Bolz problem

Boltz 's problem is a problem of the theory of optimal control of the form:

{\dot {x}}(t)=f(t,x(t),u(t)),t_{0}\leq t\leq T,x(t_{0})=x_{0}

{\ displaystyle {\ dot {x}} (t) = f (t, x (t), u (t)), t_ {0} \ leq t \ leq T, x (t_ {0}) = x_ { 0}}

{\ displaystyle {\ dot {x}} (t) = f (t, x (t), u (t)), t_ {0} \ leq t \ leq T, x (t_ {0}) = x_ { 0}}

J(u)=\int \limits _{t_{0}}^{T}F(t,x(t),u(t))dt+\varphi (x(t_{0}),x(T))\to \inf

{\ displaystyle J (u) = \ int \ limits _ {t_ {0}} ^ {T} F (t, x (t), u (t)) dt + \ varphi (x (t_ {0}), x (T)) \ to \ inf}

{\ displaystyle J (u) = \ int \ limits _ {t_ {0}} ^ {T} F (t, x (t), u (t)) dt + \ varphi (x (t_ {0}), x (T)) \ to \ inf}

,

in which you want to minimize functionality $J(u)$ ${\ displaystyle J (u)}$ ${\ displaystyle J (u)}$ mixed type. The problem easily reduces to the Mayer problem , which allows us to use the theorem on the necessary optimality conditions to solve the problem.

Formulated in 1913 by Oscar Bolzey .

Links

Bolza's challenge - an article from the Mathematical Encyclopedia . I. B. Vapnyarsky

Bolz problem

Links

More articles: