Optimal H₂ and H_∞ LQ stochastic feedforward control

Abstract

This paper deals with the solution of the discrete-time LQ stochastic tracking and servo problems for a general system configuration. It is shown that the resultant solution is in the form of a three-degree-of-freedom controller when the vector of the exogeneous signal is extended to include accessible disturbances. In particular, it is shown that a separation property between feedback, reference and accessible disturbance feedforward actions, proved for a two-degree-of-freedom optimal LQ stochastic control scheme, also holds true for the general system configuration here addressed. Further, this separation property can be suitably extended, when a linear control law is assumed, to the minimax LQ stochastic tracking and servo problems.