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.

💡 Research Summary

The paper addresses active fault‑tolerant control (FTC) for cyber‑physical systems (CPS) composed of strictly passive linear‑time‑invariant (LTI) subsystems whose interconnections are power‑preserving. Under these structural assumptions each subsystem is internally stable and the overall plant Σₚ is “shifted‑passive,” which enables the construction of a quadratic storage function via a Lyapunov equation. When a fault occurs at time t_f, the affected subsystem’s dynamics are re‑parameterized, possibly causing steady‑state, output, or constraint violations. The authors formulate the post‑fault operating point as the solution of a convex optimization problem that minimizes a cost J(·) (typically a strongly convex, smooth quadratic) subject to linear equality constraints (steady‑state power flow) and affine inequality constraints (state, output, and input limits).

To solve this problem in real time, they derive a continuous‑time augmented primal‑dual gradient dynamics (Aug‑PDGD). The decision vector ξ̄ =