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Robust model predictive control (MPC) is an essential tool for control systems under uncertainty as it allows for constraint satisfaction even if disturbances occur. When a system suffers malicious attacks, in contrast to parametric uncertainties or known systems faults, it is difficult to specify tight uncertainty ranges within which possible disturbances lie. In this case, very conservative solutions or even infeasible problems are obtained. To address this issue, we propose an adaptively robust MPC scheme that adjusts the uncertainty ranges to available knowledge about the attackers. To this end, we combine a recently proposed method identifying unknown attacks on nonlinear systems with a multi-stage approach to robust MPC. We illustrate the potential of the method in a numerical case study with a distributed nonlinear system.

Adaptively robust nonlinear model predictive control based on attack identification