LQ Non-Gaussian Regulator with Markovian Control

Massimiliano D'angelo1, Stefano Battilotti2, Filippo Cacace3, Alfredo Germani4, Bruno Sinopoli5

  • 1Università di Roma "La Sapienza"
  • 2Univ. La Sapienza
  • 3Università Campus Biomedico di Roma
  • 4Universita' dell'Aquila
  • 5Carnegie Mellon University

Details

11:00 - 11:20 | Wed 11 Dec | Gallieni 5 | WeA19.4

Session: Advances in Nonlinear Filtering and Stochastic Control with Partial Information I

Abstract

The paper 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.