The American mathematician Norbert Wiener (1894–1964) published his great work “Cybernetics” in 1948, and the American mathematician Richard E. Bellman (1920–1984) published his important work “Dynamic Programming” in 1957. In the 5 years from 1955 to 1959, the Soviet mathematician L. Pontryagin (1908–1988) and his students developed a very general maximum principle in the theory of optimal control, which defined the extremal function by Hamiltonian equations and transversal conditions, and elevated the Euler-Lagrange equation in the necessary condition of the extremal function to a very general theorem, thus proposing the very general maximum principle.

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Pontryagin Maximum Principle and Its Applications

  • Shiqing Zhang

摘要

The American mathematician Norbert Wiener (1894–1964) published his great work “Cybernetics” in 1948, and the American mathematician Richard E. Bellman (1920–1984) published his important work “Dynamic Programming” in 1957. In the 5 years from 1955 to 1959, the Soviet mathematician L. Pontryagin (1908–1988) and his students developed a very general maximum principle in the theory of optimal control, which defined the extremal function by Hamiltonian equations and transversal conditions, and elevated the Euler-Lagrange equation in the necessary condition of the extremal function to a very general theorem, thus proposing the very general maximum principle.