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Singular perturbation analysis of the closed‐loop discrete optimal control problem
Author(s) -
Naidu D. S.,
Rao A. K.
Publication year - 1984
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660050103
Subject(s) - riccati equation , mathematics , singular perturbation , algebraic riccati equation , perturbation (astronomy) , series (stratigraphy) , control theory (sociology) , matrix (chemical analysis) , mathematical analysis , optimal control , control (management) , mathematical optimization , differential equation , computer science , physics , paleontology , quantum mechanics , artificial intelligence , biology , materials science , composite material
The closed‐loop optimal control of a linear, time‐invariant, singularly perturbed discrete system is considered. The resulting matrix Riccati difference equation is formulated in the singularly perturbed structure. It is observed that the degeneration affects some of the final conditions of the Riccati equation. A singular perturbation method is developed to obtain approximate solutions in terms of an outer series and a final correction series. The outer series takes advantage of the order reduction associated with degeneration and the correction series takes care of the affected final conditions. Two examples are given to illustrate the proposed method.