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Bolz problem

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

x˙(t)=f(t,x(t),u(t)),t0≤t≤T,x(t0)=x0{\ 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)=∫t0TF(t,x(t),u(t))dt+φ(x(t0),x(T))→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 functionalityJ(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
Source - https://ru.wikipedia.org/w/index.php?title= Bolza_Task&oldid = 96705463


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Clever Geek | 2019