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State identification concept in structural dynamics. (English) Zbl 0559.93023

The paper presents the problem and connected with it mathematical methods of state identification for space-time systems in structural dynamics in the case of incomplete information about the system. The state identification problem is formulated with the use of a mathematical model of the dynamics and observations of the system as well as a proposed identification quality index. A characterization of the solution is given, based on modern variational calculus and analytical mechanics. Mathematical methods of the state identification for some class of systems are presented with the use of Lagrange’s functionals, dynamic programming, maximum principle, finite differences, finite elements, invariant imbedding and multilevel optimization. Examples of application of the presented state identification concept are given.

MSC:

93B30 System identification
93C20 Control/observation systems governed by partial differential equations
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B07 Observability
49K15 Optimality conditions for problems involving ordinary differential equations
49L20 Dynamic programming in optimal control and differential games
49M15 Newton-type methods
49M25 Discrete approximations in optimal control
93B40 Computational methods in systems theory (MSC2010)
90C31 Sensitivity, stability, parametric optimization
90C39 Dynamic programming
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