On stability and convergence of suboptimal estimation for systems over lossy networks without acknowledgement

This paper concentrates on the suboptimal state estimation problem for systems without acknowledgement (ACK). The ACK signal is used for informing the estimator of whether control-input packets have been lost during the transmission or not. For such systems, which are usually regarded as NACK systems, the optimal estimator has been proved to be beset by exponentially increasing computational burden so that it is scarcely possible to be implemented in practice and then the suboptimal estimation becomes a necessary need. Inspired by the idea of multiple-model approaches, we first design an efficient suboptimal estimator for NACK systems to significantly improve computational efficiency. More importantly, we obtained a sufficient and necessary condition to characterise the stability of this proposed suboptimal estimator, which depends only on the packet loss rate (PLR) of the observation regardless of the control-input PLR. We also prove that its estimation error will converge to that of the optimal estimator under a certain condition. A distinguishing feature of the suboptimal estimator proposed in this paper is that not only its stability and convergence can be determined theoretically, but also they are proved to be the same as those of the optimal one for NACK systems.