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Communication-Aware Synthesis of Safety Controller for Networked Control Systems

Yihan Liu, Meiqi Tian, teng Yan, Bingzhuo Zhong

Abstract

Networked control systems (NCS) are widely used in safety-critical applications, but they are often analyzed under the assumption of ideal communication channels. This work focuses on the synthesis of safety controllers for discrete-time linear systems affected by unknown disturbances operating in imperfect communication channels. The proposed method guarantees safety by constructing ellipsoidal robust safety invariant (RSI) sets and verifying their invariance through linear matrix inequalities (LMI), which are formulated and solved as semi-definite programming (SDP). In particular, our framework simultaneously considers controller synthesis and communication errors without requiring explicit modeling of the communication channel. A case study on cruise control problem demonstrates that the proposed controller ensures safety in the presence of unexpected disturbances and multiple communication imperfections simultaneously.

Communication-Aware Synthesis of Safety Controller for Networked Control Systems

Abstract

Networked control systems (NCS) are widely used in safety-critical applications, but they are often analyzed under the assumption of ideal communication channels. This work focuses on the synthesis of safety controllers for discrete-time linear systems affected by unknown disturbances operating in imperfect communication channels. The proposed method guarantees safety by constructing ellipsoidal robust safety invariant (RSI) sets and verifying their invariance through linear matrix inequalities (LMI), which are formulated and solved as semi-definite programming (SDP). In particular, our framework simultaneously considers controller synthesis and communication errors without requiring explicit modeling of the communication channel. A case study on cruise control problem demonstrates that the proposed controller ensures safety in the presence of unexpected disturbances and multiple communication imperfections simultaneously.

Paper Structure

This paper contains 14 sections, 6 theorems, 43 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. System Model
  5. Problem Statement
  6. Communication Error bound analysis
  7. Uplink Communication Error Bound
  8. System State Error Bound
  9. Safety Controllers for Communication-Aware Systems
  10. $(\gamma,\varepsilon)$-Robust Safety Invariant Set
  11. LMI-Based Controller Synthesis
  12. Case Study
  13. Conclusion
  14. Proof of Theorems

Key Result

Theorem 1

Li2016 Considering the Kalman filter as in Definition def:definition3, the error covariance $P_k$ has an upper bound where $p_k$ is recursively defined as with $\bar{g} \in \mathbb{R}$ satisfying $G G^\top \preceq \bar{g}^2 I_n$, $\bar{q} \in \mathbb{R}$ satisfying $Q\preceq \bar{q} I_n$, and $P_0 \in \mathbb{R}^{n \times n}$ denoting the initial estimation error covariance.

Figures (4)

  • Figure 1: Overall Architecture of the Communication-aware Control System
  • Figure 2: Cruise control for a truck-trailer system. The coupling between truck and trailer is modeled as a spring-damper mechanism with stiffness $k_s = 4500$ N/kg and damping coefficient $k_d = 4600$ Ns/m. The mass of trailer is set to $m = 1000$ kg, and $d$ represents the distance between the truck and the trailer.
  • Figure 3: State trajectories of the system evolving within the $(\gamma,\varepsilon)$-RSI set under communication constraints
  • Figure 4: Control inputs $u_k$ applied to the system

Theorems & Definitions (18)

  • Remark 1
  • Definition 1
  • Theorem 1
  • Remark 2
  • Definition 2
  • Theorem 2
  • Remark 3
  • Remark 4
  • Theorem 3
  • Definition 3
  • ...and 8 more