Temporal Logic Resilience for Cyber-Physical Systems

We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use temporal logic to express the requirements on the acceptable functionality and define the resilience metric as the maximum disturbance under which the system satisfies the temporal requirements. We fix a parameterized template for the set of disturbances and form a robust optimization problem under the system dynamics and the temporal specifications to find the maximum value of the parameter. From the computational point of view, we show how this optimization can be solved for linear systems and provide under-approximations of the resilience metric for nonlinear systems using linear programs. The computations are demonstrated on the temperature regulation of buildings and adaptive cruise control.