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$$H_{2}$$-optimal rejection with preview in the continuous-time domain. (English) Zbl 1093.93008
Automatica 41, No. 5, 815-821 (2005); corrigendum ibid. 46, No. 7, 1241 (2010).
Summary: The synthesis of a feedforward unit for $$H_2$$-optimal rejection of previewed signals in continuous time-invariant linear systems is considered. The $$H_2$$-optimal compensator herein devised consists of a finite impulse response system working in connection with a standard dynamic unit. The design strategy is based on a simple interpretation of the $$H_2$$-optimal rejection problem with preview as a compound optimal control problem, i.e. as a problem consisting of a finite-horizon LQ control problem with constrained final state, an infinite-horizon LQ control problem, and the problem of minimizing the global cost functional. An explicit description of the compensator is derived by exploiting some results on the parameterization of the solutions of the associated autonomous Hamiltonian system.

##### MSC:
 93B36 $$H^\infty$$-control 93C05 Linear systems in control theory
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##### References:
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