Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Collaborative design of fault diagnosis and fault tolerance control under nested signal temporal logic specifications

Penghong Lu, Gang Chen, Rong Su

TL;DR

The paper tackles robust fault diagnosis and fault-tolerant control for nonlinear CPS under nested signal temporal logic specifications. It advances a collaborative framework (CoD) that integrates STLT-based NSTL decoding, fault-detection observers, online monitoring, and CBF-driven MPC with a fault-tolerant recursive feasibility guarantee to ensure NSTL satisfaction despite faults. Key contributions include the STLT encoding for nested specifications, the construction of fault-tolerant feasible sets with a backward-recursion mechanism, and a hierarchical MPC/CBF control architecture that guarantees periodic safety and constraint satisfaction. The approach is validated in simulation on integrator and unicycle models, demonstrating improved fault detection fidelity and sustained STL-compliant performance, with potential impact on safety-critical CPS in transportation, robotics, and automation.

Abstract

Signal Temporal Logic (STL) specifications play a crucial role in defining complex temporal properties and behaviors in safety-critical cyber-physical systems (CPS). However, fault diagnosis (FD) and fault-tolerant control (FTC) for CPS with nonlinear dynamics remain significant challenges, particularly when dealing with nested signal temporal logic (NSTL) specifications. This paper introduces a novel framework for the collaborative design of FD and FTC, aimed at optimizing fault diagnostic performance while ensuring fault tolerance under NSTL specifications. The proposed framework consists of four key steps: (1) construction of the Signal Temporal Logic Tree (STLT), (2) fault detection via the construction of fault-tolerant feasible sets, (3) evaluation of fault detection performance, and (4) synthesis of fault-tolerant control. Initially, a controller for nonlinear systems is designed to satisfy NSTL specifications, and a fault detection observer is developed alongside fault-tolerant feasible sets. To address the challenge of maintaining solution feasibility in dynamic optimization control problems, the concept of fault-tolerant control recursive feasibility is introduced. Subsequently, suboptimal controller gains are derived through a quadratic programming approach to ensure fault tolerance. The collaborative design framework enables more rapid and accurate fault detection while preserving FTC performance. A simulation study is presented to demonstrate the effectiveness of the proposed framework.

Collaborative design of fault diagnosis and fault tolerance control under nested signal temporal logic specifications

TL;DR

The paper tackles robust fault diagnosis and fault-tolerant control for nonlinear CPS under nested signal temporal logic specifications. It advances a collaborative framework (CoD) that integrates STLT-based NSTL decoding, fault-detection observers, online monitoring, and CBF-driven MPC with a fault-tolerant recursive feasibility guarantee to ensure NSTL satisfaction despite faults. Key contributions include the STLT encoding for nested specifications, the construction of fault-tolerant feasible sets with a backward-recursion mechanism, and a hierarchical MPC/CBF control architecture that guarantees periodic safety and constraint satisfaction. The approach is validated in simulation on integrator and unicycle models, demonstrating improved fault detection fidelity and sustained STL-compliant performance, with potential impact on safety-critical CPS in transportation, robotics, and automation.

Abstract

Signal Temporal Logic (STL) specifications play a crucial role in defining complex temporal properties and behaviors in safety-critical cyber-physical systems (CPS). However, fault diagnosis (FD) and fault-tolerant control (FTC) for CPS with nonlinear dynamics remain significant challenges, particularly when dealing with nested signal temporal logic (NSTL) specifications. This paper introduces a novel framework for the collaborative design of FD and FTC, aimed at optimizing fault diagnostic performance while ensuring fault tolerance under NSTL specifications. The proposed framework consists of four key steps: (1) construction of the Signal Temporal Logic Tree (STLT), (2) fault detection via the construction of fault-tolerant feasible sets, (3) evaluation of fault detection performance, and (4) synthesis of fault-tolerant control. Initially, a controller for nonlinear systems is designed to satisfy NSTL specifications, and a fault detection observer is developed alongside fault-tolerant feasible sets. To address the challenge of maintaining solution feasibility in dynamic optimization control problems, the concept of fault-tolerant control recursive feasibility is introduced. Subsequently, suboptimal controller gains are derived through a quadratic programming approach to ensure fault tolerance. The collaborative design framework enables more rapid and accurate fault detection while preserving FTC performance. A simulation study is presented to demonstrate the effectiveness of the proposed framework.

Paper Structure

This paper contains 20 sections, 8 theorems, 59 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem statement and preliminary
  3. Systems dynamics
  4. Signal temporal logic
  5. Reachability operators
  6. Nested STL formula and STLT
  7. Collaborative design of FD and FTC
  8. Fault detection observer with fault tolerant feasible sets
  9. Online monitoring
  10. CBF time interval encoding
  11. Model predictive control synthesis with CBF
  12. High-level reference planning
  13. Low-level control synthesis
  14. Closed-loop straint properties
  15. MPC recursive feasibility and closed-Loop constraint satisfaction
  16. ...and 5 more sections

Key Result

Lemma 1

Consider the system (x0) and predicates $\mu_1,$ and $\mu_2$. Then, one has chen2018signal where $\mathbb{S}_{\mu_1 \mathsf{U}_{[a, b]} \mu_2}, \mathbb{S}_{\mathsf{F}_{[a, b]}\mu_1}$ and $\mathbb{S}_{\mathsf{G}_{[a, b]}\mu_1}$ are the satisfying sets for $\mu_1 \mathsf{U}_{[a, b]} \mu_2$, $\mathsf{F}_{[a, b]}\mu_1$ and $\mathsf{G}_{[a, b]}\mu_1$, respectively.

Figures (6)

  • Figure 1: The STLT for the nested STL formula $\varphi=\mathsf{G}_{[0, 16]}\mathsf{F}_{[2, 10]}\mu_1 \vee \mathsf{F}_{[0, 14]}( \mu_2 \mathsf{U}_{[5, 10]}\mu_3)$, where $\mu_i, i=\{1,2,3\}$ are predicates.
  • Figure 2: Framework of cooperative design of FD and FTC .
  • Figure 3: Two trajectories for the single integrator dynamics system. The yellow, blue, and gray regions denote the target regions $S_{\mu_1}$, $S_{\mu_2}$, and $S_{\mu_3}$, respectively, while the light yellow, light blue, and light gray regions represent their corresponding fault-tolerant feasible sets $X'_{t_k}$. The red circle marks a state $x_{t_k} \notin X'_{t_k}$, indicating that the monitor can predict task failure in advance.
  • Figure 4: Two trajectories of a mobile robot with single integrator dynamics are synthesized using the proposed method under the STL specification $\varphi=\mathsf{G}_{[0, 16]}\mathsf{F}_{[2, 10]}\mu_1 \vee \mathsf{F}_{[10, 14]}( \mu_2 \mathsf{U}_{[5, 10]}\mu_3)$. The yellow, blue, and gray regions denote the target regions $S_{\mu_1}$, $S_{\mu_2}$, and $S_{\mu_3}$.
  • Figure 5: Two trajectories for the unicycle dynamics system. The yellow, blue, and gray regions denote the target regions $S_{\mu_1}$, $S_{\mu_2}$, and $S_{\mu_3}$, respectively, while the light yellow, light blue, and light gray regions represent their corresponding fault-tolerant feasible sets $X'_{t_k}$. The red circle marks a state $x_{t_k} \notin X'_{t_k}$, indicating that the monitor can predict task failure in advance.
  • ...and 1 more figures

Theorems & Definitions (32)

  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 1
  • Definition 4: STLT 8
  • Definition 5
  • Definition 6
  • Example
  • Definition 7
  • Definition 8: Potential index set 10
  • ...and 22 more