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A Hamiltonian system based approach for the computation of the maximal rank-minimizing solution of the LMI arising from a singular LQR problem
Journal
2022 European Control Conference, ECC 2022
Date Issued
2022-01-01
Author(s)
Qais, Imrul
Bhawal, Chayan
Pal, Debasattam
Abstract
In this paper we deal with the linear matrix inequality (LMI) arising from a singular linear quadratic regulator (LQR) problem. The maximal rank-minimizing solution Kmax of the LMI plays a central role in obtaining a proportional-derivative feedback law for the optimal input. The optimal cost of the LQR, too, depends on this solution Kmax. In this paper, we provide a method to compute this maximal rank-minimizing solution Kmax of the singular LQR LMI. We compute this solution using the notions of the weakly unobservable or the slow space and the strongly reachable or the fast space of the Hamiltonian system arising from the singular LQR problem. In this process, we also provide a novel characterization of the fast space in terms of the system matrices.