Biblio

Cyber-Physical Systems (CPS) use computational resources to control physical processes and provide critical services. For this reason, an attack in these systems may have dangerous consequences in the physical world. Hence, cyber- resilience is a fundamental property to ensure the safety of the people, the environment and the controlled physical processes. In this paper, we present metrics to quantify the cyber-resilience level based on the design, structure, stability, and performance under the attack of a given CPS. The metrics provide reference points to evaluate whether the system is better prepared or not to face the adversaries. This way, it is possible to quantify the ability to recover from an adversary using its mathematical model based on actuators saturation. Finally, we validate our approach using a numeric simulation on the Tennessee Eastman control challenge problem.

The limited output of various drives means a challenge in controller design whenever the acceleration need of the "nominal trajectory to be tracked" temporarily exceeds the abilities of the saturated control system. The prevailing control design methods can tackle this problem either in a single theoretical step or in two consecutive steps. In this latter case in the first step the design happens without taking into account the actuator constraints, then apply a saturation compensator if the phenomenon of windup is observed. In the Fixed Point Iteration- based Adaptive Control (FPIAC) that has been developed as an alternative of the Lyapunov function-based approach the actuator saturation causes problems in its both elementary levels: in the kinematic/kinetic level where the desired acceleration is calculated, and in the iterative process that compensates the effects of modeling errors of the dynamic system under control and that of the external disturbances. The here presented approach tackles this problem in both levels by relatively simple considerations. To illustrate the method's efficiency simulation investigations were done in the FPIAC control of a modification of the van der Pol oscillator to which an additional strongly nonlinear term was added.

For LTI control systems, we provide mathematical tools - in terms of Linear Matrix Inequalities - for computing outer ellipsoidal bounds on the reachable sets that attacks can induce in the system when they are subject to the physical limits of the actuators. Next, for a given set of dangerous states, states that (if reached) compromise the integrity or safe operation of the system, we provide tools for designing new artificial limits on the actuators (smaller than their physical bounds) such that the new ellipsoidal bounds (and thus the new reachable sets) are as large as possible (in terms of volume) while guaranteeing that the dangerous states are not reachable. This guarantees that the new bounds cut as little as possible from the original reachable set to minimize the loss of system performance. Computer simulations using a platoon of vehicles are presented to illustrate the performance of our tools.