Game-Theoretical Control Problems

1. Game-Theoretical Control.- 1.1 Minimax Control Problems.- 1.2 Equations of Motion.- 1.3 Positional Strategies.- 1.4 Quality Criterion.- 1.5 Differential Games.- 2. Differential Game of Approach-Evasion.- 2.1 Game-Theoretical Problems of Approach and Evasion.- 2.2 Stable Bridges.- 2.3 Local Estimates.- 2.4 Extremal Strategies.- 2.5 Construction of Stable Bridges.- 3. Existence of the Value for a Positional Differential Game.- 3.1 A Differential Game with a Fixed Termination Time.- 3.2 Differential Games of Pursuit-Evasion.- 3.3 Differential Games with a Bounded Duration.- 3.4 Value Function.- 3.5 Examples.- 4. Dynamic Programming.- 4.1 The Main Equation for a Smooth Value Function.- 4.2 Properties of Value Functions.- 4.3 Directional Differentiability.- 4.4 Generalization of the Main Equation.- 4.5 Examples.- 5. Extremal Aiming.- 5.1 Programmed Maximin and Programmed Absorption.- 5.2 Extremal Aiming in Linear Controlled Systems.- 5.3 Extremal Aiming in Problems of Pursuit and Evasion.- 5.4 Regularity Conditions for a Programmed Maximin.- 5.5 Differentiability of the Value Function and Regularity Condition for the Programmed Maximin.- 6. Extremal Aiming for Nonlinear Differential Games.- 6.1 Generalized Programmed Controls.- 6.2 Programmed Maximin.- 6.3 The Minimum Principle and Maximin Rule.- 6.4 Directional Derivatives of Functions of a Programmed Maximin.- 6.5 Stability Conditions for the Programmed Maximin.- 7. Prior Stable Sets.- 7.1 Prior Stable Path.- 7.2 Stable Integral Manifolds.- 7.3 Prior Stable Sets for a Linear System.- 7.4 Comparison of Controlled Systems.- 8. Qualitative Problems in the Theory of Differential Games.- 8.1 The Problem of Stability of Solutions.- 8.2 Guidance Control.- 8.3 Stabilization of Solutions of Game-Theoretical Control Problems.- 8.4 Evasion on an Infinite Time Interval.- 8.5 Universal Optimal Strategies.- 9. Mixed Strategies in Differential Games.- 9.1 Deterministic and Stochastic Controls.- 9.2 Mixed Strategies.- 9.3 Dynamic

Samuel Kotz, PhD, honorary Doctor of Science, is professor and research scholar at the Department of Engineering Management and Systems Engineering at George Washington University in Washington, D.C.