Metrics to enhance the resilience of cyber-physical systems

We focus on resilience towards covert attacks on Cyber-Physical Systems (CPS). We define the new k-steerability and l-monitorability control-theoretic concepts. k-steerability reflects the ability to act on every individual plant state variable with at least k different groups of functionally diverse input signals. l-monitorability indicates the ability to monitor every individual plant state variable with £ different groups of functionally diverse output signals. A CPS with k-steerability and l-monitorability is said to be (k, l)-resilient. k and l, when both greater than one, provide the capability to mitigate the impact of covert attacks when some signals, but not all, are compromised. We analyze the influence of k and l on the resilience of a system and the ability to recover its state when attacks are perpetrated. We argue that the values of k and l can be augmented by combining redundancy and diversity in hardware and software techniques that apply the moving target paradigm.