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Computation of the digital lqg regulator and tracker for time‐varying systems
Author(s) -
Van Willigenburg L. G.
Publication year - 1992
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.4660130403
Subject(s) - linear quadratic gaussian control , optimal projection equations , control theory (sociology) , computation , digital control , linear quadratic regulator , optimal control , regulator , controller (irrigation) , mathematics , computer science , mathematical optimization , control (management) , engineering , algorithm , artificial intelligence , agronomy , biochemistry , chemistry , biology , electrical engineering , gene
Digital optimal control problems, i.e. problems where a continuous‐time system is controlled by a digital computer, are very often approximated by either discrete‐time or continuous‐time optimal control problems. A digital controller based on one of these approximations requires a small sampling time and constitutes only an approximate solution. The digital LQG regulator and tracker constitute solutions to real digital control problems which involve sampled‐data, piecewise constant controls and integral criteria. Until now only the numerical computation of the digital LQG regulator in the case of time‐invariant system and criterion matrices has been considered in the literature. The control of non‐linear stochastic systems about state trajectories is very often performed by an LQG regulator based on the linearized dynamics about the trajectory, which constitute a time‐varying system. We present a numerical procedure to compute the digital LQG regulator and tracker in the case where the system and criterion matrices are time‐varying. Finally we present a numerical example.