Differential games: theory and methods for solving game problems with singular surfaces
Differential games theory is the most appropriate discipline for the modelling and analysis of real life conflict problems.The theory of differential games is here treated with an emphasis on the construction of solutions to actual problems with singular surfaces. The reader is provided with the knowledge necessary to put the theory of differential games into practice.
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A Preview Example
The Solution Concept
Semipermeability of Surfaces
11 other sections not shown
adjoint equations admissible controls assume barrier paths boundary candidate optimal control candidate optimal trajectories candidate solution capture-set chapter chatter equivalent choice of control components construction corner surface curve defined denote deviation differential games dispersal surface equations of motion equivocal surface escape-set Example field of candidate field-2 Figure focal surface game model game-set guarantees termination Hamiltonian Hamiltonian function Homicidal Chauffeur Isaacs equation jump discontinuity Jx(x Lemma necessary conditions nonadmissible control law nontermination normal obtain optimal control laws optimal strategies outcome functional Player P chooses Proof The proof pursuer pursuit evasion game quadratic differential recall reference frame regular optimal trajectories relation relative frame Riccati equation safe contact arc satisfy segments semipermeable surfaces side singular arc singular surface solve strategy that guarantees surface Q Surveillance Evasion switch envelope switch function switch surface Tag game tangent target-set Theorem transversely tributaries universal surface velocity vector VJ(x