Continuous time stochastic adaptive control: non-explosion, ε-consistency and stability

For completely observed continuous time constant parameter stochastic linear systems, an indirect adaptive control law is presented which, subject principally to a weak location hypothesis concerning the true parameter, and a persistent excitation hypothesis, generates ε-consistent recursive least squares parameter estimates and ensures the system is mean square sample path stable. The adaptive control algorith mentails (i) recursively calculating the least squares estimate of the system parameter, and (ii) recursively generating the LQR feedback gain matrix lying in a set of matrix gains γ known to contain a stabilizing gain. The a.s. non-explosion of the system is a direct consequence of this construction.