A Primal-Dual-Based Active Fault-Tolerant Control Scheme for Cyber-Physical Systems: Application to DC Microgrids

We consider the problem of active fault-tolerant control in cyber-physical systems composed of strictly passive linear-time invariant dynamic subsystems. We cast the problem as a constrained optimization problem and propose an augmented primal-dual gradient dynamics-based fault-tolerant control framework that enforces network-level constraints and provides optimality guarantees for the post-fault steady-state operation. By suitably interconnecting the primal-dual algorithm with the cyber-physical dynamics, we provide sufficient conditions under which the resulting closed-loop system possesses a unique and exponentially stable equilibrium point that satisfies the Karush--Kuhn--Tucker (KKT) conditions of the constrained problem. The framework's effectiveness is illustrated through numerical experiments on a DC microgrid.