“Pontryagin's maximum principle”的概念、定义、翻译、参考文献-科学参考

A theorem giving a necessary condition for the solution of optimal control problems: let θ(τ), τ₀ ≤ τ ≤ T be a piecewise continuous vector function satisfying certain constraints; in order that the scalar function S = ∑c_ix_i(T ) be minimum for a process described by the equation ∂x_i /∂τ = (∂H /∂z_i )[z(τ), x(τ), θ(τ)] with given initial conditions x(τ₀) = x⁰ it is necessary that there exist a nonzero continuous vector function z(τ) satisfying dz_i /dτ = -(∂H /∂x_i )[z(τ), x(τ), θ(τ)], z_i(T ) = -c_i , and that the vector θ(τ) be so chosen that H[z(τ), x(τ), θ(τ)] is maximum for all τ, τ₀ ≤ τ ≤ T.

单词	Pontryagin's maximum principle
释义	Pontryagin's maximum principle [´pän·trē`ä·gǝnz `mak·sǝ·mǝm ´prin·sǝ·pǝl] ^MATHEMATICS A theorem giving a necessary condition for the solution of optimal control problems: let θ(τ), τ₀ ≤ τ ≤ T be a piecewise continuous vector function satisfying certain constraints; in order that the scalar function S = ∑c_ix_i(T ) be minimum for a process described by the equation ∂x_i /∂τ = (∂H /∂z_i )[z(τ), x(τ), θ(τ)] with given initial conditions x(τ₀) = x⁰ it is necessary that there exist a nonzero continuous vector function z(τ) satisfying dz_i /dτ = -(∂H /∂x_i )[z(τ), x(τ), θ(τ)], z_i(T ) = -c_i , and that the vector θ(τ) be so chosen that H[z(τ), x(τ), θ(τ)] is maximum for all τ, τ₀ ≤ τ ≤ T.
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