LQ Non-Gaussian Regulator With Markovian Control

This letter concerns the linear quadratic non-Gaussian (LQnG) sub-optimal control problem when the input signal travels through an unreliable network, namely a Gilbert-Elliot channel. In particular, the control input packet losses are modeled by a two-state Markov chain with known transition probability matrix, and we assume that the moments of the non-Gaussian noise sequences up to the fourth order are known. By mean of a suitable rewriting of the system through an output injection term, and by considering an augmented system with the second-order Kronecker power of the measurements, a simple solution is provided by substituting the Kalman predictor of the LQG control law with a quadratic optimal predictor. Numerical simulations show the effective ness of the proposed method.