[Paper Review] A Framework for Checkpointing and Recovery of Hierarchical Cyber-Physical Systems

Kaustubh Sridhar, Radoslav Ivanov+7 more|arXiv (Cornell University)|May 17, 2022

Fault Detection and Control Systems4 citations

TL;DR

This paper proposes a checkpointing and roll-forward recovery framework for nonlinear, hierarchical cyber-physical systems (CPS) to ensure resilient state-estimate recovery during sensor anomalies. By introducing three consistency paradigms and efficient roll-forward algorithms, the framework achieves accurate, time-efficient recovery while managing resource tradeoffs, outperforming standard EKFs in simulations of a ground robot under anomalous sensor data.

ABSTRACT

This paper tackles the problem of making complex resource-constrained cyber-physical systems (CPS) resilient to sensor anomalies. In particular, we present a framework for checkpointing and roll-forward recovery of state-estimates in nonlinear, hierarchical CPS with anomalous sensor data. We introduce three checkpointing paradigms for ensuring different levels of checkpointing consistency across the hierarchy. Our framework has algorithms implementing the consistent paradigm to perform accurate recovery in a time-efficient manner while managing the tradeoff with system resources and handling the interplay between diverse anomaly detection systems across the hierarchy. Further in this work, we detail bounds on the recovered state-estimate error, maximum tolerable anomaly duration and the accuracy-resource gap that results from the aforementioned tradeoff. We explore use-cases for our framework and evaluate it on a case study of a simulated ground robot to show that it scales to multiple hierarchies and performs better than an extended Kalman filter (EKF) that does not incorporate a checkpointing procedure during sensor anomalies. We conclude the work with a discussion on extending the proposed framework to distributed systems.

Motivation & Objective

• Address the challenge of sensor anomaly resilience in resource-constrained, nonlinear, hierarchical cyber-physical systems (CPS).
• Enable accurate and efficient state-estimate recovery during sensor anomalies through checkpointing and roll-forward mechanisms.
• Manage the tradeoff between system resource usage (memory, computation) and recovery accuracy in hierarchical CPS.
• Ensure consistency of checkpoints across multiple system layers despite diverse anomaly detection systems (ADS) and dynamic sensor behaviors.
• Provide theoretical bounds on recovery error, maximum tolerable anomaly duration, and the accuracy-resource gap.

Proposed method

• Introduce three checkpointing paradigms—consistent, partially consistent, and inconsistent—offering varying levels of consistency across hierarchical subsystems.
• Design a time-efficient roll-forward algorithm that replays control inputs from a secure checkpoint to reconstruct system states forward in time.
• Integrate anomaly detection systems (ADS) at each subsystem level to trigger recovery only when anomalies are detected.
• Formulate state-estimate error bounds using a recursive error propagation model, with theoretical guarantees via Proposition 5.1 and Corollary 5.2.
• Use a hierarchical control architecture with inner and outer loops, modeling dynamics via nonlinear state-space equations and measurement models with process and measurement noise.
• Apply checkpointing every second (1 Hz) and store control inputs and state snapshots securely to enable roll-forward recovery during anomaly intervals.

Experimental results

Research questions

• RQ1 How can consistent checkpointing be achieved across multiple hierarchical subsystems with heterogeneous anomaly detection systems?
• RQ2 What is the maximum tolerable duration of sensor anomalies for reliable state-estimate recovery under the proposed framework?
• RQ3 How does the framework balance recovery accuracy against system resource usage (memory, computation) in embedded CPS?
• RQ4 What theoretical bounds can be established for the error in recovered state-estimates compared to ground truth?
• RQ5 Can the framework be extended to distributed CPS with bounded communication delays?

Key findings

• The framework successfully recovers state-estimates with significantly lower error than an extended Kalman filter (EKF) during sensor anomalies, as shown in simulation plots of robot position and motor angular velocity.
• Recovered state-estimate error (RSEE) and estimation error (EE) both remain comfortably within theoretical bounds derived from Equation 15 and Proposition 5.1/Corollary 5.2.
• The anomalous EKF estimate error was substantially larger than the RSEE for both x-position and angular velocity, demonstrating the superiority of the checkpointing and roll-forward approach.
• The framework scales effectively to multiple hierarchical levels, as validated in a simulated ground robot with outer-loop and inner-loop control subsystems.
• The maximum tolerable anomaly duration is bounded by the checkpoint interval and the system’s ability to maintain state consistency during roll-forward.
• The accuracy-resource gap—the tradeoff between checkpoint frequency, recovery accuracy, and system resource cost—is formally bounded and analytically quantified in the framework.