This work concerns a new methodology to solve the ℋ2-optimal disturbance rejection problem by measurement feedback in the singular case: namely, when the plant has no feedthrough terms from the control input and the disturbance input to the controlled output and the measured output, respectively. A necessary and sufficient condition for problem solvability is expressed as the inclusion of two subspaces-a controlled-invariant subspace and a conditioned-invariant subspace. Such subspaces are directly derived from the Hamiltonian systems associated to the ℋ2-optimal control problem and, respectively, to the ℋ2-optimal filtering problem. The proof of sufficiency, which is constructive, provides the computational tools for the synthesis of the feedback regulator. A numerical example is worked out in order to illustrate how to implement the devised procedure.

Zattoni, E. (2016). ℋ2-Optimal disturbance rejection by measurement feedback: The singular case. INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS, 109(4), 975-992 [10.12732/ijpam.v109i4.18].

ℋ2-Optimal disturbance rejection by measurement feedback: The singular case

ZATTONI, ELENA
2016

Abstract

This work concerns a new methodology to solve the ℋ2-optimal disturbance rejection problem by measurement feedback in the singular case: namely, when the plant has no feedthrough terms from the control input and the disturbance input to the controlled output and the measured output, respectively. A necessary and sufficient condition for problem solvability is expressed as the inclusion of two subspaces-a controlled-invariant subspace and a conditioned-invariant subspace. Such subspaces are directly derived from the Hamiltonian systems associated to the ℋ2-optimal control problem and, respectively, to the ℋ2-optimal filtering problem. The proof of sufficiency, which is constructive, provides the computational tools for the synthesis of the feedback regulator. A numerical example is worked out in order to illustrate how to implement the devised procedure.
2016
Zattoni, E. (2016). ℋ2-Optimal disturbance rejection by measurement feedback: The singular case. INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS, 109(4), 975-992 [10.12732/ijpam.v109i4.18].
Zattoni, Elena
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/592297
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