Differential Games: Theory and Methods for Solving Game Problems with Singular Surfaces

摘要: 1 A Preview Example.- 1.1 Introduction.- 1.2 Simple Differential Game.- 1.3 Preliminary Analysis.- 1.4 Heuristic Solution.- 1.5 Problems.- 2 The Vocabulary For Games.- 2.1 2.2 State Vector and the Game-Set.- 2.3 Equations of Motion.- 2.4 Termigation a 2.5 Plays.- 2.6 Outcomes.- 2.7 Strategies.- 2.7.1 Decisions Information.- 2.7.2 Realizations 2.7.3 Strategies that Guarantee Nontermination.- 2.7.4 Termination.- 2.7.5 Admissibility 2.8 3 Solution Concept.- 3.1 3.2 Quintet.- 3.3 Extended 3.4 4 Semipermeability Surfaces.- 4.1 4.2 Smooth Semipermeable 4.3 Composite 4.3.1 Leaking Corners.- 4.3.2 Modified Definition Semipermeability.- 4.4 5 Necessary Conditions.- 5.1 5.2 Properties Target Set.- 5.2.1 Partitioning 5.2.2 Relation Between J(x) G(x).- 5.3 Boundary Escape Set F.- 5.4 Optimal Trajectories.- 5.4.1 Principle Optimality (weak).- 5.4.2 Continuity Of Value Function.- 5.4.3 j(x) Along 5.4.4 Hamiltonian on 5.5 Isaacs Equations.- 5.5.1 Semi-Local Deviations From Optimality.- 5.5.2 Main 5.5.3 hodograph representations ME1.- 5.5.4 Viscosity Form 5.6 Adjoint 5.6.1 Retro Time 5.7 6 Sufficient 6.1 6.2 Sufficiency Theorem.- 6.3 Validity Partial Solutions.- 6.4 Estimatioms 6.5 7 Regular Construction.- 7.1 7.2 Procedure.- 7.2.1 Target-Set.- 7.2.2 Candidate Control Laws.- 7.2.3 Retro-Integration 7.2.4 Manifolds 7.3 Examples.- 7.4 Linear Quadratic 7.4.1 7.4.2 LQG with Fixed Duration Unbounded Controls.- 7.4.3 Infinite Horizon 7.4.4 Controller Design.- 7.5 8 Construction SPS.- 8.1 8.2 8.2.1 8.2.2 Constructed Manifold.- 8.3 8.4 9 Topography Map.- 9.1 9.2 Barriers Safe Contact.- 9.2.1 Barriers.- 9.2.2 Costraints.- 9.2.3 9.2.4 Tributaries.- 9.3 Switch 9.4 Dispersal 9.5 Universal Focal 9.5.1 General characterization.- 9.5.2 9.5.3 9.6 Corner 9.6.1 9.6.2 Equivocal 9.6.3 Envelopes.- 10 Conditions (Singular).- 10.1 10.2 Projection Lemma.- 10.3 Open 10.4 for Singular Arcs.- 10.4.1 10.4.2 Theorems 10.4.3 Hamiltonians Seams.- 10.5 Junctions to 10.5.1 Controls 10.5.2 Junction 10.6 10.7 10.8 Chatter Equivalent 10.8.1 10.8.2 Arcs Tributaries Joining Transversely.- 10.8.3 Tangentially.- 10.9 conditions.- 10.l0 11 11.1 introduction.- 11.2 Region Multiple Choices.- 11.3 Characterization 11.4 11.5 12 12.1 12.2 12.3 Contact 12.3.1 12.3.2 Tangential Junctions.- 12.3.3 Transversal 12.4 12.5 13 13.1 13.2 13.3 13.3.1 Equivalent.- 13.4 13.5 13.6 An Example Surface.- 13.6.1 13.7 14 14.1 14.2 14.3 Envelope.- 14.4 SE.- 14.5 14.6 ES.- 14.7 15 Envelope Barrier.- 15.1 15.2 15.2.1 Dominated 15.2.2 15.3 Examples.