On Regularizability and its Application to Online Control of Unstable LTI Systems. (arXiv:2006.00125v3 [eess.SY] UPDATED)

Learning, say through direct policy updates, often requires assumptions such
as knowing a priori that the initial policy (gain) is stabilizing, or
persistently exciting (PE) input-output data, is available. In this paper, we
examine online regulation of (possibly unstable) partially unknown linear
systems with no prior access to an initial stabilizing controller nor PE
input-output data; we instead leverage the knowledge of the input matrix for
online regulation. First, we introduce and characterize the notion of
"regularizability" for linear systems …

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