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The principle of equivalence in controlling a motion. I. (English. Russian original) Zbl 1055.93517
Autom. Remote Control 60, No. 10, Part 1, 1437-1443 (1999); translation from Avtom. Telemekh. 1999, No. 10, 89-96 (1999).
Summary: It is shown that any controlled motion can be characterized by a triple: metric of the phase space-pilot function-vector field. Three basic structures in controlling a motion are considered: the direct process of the propagation of excitation and the inverse problems of nonlocal search for extremum and stabilization of a motion. The principle of equivalence in controlling a motion is formulated, and the partial differential equations for these basic structures are obtained.

93C10 Nonlinear systems in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)