Finite memory controls for discrete-time state-space systems

As a new type of output feedback control for a stochastic discrete-time state-space system, a finite memory control (FMC) is proposed and its properties are investigated. Instead of using an internal state involved with old data, the FMC is required to have finite memory with respect to inputs and outputs together with the future reference signals and minimize a conditional receding horizon quadratic performance criterion. It turns out that the FMC is linearly expressed in terms of inputs and outputs on the recent time, and the future reference signals on the finite time. As the linear quadratic Gaussian (LQG) controls with infinite memory structure can be separated into the linear quadratic (LQ) controls and the Kalman filters, the proposed FMC consists of a receding horizon control (RHC) for state feedback control and a minimum variance finite impulse response (MVFIR) filter for state estimation. It is shown that closed loop poles are made up of those involved with the RHC and the rest of zeros. The stability is also shown to be guaranteed under some condition.