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Problems of control and stabilization in dynamical systems. (English. Russian original) Zbl 0969.49022

J. Math. Sci., New York 100, No. 5, 2458-2469 (2000); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat Obz. 60, 24-41 (1998).
The article, containing the plenary talk given by the author at a recent International Conference dedicated to L. S. Pontryagin, discusses several ideas, concepts and results concerning, mainly, “mixed strategies”, \(S_u, \;S_v\), defined as “triples of conditional probability measures”, for differential games described by “differential equations with aftereffect” of the form: \[ x'=f(t,x[t_*[.]t],u,v), \;t_*<t_0<t, \;u\in U, \;v\in V \] and a “performance index” \(\gamma =\gamma (x[t_0[.]\theta)\).
This very general and rather elliptic exposition uses concepts and results from most of author’s books, in particular from one of the latest [A. N. Krasovskii and N. N. Krasovskii, “Control under lack of information”. Basel: Birkhäuser (1995; Zbl 0827.93001)].

MSC:

49N70 Differential games and control
93C41 Control/observation systems with incomplete information
49N35 Optimal feedback synthesis
49N30 Problems with incomplete information (optimization)

Citations:

Zbl 0827.93001
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References:

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