On discrete-time Riccati-like matrix difference equations with random coefficients

Abstract

In the present paper it is shown that the optimal solution to the stochastic adaptive control of linear dynamic systems with uncertainties depends on the unconditional means and covariances of the uncertainties. The random Riccati-like systems of equations generated as a result of the presence of multiplicative and additive noise leads to the necessity of constraint on the means and covariances of the uncertainties. Furthermore, the existence and uniqueness of an optimal solution of the given system depends upon the above constraints : steady-state solutions exist only under restrictive statistical conditions of the system parameters