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Solution by means of the maximum principle of a problem of energetically optimal control of train motion. (Russian) Zbl 0589.49020

The authors consider the problem: \(J(x,u)=\int^{T}_{0}x(u^+- \epsilon u^-)dt\to \min\), \(\dot x=-w(x)+u\), \(x(0)=x_ 0\), \(x(T)=x_ T\), \(\int^{T}_{0}xdt=S\), -1\(\leq u\leq a\), \(0\leq x\leq V\), where a,V,T,S are constant positive parameters, \(x_ 0,x_ T\in [0,V]\), \(0\leq \epsilon \leq 1\), \(u^+=\max (0,u)\geq 0\), \(u^-=\max (0,-u)\geq 0\). The results permit the construction of an optimal synthesis of the train motion which can be realised in the form of an algorithm.
Reviewer: S.Balint

MSC:

49M05 Numerical methods based on necessary conditions
65K10 Numerical optimization and variational techniques
93C15 Control/observation systems governed by ordinary differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
93B40 Computational methods in systems theory (MSC2010)
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