Resilience estimation of cyber-physical systems via quantitative metrics

This paper is about the estimation of the cyber-resilience of CPS. We define two new resilience estimation metrics: k-steerability and l -monitorability. They aim at assisting designers to evaluate and increase the cyber-resilience of CPS when facing stealthy attacks. The k-steerability metric reflects the ability of a controller to act on individual plant state variables when, at least, k different groups of functionally diverse input signals may be processed. The l -monitorability metric indicates the ability of a controller to monitor individual plant state variables with l different groups of functionally diverse outputs. Paired together, the metrics lead to CPS reaching (k, l )-resilience. When k and l are both greater than one, a CPS can absorb and adapt to control-theoretic attacks manipulating input and output signals. We also relate the parameters k and l to the recoverability of a system. We define recoverability strategies to mitigate the impact of perpetrated attacks. We show that the values of k and l can be augmented by combining redundancy and diversity in hardware and software, in order to apply the moving target paradigm. We validate the approach via simulation and numeric results.