Yu. V. Zaika
Russia, 185640, Petrozavodsk, Lenin's pr., 33,
Petrozavodsk State University,
Faculty of mathematics,
We consider the problem of phase state observation and prediction in nonlinear dynamical systems using an incomplete feedback. We develop N.N. Krasovskii's approach based on integral solving operators of observation. Nonlinear version of the method was suggested by N.E. Kirin. We introduce a notion of a finite basis of observable functions in terms of a functional dependence. By using integral operators of data processing, we prove theorems on the existence of such bases. The main result is nonlocal. Proofs are based on techniques of the complex analytic set theory. A generalization of the duality principle for nonlinear observable systems is obtained. For the conjugate control system we study the analytic structure of its set of accessibility. The existence of locally stable (in some sense) bases of observable functions is proved. We treat the problem of ideal observability in the case where perturbations are noncontrolled. Some approximate methods are outlined.