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On the perfect regulation of optimal regulators

✍ Scribed by Takao Fujii

Book ID
104300868
Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
219 KB
Volume
1
Category
Article
ISSN
0167-6911

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✦ Synopsis

is square and nonsingular, as well as a sufficient condition for the general case. Recent[y Francis [I, Section IV) established the following complete result for the general case by use of a geometric approach, although this fact was first stated without proof by Godbole [4):

Theorem. The pe/jeet regulation can be achieved, i.e. tf and only if G( s) is right-invertible and minimum phase (which we call right-minimum phase in the sequel for convenience) 2, or eqUivalently, An alternative proof is provided for an earlier result of Francis [I] on the perfect regulation of optimal regulators. Our proof shown in the present paper I is an interesting application of Anderson's result on the spectral factorization. and may be simpler and more transparent than the one in [1].

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The linear quadratic regulator is one of the most widely used tools for control systems design. Many real world systems, however, are inherently nonlinear and can only be optimally regulated using a nonlinear controller. This is, in general, much more difficult to achieve than the linear quadratic c