Stochastic adaptive control with unknown interactor matrix

The general optimal solution of the one-step-ahead criterion for adaptive control of a MIMO system having white noise and nondiagonal interactor matrix is obtained and expressed analytically in a closed form. The solution is shown to include the most important cases discussed in the literature, which can be considered as special cases. It is shown that the MIMO optimal control can be obtained only if the interactor matrix is known; otherwise approximation methods must be employed. The certainty equivalence principle is employed to design an adaptive controller based on knowledge of the degrees of the diagonal entries of the interactor matrix. Simulation results show that the proposed algorithm converges and perfect tracking is ultimately achieved