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Impact analysis of hidden faults in nonlinear control systems using output-to-output gain

Ruslan Seifullaev, André Teixeira

TL;DR

The paper tackles the vulnerability of nonlinear networked control systems to hidden faults and attacks by extending the output-to-output gain ($OOG$) concept to nonlinearities that satisfy quadratic constraints. It develops absolute stability conditions using a generalized Yakubovich criterion and provides computationally efficient LMI-based bounds for $OOG$ via dissipativity theory, complemented by frequency-domain tests. A key contribution is showing how stealthy nonlinear sensor attacks can significantly increase $OOG$, even under residual-based detection. The results offer practical tools for assessing and mitigating the impact of hidden faults in nonlinear NCSs, with potential extensions to more complex attack models and time-delay effects.

Abstract

Networked control systems (NCSs) are vulnerable to faults and hidden malfunctions in communication channels that can degrade performance or even destabilize the closed loop. Classical metrics in robust control and fault detection typically treat impact and detectability separately, whereas the output-to-output gain (OOG) provides a unified measure of both. While existing results have been limited to linear systems, this paper extends the OOG framework to nonlinear NCSs with quadratically constrained nonlinearities, considering false-injection attacks that can also manipulate sensor measurements through nonlinear transformations. Specifically, we provide computationally efficient linear matrix inequality conditions and complementary frequency-domain tests that yield explicit upper bounds on the OOG of this class of nonlinear systems. Furthermore, we derive frequency-domain conditions for absolute stability of closed-loop systems, generalizing the Yakubovich quadratic criterion.

Impact analysis of hidden faults in nonlinear control systems using output-to-output gain

TL;DR

The paper tackles the vulnerability of nonlinear networked control systems to hidden faults and attacks by extending the output-to-output gain () concept to nonlinearities that satisfy quadratic constraints. It develops absolute stability conditions using a generalized Yakubovich criterion and provides computationally efficient LMI-based bounds for via dissipativity theory, complemented by frequency-domain tests. A key contribution is showing how stealthy nonlinear sensor attacks can significantly increase , even under residual-based detection. The results offer practical tools for assessing and mitigating the impact of hidden faults in nonlinear NCSs, with potential extensions to more complex attack models and time-delay effects.

Abstract

Networked control systems (NCSs) are vulnerable to faults and hidden malfunctions in communication channels that can degrade performance or even destabilize the closed loop. Classical metrics in robust control and fault detection typically treat impact and detectability separately, whereas the output-to-output gain (OOG) provides a unified measure of both. While existing results have been limited to linear systems, this paper extends the OOG framework to nonlinear NCSs with quadratically constrained nonlinearities, considering false-injection attacks that can also manipulate sensor measurements through nonlinear transformations. Specifically, we provide computationally efficient linear matrix inequality conditions and complementary frequency-domain tests that yield explicit upper bounds on the OOG of this class of nonlinear systems. Furthermore, we derive frequency-domain conditions for absolute stability of closed-loop systems, generalizing the Yakubovich quadratic criterion.

Paper Structure

This paper contains 8 sections, 5 theorems, 50 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Observer-based control and anomaly detector
  4. Problem formulation
  5. Absolute stability analysis
  6. Main result: performance analysis using the output-to-output gain
  7. Numerical Example
  8. Conclusions

Key Result

Theorem 1

Assume that the matrix $G_{\rm m}(s)$ has no poles on the imaginary axis and the closed-loop system sys_lin is minimally stable in the class $\mathfrak{M}_{F_{\rm m}}$. Then it is absolutely stable if the following frequency conditionAn obvious advantage of frequency methods is the conceptual simpli where the Hermitian form $\tilde{F}_{\rm m}$ is the extension of $F_{\rm m}$ obtained as follows:

Figures (5)

  • Figure 1: The closed-loop system
  • Figure 2: Nonlinear and additive attacks
  • Figure 3: The suboptimal injection attack signal that maximizes the output-to-output gain of the sampled-data system \ref{['sys_ex']}, with a sampling step of $t_s=0.1$ and a finite time horizon of $T=15$, for $\varphi(y_{\rm m})=y_{\rm m}$.
  • Figure 4: The corresponding performance and residual output energy for the suboptimal signal $a(t)$ from Figure \ref{['subopt_a']} in the linear case, yielding $OOG=1.79$.
  • Figure 5: The performance and residual output energy for the signal $a(t)$ from Figure \ref{['subopt_a']} in the nonlinear case with $\varphi(y_{\rm m})=x_1-0.5\sin{x_1}x_3$, yielding $OOG=5.4$, which is three times larger than in the linear case.

Theorems & Definitions (23)

  • Example 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4: Anomaly detector
  • Remark 5
  • Definition 1
  • Definition 2
  • Theorem 1: The Yakubovich quadratic criterion
  • Remark 6
  • ...and 13 more