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We present ResilienC, a framework for resilient control of Cyber- Physical Systems subject to STL-based requirements. ResilienC uti- lizes a recently developed formalism for specifying CPS resiliency in terms of sets of (rec,dur) real-valued pairs, where rec repre- sents the system’s capability to rapidly recover from a property violation (recoverability), and dur is reflective of its ability to avoid violations post-recovery (durability). We define the resilient STL control problem as one of multi-objective optimization, where the recoverability and durability of the desired STL specification are maximized. When neither objective is prioritized over the other, the solution to the problem is a set of Pareto-optimal system trajectories. We present a precise solution method to the resilient STL control problem using a mixed-integer linear programming encoding and an a posteriori n-constraint approach for efficiently retrieving the complete set of optimally resilient solutions. In ResilienC, at each time-step, the optimal control action selected from the set of Pareto- optimal solutions by a Decision Maker strategy realizes a form of Model Predictive Control. We demonstrate the practical utility of the ResilienC framework on two significant case studies: autonomous vehicle lane keeping and deadline-driven, multi-region package delivery. 

Resiliency is the ability to quickly recover from a violation and avoid future violations for as long as possible. Such a property is of fundamental importance for Cyber-Physical Systems (CPS), and yet, to date, there is no widely agreed-upon formal treatment of CPS resiliency. We present an STL-based framework for reasoning about resiliency in CPS in which resiliency has a syntactic characterization in the form of an STL-based Resiliency Specification (SRS). Given an arbitrary STL formula φ, time bounds α and β, the SRS of φ, Rα,β (φ), is the STL formula ¬φU[0,α]G[0,β)φ, specifying that recovery from a violation of φ occur within time α (recoverability), and subsequently that φ be maintained for duration β (durability). These R-expressions, which are atoms in our SRS logic, can be combined using STL operators, allowing one to express composite resiliency specifications, e.g., multiple SRSs must hold simultaneously, or the system must eventually be resilient. We define a quantitative semantics for SRSs in the form of a Resilience Satisfaction Value (ReSV) function r and prove its soundness and completeness w.r.t. STL’s Boolean semantics. The r-value for Rα,β (φ) atoms is a singleton set containing a pair quantifying recoverability and durability. The r-value for a composite SRS formula results in a set of non-dominated recoverability-durability pairs, given that the ReSVs of subformulas might not be directly comparable (e.g., one subformula has superior durability but worse recoverability than another). To the best of our knowledge, this is the first multi-dimensional quantitative semantics for an STL-based logic. Two case studies demonstrate the practical utility of our approach. https://doi.org/10.1007/978-3-031-15839-1_7