A Progammed Construction for the Positional Control

  • V. D. Batuhtin
Part of the Lecture Notes in Computer Science book series (LNCIS)

Abstract

Let the motion of a competitively controlled system be described by the differential equation
$$dx/dt = f(t,x,u,v),{\kern 1pt} x({t_0}) = {x_0},$$
(1)
(1) where x ∊ Rn is the phase vector of the system; u and v are the vectors controlling the actions of the players with restrictions u[t] ∊ P ⊂RP; v[t] ∊ Q ⊂ Ra; P and Q are compacts; the function f(t, x, u, v) is continuous in the totality of the arguments and continuously differentiable in x. In addition, we will assume that the formulated in [1] condition of uniform ex-tendability of the solutions for the equation (1) is fulfilled.

Keywords

Dition Mist Guaran 

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References

  1. 1.
    V.D, Batuhtin, N.N. Krasovskii. The problem of programmed control on maximin, Izv. AN SSSR, Tehnicheskaja kibernetika, 1972, No 6.(Russian).Google Scholar
  2. 2.
    L.S. Pontrjagin, V.G. Boltjanskii, R.V. Gamkrelidze, E.F. Mist-chenko. The mathematical theory of optimal processes, Fizmatgiz, Moseow, 1961. (Russian).Google Scholar
  3. 3.
    N.N. Krasovskii. The differential game of converging — evading, Izv. AN SSSR, Tehnicheskaja kibernetika, 1973, N=0 N=0, 30 (Russian).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • V. D. Batuhtin
    • 1
  1. 1.Institute of Mathematics and Mechanics, UralScientific Center of the Academy of Scienes of the USSRSverdlovskUSSR

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