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 $\ell $ -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 $\ell $ -monitorability metric indicates the ability of a controller to monitor individual plant state variables with $\ell $ different groups of functionally diverse outputs. Paired together, the metrics lead to CPS reaching $(k,\ell)$ -resilience. When $k$ and $\ell $ 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 $\ell $ 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 $\ell $ 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.