Vol.2, No 7, 1997 pp. 241 - 253
UDC 62-50:62-52
INVERSE PROBLEMS OF NONLINEAR CONTROL
SYSTEMS
Alexander M. Kovalev, Vladimir F. Shcherbak
AMS subject classification 93B05, 93B07, 70E15
Abstract. The inverse problems for nonlinear control system, described
by ordinary differential equations in values of a output considered on
one or more trajectories are being studied. The criterions of observability,
invertibility, identifiability of nonlinear systems with using the extended
output have been proved. On the basis of the modified implicit functions
theorem the sufficient conditions are obtained in terms of Jacobi matrices
ranks which permit the effective check-up. The set trajectories method
proposed extends classes of systems for which it is possible to find unknowns
of their mathematical models and is the base of new computing algorithms.
It is shown that problem of determing input in the values of state known
on the several trajectories always can be reduced (at least locally) to
the algebraic relations and has solution for any system. The possibilities
of determining the moments of inertia of a rigid body on the basis of measurements
of the projection of the angular velocity onto a principal axis are studied.
INVERZNI
PROBLEM NELINEARNIH UPRAVLJAČKIH SISTEMA
U radu se proučavaju inverzni problemi za
nelinearne upravljačke sisteme, opisane običnim diferencijalnim jednačinama
po vrednostima izlaza razmatranim na jednoj ili više trajektorija. Dokazani
su kriterijumi opservabilnosti, invertibilnosti i mogućnosti identifikacije
sa korišćenjem proširenog izlaza. Na osnovu modifikovane teoreme implicitnih
funkcija dobijeni su dovoljni uslovi u obliku ranga Jakobijevih matrica
što dozvoljava efikasnu proveru. Predloženi metod skupa trajektorija proširuje
klase sistema za koje je moguće naći nepoznate njihovih matematičkih modela
i predstavlja osnovu novih računskih algoritama. Pokazano je da se problem
odredjivanja ulaza po poznatim veličinama stanja na nekoliko trajektorija,
uvek može redukovati (barem lokalno) na algebarske relacije i ima rešenje
za svaki sistem. Proučene su i mogućnosti odredjivanja momenata inercije
krutog tela na osnovu merenja projekcije ugaone brzine na glavnu osu.
