Bicycle Routing for Maximum Suntan
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A simple optimal control problem is formulated in which one must find the optimal path along which to bike in order to get maximum suntan, using the maximum principle and the Euler equation of the classical calculus of variations.Abstract:
A simple optimal control problem is formulated in which one must find the optimal path along which to bike in order to get maximum suntan. Both the maximum principle and the Euler equation of the classical calculus of variations are used to calculate this optimal path. The interrelationship of the two approaches is elucidated; the adjoint variables in the maximum principle approach (which happen to be constants) are integration constants when solving via the Euler equation. Several slightly different versions of this problem are treated, with some surprising phenomena in the solution.read more
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Dissertation
Techniques for solving Nonlinear Programming Problems with Emphasis on Interior Point Methods and Optimal Control Problems
TL;DR: The document contains a detailed discussion of nonlinear programming, introducing different methods used to find solutions to NLP problems and then describing a large variety of algorithms from the literature, highlighting key algorithmic differences between solvers.
References
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Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
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Dynamic Noncooperative Game Theory
Tamer Basar,Geert Jan Olsder +1 more
TL;DR: In this paper, the authors present a general formulation of non-cooperative finite games: N-Person nonzero-sum games, Pursuit-Evasion games, and Stackelberg Equilibria of infinite dynamic games.
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Deterministic and stochastic optimal control
TL;DR: In this paper, the authors considered the problem of optimal control of Markov diffusion processes in the context of calculus of variations, and proposed a solution to the problem by using the Euler Equation Extremals.
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