Set-Membership Estimation for Networked Nonlinear Systems under Communication Constraints: A Survey

Set-membership estimation (SME) has attracted increasing attention in recent years due to its capability of providing guaranteed state bounds for systems subject to unknown-but-bounded uncertainties. Compared with the estimation methods dealing with stochastic noises, SME does not rely on probabilistic assumptions on noises, making it particularly suitable for safety-critical systems and the systems in networked environments with incomplete statistical information. Meanwhile, the rapid development of communication networks has significantly promoted the deployment of networked systems, where communication constraints such as time delays, packet dropouts, communication protocols, quantization effects, event-triggered schemes, and cyber attacks inevitably introduce additional challenges to the state estimation. Motivated by these developments, this paper presents a comprehensive survey on SME for networked nonlinear systems under communication constraints. First, the fundamental concepts and the recursive principles of SME are reviewed. Then, representative set representations and the corresponding SME methods for nonlinear systems are systematically summarized, with particular emphasis on the techniques for handling the nonlinear mappings as well as the ellipsoidal and the zonotopic SME approaches. Subsequently, existing SME methods under various communication constraints are classified and reviewed from a unified perspective according to their influences on the measurement transmission and the estimator design. Finally, several open problems and future research directions are discussed.