Contact geometry of the Pontryagin maximum principle
Copyright policy )Contact geometry of the Pontryagin maximum principle
This paper gives a brief contact-geometric account of the Pontryagin maximum principle. We show that key notions in the Pontryagin maximum principle---such as the separating hyperplanes, costate, necessary condition, and normal/abnormal minimizers---have natural contact-geometric interpretations. We then exploit the contact-geometric formulation to give a simple derivation of the transversality condition for optimal control with terminal cost.
10 pages, 4 figures
- The University of Texas at Dallas United States
differential geometric methods, Geometric methods, Optimality conditions for problems involving ordinary differential equations, optimal control, maximum principle, Mathematics - Symplectic Geometry, Optimization and Control (math.OC), FOS: Mathematics, Symplectic Geometry (math.SG), geometric approaches, Mathematics - Optimization and Control, Control/observation systems governed by ordinary differential equations, 37J55, 49J15, 53D10
differential geometric methods, Geometric methods, Optimality conditions for problems involving ordinary differential equations, optimal control, maximum principle, Mathematics - Symplectic Geometry, Optimization and Control (math.OC), FOS: Mathematics, Symplectic Geometry (math.SG), geometric approaches, Mathematics - Optimization and Control, Control/observation systems governed by ordinary differential equations, 37J55, 49J15, 53D10
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