Computationally Efficient Safe Control of Linear Systems under Severe Sensor Attacks

TL;DR

This work tackles safety-critical control of linear systems under severe sensor attacks, where full secure state reconstruction (SSR) is computationally prohibitive for real-time use. It shifts from a two-stage SSR-plus-safety-filter approach to a data-driven, safety-first method that directly bounds the control barrier function (CBF) condition using past input-output data, enabling online Safe control without exact state recovery. To handle severe attacks, the authors extend a generalized eigenspace decomposition-based SSR to the q-eigenvalue observable setting, proposing threshold-voting schemes and providing guarantees under certain observability conditions while highlighting computational bottlenecks. They then introduce a computationally efficient upper-bound strategy for M(Y), yielding a conservative but fast CBF constraint that can be enforced via a quadratic program, and they demonstrate trade-offs between conservatism and optimality through simulations and discuss attacker strategies and potential improvements.

Abstract

Cyber-physical systems are prone to sensor attacks that can compromise safety. A common approach to synthesizing controllers robust to sensor attacks is secure state reconstruction (SSR) -- but this is computationally expensive, hindering real-time control. In this paper, we take a safety-critical perspective on mitigating severe sensor attacks, leading to a computationally efficient solution. Namely, we design feedback controllers that ensure system safety by directly computing control actions from past input-output data. Instead of fully solving the SSR problem, we use conservative bounds on a control barrier function (CBF) condition, which we obtain by extending the recent eigendecomposition-based SSR approach to severe sensor attack settings. Additionally, we present an extended approach that solves a smaller-scale subproblem of the SSR problem, taking on some computational burden to mitigate the conservatism in the main approach. Numerical comparisons confirm that the traditional SSR approaches suffer from combinatorial issues, while our approach achieves safety guarantees with greater computational efficiency.

Figures (3)

• Figure 1: Comparison of execution times of different algorithms. Each datapoint corresponds to an average of $100$ runs. Subfigure (a): fixed number of attacks $s$, eigenvalue observability index $q$, and a varying number of total sensors $p$. Subfigure (b): fixed number of sensors $p$, attacks $s$, the eigenvalue observability index $q$, and a varying Varying number of eigenspaces $r$.
• Figure 2: Comparison of the closed-loop system trajectories. While the nominal input derives the system out of the safety region (within the black box), all three safety filters render the system safe. Notably, the SSR-based approaches have the same safe trajectory, and the trajectory resulting from the computationally efficient approach shows a larger safety buffer.
• Figure 3: Step-wise cost comparison of different approaches along the trajectory under the proposed controller \ref{['eq:conservative_controller']}.

Theorems & Definitions (16)

• Lemma 1
• Definition 1: $k$-sparse observability
• Remark 1
• Lemma 2: tan2024safetyfawzi2014secure
• Definition 2: Eigenvalue observability
• Definition 3
• Lemma 3: Eigenvalue observability and sparse observability,mao2022computational
• Lemma 4: mao2022computational
• Proposition 1
• proof