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Hierarchical optimal control and stability of large-scale systems. (English) Zbl 0666.93002
There are three parts in this paper: (1) a state-regulating problem is solved for a very-large-scale system. The optimal-control laws are formulated with multiechelon-dynamical-hierarchical structure. A set of matrix equations which arises in formulating optimal-control laws is shown to be solvable in an alternative way; (2) the stability of such formulated multiechelon-hierarchical structure is analysed; (3) the number of levels of hierarchy needed in a multiechelon structure is calculated and also the order of the dynamic-state regulator required.
MSC:
93A13 Hierarchical systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93A15 Large-scale systems
93B35 Sensitivity (robustness)
15A24 Matrix equations and identities
93C05 Linear systems in control theory
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