Stability and the separation principle in output-feedback stochastic MPC with random packet losses

This paper considers a linear quadratic Gaussian (LQG) control problem with constraints on system inputs and random packet losses occurring on the communication channel between plant and controller. It is well known that, in the absence of constraints, the Separation Principle between estimator and controller holds when the channel employs a TCP-like protocol but not so under a UDP-like protocol. This paper gives a counterexample that shows that, under a model predictive control (MPC) scheme that handles the constraints, the Separation Principle does not hold even in the TCP-like case. Theoretical analysis characterizes and reveals a trade-off between estimation errors in the estimator and prediction errors in the controller. Counterintuitively, the poorer on-average performance of the estimator in the UDP case may be compensated by smaller prediction errors in the controller.