A quasi-separation theorem for LQG optimal control with IQ constraints

We consider the deterministic, the full observation and the partial observation LQG optimal control problems with finitely many IQ (integral quadratic!) constraints, and show that Wohnam's famous Separation Theorem for stochastic control has a generalization to this case. Although the problems...

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Bibliographic Details
Published inSystems & control letters Vol. 32; no. 1; pp. 21 - 33
Main Authors Lim, Andrew E.B., Moore, John B.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 26.10.1997
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Control theory. Systems
Duality theory
Exact sciences and technology
Integral quadratic constraints
Optimal control
Optimization theory
Separation Theorem
Optimization theory
Integral quadratic constraints
Duality theory
Separation Theorem
Stresses
Gradient
LQ control
LQG control
Duality
Optimization
Optimal control systems
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Summary:We consider the deterministic, the full observation and the partial observation LQG optimal control problems with finitely many IQ (integral quadratic!) constraints, and show that Wohnam's famous Separation Theorem for stochastic control has a generalization to this case. Although the problems of filtering and control are not independent, we show that the interdependence of these two problems is so superficial that in effect, they are problems which can be treated separately. It is in this context that the label Quasi-Separation Theorem is to be understood. We conclude with a discussion of computation issues and show how gradient-type optimization algorithms can be used to solve these problems. In this way, a systematic computation algorithm is derived.
ISSN:0167-6911
1872-7956
DOI:10.1016/S0167-6911(97)00058-3