A Progammed Construction for the Positional Control

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


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) 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.


Mixed Strategy Differential Game Elementary Program Phase Vector Program Motion 
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  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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