We propose a novel framework for designing a resilient Model Predictive
Control (MPC) targeting uncertain linear systems under cyber attack. Assuming a
periodic attack scenario, we model the system under Denial of Service (DoS)
attack, also with measurement noise, as an uncertain linear system with
parametric and additive uncertainty. To detect anomalies, we employ a Kalman
filter-based approach. Then, through our observations of the intensity of the
launched attack, we determine a range of possible values for the system
matrices, as well as establish bounds of the additive uncertainty for the
equivalent uncertain system. Leveraging a recent constraint tightening robust
MPC method, we present an optimization-based resilient algorithm. Accordingly,
we compute the uncertainty bounds and corresponding constraints offline for
various attack magnitudes. Then, this data can be used efficiently in the MPC
computations online. We demonstrate the effectiveness of the developed
framework on the Adaptive Cruise Control (ACC) problem.Comment: To Appear in ICINCO 202