Distributed interval state estimation with l_∞-gain optimization for cyber-physical systems subject to bounded disturbance and random stealthy attacks

This paper studies the distributed interval state estimation problem for cyber-physical systems with bounded disturbance and random stealthy attacks. Since conventional interval observers cannot complete the task of real-time monitoring system under random attacks, an attack-resistant distributed interval observer is designed by using attack frequency and interval attack estimation. Using the designed observer, upper- and lower-bounding estimation error systems are modeled by positive interconnected systems with hybrid deterministic and random bounded inputs. To explicitly attenuate the effect of disturbance and attacks, the resulting deterministic positive error system between upper- and lower-bounding estimates is formulated. By linear programming, the results of interval observer design and l_∞-gain optimization are proposed. The remote monitoring of vehicle lateral dynamic is given for numerical verification of the results.