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

Wasif H. Syed, Juan E. Machado, Johannes Schiffer

TL;DR

This work addresses active fault-tolerant control for networked cyber-physical systems formed by strictly passive LTI subsystems. It casts post-fault operation as a constrained convex optimization and solves it online using an augmented primal-dual gradient dynamics (Aug-PDGD) that is tightly integrated with the plant through control-by-interconnection (CbI). The design guarantees exponential convergence to the unique KKT-based post-fault equilibrium while enforcing network-wide constraints such as voltage and current bounds, and is validated on a DC microgrid example showing feasible, near pre-fault performance under faults. The framework provides a principled, energy-/cost-aware reconfiguration mechanism with explicit stability guarantees and invites future work on distributed implementations and hardware-in-the-loop validation.

Abstract

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.

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

TL;DR

This work addresses active fault-tolerant control for networked cyber-physical systems formed by strictly passive LTI subsystems. It casts post-fault operation as a constrained convex optimization and solves it online using an augmented primal-dual gradient dynamics (Aug-PDGD) that is tightly integrated with the plant through control-by-interconnection (CbI). The design guarantees exponential convergence to the unique KKT-based post-fault equilibrium while enforcing network-wide constraints such as voltage and current bounds, and is validated on a DC microgrid example showing feasible, near pre-fault performance under faults. The framework provides a principled, energy-/cost-aware reconfiguration mechanism with explicit stability guarantees and invites future work on distributed implementations and hardware-in-the-loop validation.

Abstract

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.
Paper Structure (16 sections, 7 theorems, 159 equations, 2 figures)

This paper contains 16 sections, 7 theorems, 159 equations, 2 figures.

Table of Contents

  1. Introduction
  2. CPS Model
  3. Subsystem dynamics and interconnection rule
  4. Compact model
  5. Problem Statement and Solution Approach
  6. Problem Statement
  7. Solution Approach
  8. Proposed Active Primal-Dual FTC Scheme
  9. Derivation of the Aug-PDGD
  10. Aug-PDBD-based CbI Framework
  11. Conditions for Closed-Loop Stability
  12. Application to DC Microgrids
  13. System Model
  14. Fault Scenario and Numerical Simulations
  15. Conclusions
  16. ...and 1 more sections

Key Result

Lemma 1

Fix $0<\tau_1<2\min_i\{-\text{Re}(\lambda_i(A_\mathrm{p}))\}$. With $A_{\mathrm p}=A+G\Omega E$, there is a unique solution $P_1\succ 0$ to the Lyapunov equation and the plant dynamics eq:CompactModel are strictly shifted-passive with quadratic storage function $S_{\mathrm p}(\tilde{x})= \tfrac{1}{2} \|\tilde{x}\|_{P_1}^2$ and with respect to the input--output pair $(\tilde{u},\tilde{y})$. In par

Figures (2)

  • Figure 1: System overview: (a) DC microgrid partitioned into clusters and (b) bus-type schematic.
  • Figure 2: Closed-loop trajectories of the DC microgrid under the proposed FTC scheme.

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Remark 1
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4