Multiple descriptions for packetized predictive control over erasure channels

We consider a networked control system with random delays and erasures on a data-rate limited forward channel between the controller and the plant. The feedback channel from the plant to the controller is assumed noiseless. We combine two techniques to enhance the reliability of the system. First, we use packetized predictive control, where a quantized control vector with future predicted control signals is transmitted to the plant at each time instant. Second, we utilize multiple descriptions to further aid in the robustness towards packet erasures. In particular, we transmit M redundant packets, which are constructed such that when receiving any 1 ≤ J ≤ M packets, the current control signal as well as J -1 future control signals can be reliably reconstructed at the plant side. For the particular case of LTI systems and when the packets are not received out-of-order, we prove stability by showing that the system can be cast as a Markov jump linear system with M+1 states. We further show by simulations that, by use of multiple descriptions, the system state variance can be significantly reduced without increasing the total data rate.