Vol 12 (4) ◽  
pp. 93-111
Author(s):  
Анна Тур ◽  
Anna Tur ◽  
Леон Аганесович Петросян ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Network Structure ◽  
Shapley Value ◽  
The Core ◽  
Investment Game ◽  
The Shapley Value ◽  
Research Investment ◽  
Optimality Principles

The paper describes a class of differential games on networks. The construction of cooperative optimality principles using a special type of characteristic function that takes into account the network structure of the game is investigated. The core, the Shapley value and the tau-value are used as cooperative optimality principles. The results are demonstrated on a model of a differential research investment game, where the Shapley value and the tau-value are explicitly constructed.

Minimax differential game with delay

2020 ◽  
pp. 359-369
Author(s):  
Arkadii V. Kim ◽  
Gennady A. Bocharov
Keyword(s):  
Dynamic Programming ◽  
Differential Games ◽  
Differential Game ◽  
Programming Method ◽  
Dynamic Programming Method ◽  
Mixed Strategies ◽  
Dimensional Theory ◽  
Analysis Methodology ◽  
Finite Dimensional ◽  
Finite Dimensional Case

The paper considers a minimax positional differential game with aftereffect based on the i-smooth analysis methodology. In the finite-dimensional (ODE) case for a minimax differential game, resolving mixed strategies can be constructed using the dynamic programming method. The report shows that the i-smooth analysis methodology allows one to construct counterstrategies in a completely similar way to the finite-dimensional case. Moreover as it is typical for the use of i-smooth analysis, in the absence of an aftereffect, all the results of the article pass to the corresponding results of the finite-dimensional theory of positional differential games.

NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 08 (02) ◽  
pp. 231-272 ◽  
Author(s):  
M. FALCONE
Keyword(s):  
Dynamic Programming ◽  
Numerical Methods ◽  
Differential Games ◽  
Value Function ◽  
Approximation Schemes ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Feedback Controls ◽  
Dynamic Programming Approach ◽  
Discrete Time Dynamical System

In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games.

scholarly journals Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances

2020 ◽  
Vol 30 (4) ◽  
pp. 553-571
Author(s):  
M.I. Gomoyunov ◽  
D.A. Serkov
Keyword(s):  
Dynamical System ◽  
Dynamic Programming ◽  
Differential Games ◽  
Control Strategy ◽  
Optimization Problems ◽  
Dynamic Programming Principle ◽  
Functional Constraints ◽  
Constructive Solution ◽  
The Future ◽  
Games Theory

For a dynamical system controlled under conditions of disturbances, a problem of optimizing the guaranteed result is considered. A feature of the problem is the presence of functional constraints on disturbances, under which, in general, the set of admissible disturbances is not closed with respect to the operation of “gluing up” of two of its elements. This circumstance does not allow to apply directly the methods developed within the differential games theory for studying the problem and, thus, leads to the necessity of modifying them appropriately. The paper provides a new notion of a non-anticipative control strategy. It is proved that the corresponding functional of the optimal guaranteed result satisfies the dynamic programming principle. As a consequence, so-called properties of $u$- and $v$-stability of this functional are established, which may allow, in the future, to obtain a constructive solution of the problem in the form of feedback (positional) controls.

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