Cyber-physical systems often include communication networks that ensure data transmission between different components of the system (sensors, actuators, processing units, etc). The presence of such networks renders the whole system vulnerable to malicious attacks consisting, for example, in the injection of arbitrary signals. In this context, the data collected over the communication channel may be so unreliable that their use for state estimation or system identification requires design methods which are more robust than conventional ones.

Resilience is a particular robustness property which characterizes the sensitivity of some performance function of interest with respect to a class of disturbances (model uncertainties). For example, we say that a state estimator is resilient to a set of disturbances E if the estimation error induced by that estimator is (a) zero whenever the actual model uncertainty lies in E and (b) continuously dependent on the distance from the actual uncertainty to the set E. In this talk we will discuss a resilience-inducing optimization framework for secure state estimation in the scenario where E is a set of impulsive (or sparse) noise sequences. This type of noise signal can account typically for intermittent sensor failures or adversarial attacks in the context of cyber-physical systems. It can also arise artificially as a methodological device for example, in the identification, estimation and control of switched systems. We consider both batch off-line and online recursive estimation.