Pontryagin's maximum principle

[‚pän·trē′ä·gənz ′mak·sə·məm ‚prin·sə·pəl] (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_i x_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) = x ⁰ it is necessary that there exist a nonzero continuous vector function z (τ) satisfying dz_i/ d τ = -(∂ 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 Pontryagin's maximum principle [‚pän·trē′ä·gənz ′mak·sə·məm ‚prin·sə·pəl] (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_i x_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) = x ⁰ it is necessary that there exist a nonzero continuous vector function z (τ) satisfying dz_i/ d τ = -(∂ 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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