Stability and performance of packet-based feedback control over a Markov channel

This paper examines a packet-based control strategy to improve the stabitity and performance of a networked control system with transmission losses that follow a stochastic 2-state Markov model. Typically, in a discrete time network control framework, a single control value is transmitted during each sample period. In a packet-based environment, however, there is no penalty for sending additional information in each transmission up to the fixed minimum packet size. When an accurate model of the plant dynamics is available, estimated control values can be included in each packet and applied when transmission delays are longer than the sample period or dropouts occur. The effects of data losses are analyzed using a discrete dynamics switched system framework. When the network transmits data successfully, standard closed loop dynamics exist using the latest feedback measurements. When packets are dropped, an alternate open loop set of dynamics are active. These dynamics incorporate the estimated control values that are applied when information is lost or delayed. Using analvsis tools for stochastic stability of Markov jump linear systems, network operating conditions can be identified for given plant dynamics that ensure second moment stability (SMS) for zero, N, or infinitely many estimated control values per packet. Additionally, a bounded real lemma for stochastic switched svstem H-infinity norms enables comparison of the expected disturbance to output performance for different numbers of control estimates. Analysis and experiments using an inverted pendulum show that this system obtains the greatest incremental stability and performance benefit from the first estimated control value.