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Preface; Acknowledgments; Contents; 1 Introduction; 1.1 A Viability Approach; 1.2 Introducing Other Specifications; 1.3 Variational Approaches; 1.4 Organization of the Book; 2 Celerity Regulators on Networks; 2.1 Traveling Takes Time; 2.1.1 Time, Duration and Temporal Windows; 2.1.2 Temporal Window Dependent Evolutions; 2.2 Traveling Needs Space; 2.3 Celerity Regulators for Advising Viable Velocities; 2.3.1 The Double Nature of Traffic Networks; 2.3.2 The Viability Approach; 2.3.3 New Specifications: Advised Accelerations and Jerks; 2.4 Reaching Unexpected Position in Two-Dimensional Networks

2.4.1 Reaching a Target at Alarm Signals2.4.2 Reaching a Target and Stopping at Alarm Signals; 2.4.3 Starting from Junctions; 2.4.4 Application: Pursuer-Invader Dynamical Games; 3 Traveling on the Network; 3.1 One-Dimensional Traffic Illustrations; 3.1.1 Celerity Regulators; 3.1.2 Celerity Regulators for Piecewise Constant Speed Limits; 3.1.3 The Geodesic Evolutions; 3.1.4 Dynamic Acceleration Regulators; 3.1.5 One-Dimensional Traffic Concepts; 3.1.6 Eupalinian Evolutions; 3.1.7 Collision Avoidance of Two Vehicles; 3.2 Basic Traffic Viability Concepts and Results

3.2.1 Traffic Evolutionary Systems3.2.2 Averagers of Evolutionary Systems; 3.2.3 Cournot Maps and Reachable Maps; 3.2.4 Incoming and Outgoing Relations and Maps; 3.2.5 Summary of Traffics Concepts; 3.3 Concatenation of Cournot Maps; 3.4 Eupalinian Maps; 3.4.1 Pass-Through Constraints; 3.4.2 Junctions and Intermodal Traffic Systems; 3.4.3 Multijunction Maps; 3.4.4 Multijunctions Generated by Circuits; 3.5 Synaptic Networks of Ionic Networks; 3.5.1 Neurons as Ionic Networks; 3.5.2 Networks of Neurons; 4 Viability Characterizations and Construction of Celerity Regulators

4.1 A Viability Survival Kit4.1.1 Viable Capture Basins; 4.1.2 Tangents; 4.1.3 The Viability Theorem; 4.2 Viability Characterizations of Averagers, Cournot and Eupalinian Maps; 4.2.1 Viability Characterization of the Averagers; 4.2.2 The Lax-Hopf Formula; 4.2.3 Viability Characterization of the Cournot and Reachable Maps; 4.3 Construction of Celerity Regulators; 4.4 Approximations of Cournot Maps and Viability Algorithms; 4.4.1 Approximations by Piecewise Characteristic Set-Valued Maps; 4.4.2 Viability Algorithms; 4.4.3 The Curse of Dimensionality; 5 Traffic Specifications

5.1 Micro-Meso-Macro Cascade of Traffic Evolutionary Systems5.2 Micro-Meso Specific Traffic Systems; 5.3 Duration-Chaperoned Evolutions; 5.3.1 Durations with Variable Fluidities; 5.3.2 Examples of Duration Functions; 5.3.3 Fluidity Dependent Celerity Regulators; 5.4 Acceleration and Dynamic Celerity Regulators; 5.5 Collision Avoidance of a Fleet of Vehicles; 6 Valuation of Intertemporal Micro -- Meso -- Macro Systems; 6.1 Intertemporal Selection Through Indicators; 6.1.1 Numerical Relation; 6.1.2 Intertemporal Optimization of Lagrangians; 6.1.3 The Dynamic Optimization Principle