Adaptive control of multivariable linear stochastic systems. A strong approximation approach

This paper is an extension and further development of the results of [5]. It was shown there that open loop identifiability of a linear stochastic control system under persistently exiting input implies closed loop identifiability using an appropriate dither. It was assumed there that the covariance of the system noise was known, and the covariance matrix of the dither was fixed apriori. In this paper we estimate the system parameters together with the covariance of the system noise, and we let the covariance of the dither depend on the system parameters. A recursive estimation procedure will be presented and the estimator will be characterized in the form of a strong approximation theorem. The covariance-matrix of the estimation error will be expressed in terms of the covariance matrix of the system´s noise and the dither, respectively.