Reducing a Differential Game to a Pair of Optimal Control Problems

DOI10.1007/978-3-7643-8482-1_22zbMath1213.91036OpenAlexW2285885026MaRDI QIDQ3525264

Ştefan Mirică

Publication date: 12 September 2008

Published in: Progress in Nonlinear Differential Equations and Their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-7643-8482-1_22

zbMATH Keywords

value functionverification theoremHamiltonian flowfeedback strategyDifferential game

Mathematics Subject Classification ID

Optimal feedback synthesis (49N35) Differential games and control (49N70) Feedback control (93B52) Differential games (aspects of game theory) (91A23)

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Cites Work

• Generalization of the main equation of differential game theory
• Generalized solutions by Cauchy's method of characteristics
• Characterizations of the values of differential games
• Monotonicity and differential properties of the value functions in optimal control
• Tangent, quasitangent, and peritangent directions to the trajectories of differential inclusions
• Axiomatic approach in differential games
• Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman’s and Isaacs’ Equations
• The Existence of Value and Saddle Point in Games of Fixed Duration
• Viscosity Solutions of Hamilton-Jacobi Equations
• Verification Theorems for Optimal Feedback Strategies in Differential Games
• Approximate, limiting and generalized trajectories of feedback differential systems
• On the Existence of Solutions to a Differential Game
• The existence of value in differential games
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
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