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The optimal control and its multiple applications
Cristiana J. Silva, Delfim F. M. Torres, Emmanuel Trelat
In this work we refer to motivations, applications, and relations of control theory with other areas of mathematics. We present a brief historical review of optimal control theory,…
Absolute Extrema of Invariant Optimal Control Problems
Cristiana J. Silva, Delfim F. M. Torres
Optimal control problems are usually addressed with the help of the famous Pontryagin Maximum Principle (PMP) which gives a generalization of the classical Euler-Lagrange and Weier…
Two-dimensional Newton's Problem of Minimal Resistance
Cristiana J. Silva, Delfim F. M. Torres
Newton's problem of minimal resistance is one of the first problems of optimal control: it was proposed, and its solution given, by Isaac Newton in his masterful Principia Mathemat…