Full state approximation by Galerkin projection reduced order models for\n stochastic and bilinear systems Article Swipe
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·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2102.07534
· OA: W4287327953
In this paper, the problem of full state approximation by model reduction is\nstudied for stochastic and bilinear systems. Our proposed approach relies on\nidentifying the dominant subspaces based on the reachability Gramian of a\nsystem. Once the desired subspace is computed, the reduced order model is then\nobtained by a Galerkin projection. We prove that, in the stochastic case, this\napproach either preserves mean square asymptotic stability or leads to reduced\nmodels whose minimal realization is mean square asymptotically stable. This\nstability preservation guarantees the existence of the reduced system\nreachability Gramian which is the basis for the full state error bounds that we\nderive. This error bound depends on the neglected eigenvalues of the\nreachability Gramian and hence shows that these values are a good indicator for\nthe expected error in the dimension reduction procedure. Subsequently, we\nestablish the stability preservation result and the error bound for a full\nstate approximation to bilinear systems in a similar manner. These latter\nresults are based on a recently proved link between stochastic and bilinear\nsystems. We conclude the paper by numerical experiments using a benchmark\nproblem. We compare this approach with balanced truncation and show that it\nperforms well in reproducing the full state of the system. \\end{abstract}\n
