Quantifying model mismatch in a control-relevant manner is fundamental in robust control. A well-known metric for this purpose is the ν -gap, or Vinnicombe metric, which measures the discrepancy between a nominal model and the real system from a closed-loop viewpoint. However, its computation typically requires explicit knowledge of the true system. In this letter, we propose an identification-free, data-driven method to estimate the ν -gap between discrete-time SISO systems directly from input-output experiments. The method is complemented by a data-driven winding-number test, based on Welch-type averaging, to verify a required topological condition for the computation of the metric. Numerical simulations on heavy-duty gas-turbine models and a textbook example show that the proposed estimate closely matches MATLAB 0x00A9 gapmetric, while correctly detecting cases in which the admissibility conditions fail.

We develop a data-driven framework for assessing the resilience of linear time-invariant systems against malicious false-data-injection sensor attacks. Leveraging sparse observability, we propose data-driven resilience metrics and derive necessary and sufficient conditions for two data-availability scenarios. For attack-free data, we show that when a rank condition holds, the resilience level can be computed exactly from the data alone, without prior knowledge of the system parameters. We then extend the analysis to the case where only poisoned data are available and show that the resulting assessment is necessarily conservative. For both scenarios, we provide algorithms for computing the proposed metrics and show that they can be computed in polynomial time under an additional spectral condition. A numerical example illustrates the efficacy and limitations of the proposed framework.

This paper addresses the problem of distributed resilient state estimation and control for linear time-invariant systems in the presence of malicious false data injection sensor attacks and bounded noise. We consider a system operator (defender) capable of deploying cybersecurity measures to counteract malicious sensor compromises. Although such measures enhance resilience against adversarial attacks, they may incur substantial costs; hence, it is crucial to strategically select countermeasures that balance resilience gains and cost efficiency. We first demonstrate that the system's resilience against attacks is maximized through the appropriate implementation of security measures, implying that no attacker can execute undetectable sensor attacks. Building on this analysis, we formulate an optimization problem for optimal security measures under cost constraints, which is NP-hard. We then propose an exact algorithm and derive a polynomial-time approximation algorithm that achieves a constant-factor performance guarantee. Furthermore, we develop a distributed resilient state estimation and control scheme informed by the optimal security measure and establish conditions that guarantee bounded estimation and control errors. Finally, we validate the efficacy of our approach through numerical simulations of a vehicle platooning scenario.

We establish mathematical bounds on the chain, ABCD and immittance matrices of a multiconductor transmission line, based on the Telegrapher’s equation. Closed-form expressions for those matrices are also presented. Existing results that hold on the imaginary axis are extended to the complex plane, without reliance on a diagonalizability assumption that is prevalent in the literature. Therefore, the results remain valid under arbitrary arrangements of the conducting wires, which include electrical faults. The analysis ultimately reveals important system-theoretic implications of the Telegrapher’s equation, which are of general relevance to control, power systems, and signal processing involving multiconductor transmission lines.

This paper proposes a real-time solution method for a variant of the interval load flow problem. In this problem, we seek extremal bus voltages and line currents for radial power distribution systems described by the nonlinear DistFlow equations subject to uncertainties in bus power injections. We show that a single deterministic load flow run can compute all minimum bus voltages. Also, we develop a low-complexity procedure to estimate all maximum bus voltages and maximum line currents with an accuracy guarantee verifiable during actual operations. Despite the need to quantify uncertainties, our procedure requires only a few deterministic load flow runs, leading to a significant speedup over standard methods that require a loop to solve at least one optimization problem for each bus and line. Extensive benchmark case studies demonstrate the practical accuracy and efficiency performance of the proposed method. For example, we can conduct interval load flow analysis for a 10,476-bus system achieving a relative error of less than 10% in about 0.5 seconds.

Active distribution networks facilitating bidirectional power exchange with renewable energy resources are susceptible to cyberattacks due to integration of a diverse array of cyber components. This study introduces a grid-level defense strategy aimed at enhancing attack resiliency based on distribution network planning. Our proposed framework imposes a security requirement into existing planning methodologies, ensuring that voltage deviation from its rated value remains within a tolerable range against dynamically and maliciously injected power at end-user nodes. Unfortunately, the formulated problem in its original form is intractable because it is an infinite-dimensional bi-level optimization problem over a function space. To address this complexity, we develop an equivalent transformation into a tractable form as mixed- integer linear program leveraging linear dynamical system theory and graph theory. Notably, our investigation reveals that the severity of potential attacks hinges solely on the cumulative reactances over the path from the substation to the targeted node, thereby reducing the problem to a finite-dimensional problem. Further, the bi-level optimization problem is reduced to a single-level optimization problem by using a technique utilized in solving the shortest path problem. Through extensive numerical simulations conducted on a 54-node distribution network benchmark, our proposed methodology exhibits a noteworthy 29.3% enhancement in the resiliency, with a mere 2.1% uptick in the economic cost.

We characterize the impact of single-time-step sensor attacks on Kalman filtering and fixed-point optimal smoothing for state estimation in linear time-invariant systems over a finite time window. We introduce a single noiseless, unattacked, full-state (perfect) measurement into the estimation process to reduce the attack's impact on the estimation process and increase the probability of detection under static χ2 tests. In the scalar case, we show that smoothing previous estimates with the perfect measurement to update detection statistics achieves higher attack detectability at the attack time than online Kalman filter-based statistics. Numerical experiments suggest that our findings generalize to multi-dimensional systems.

In grid-connected inverter systems, frequency-domain passivity theory is increasingly employed to analyze grid-inverter interactions and guide inverter control designs. However, due to difficulties in meeting sufficient passivity-based stability conditions at low frequencies, passivity theory often falls short of achieving stable system specifications. This article introduces an extended frequency-domain passivity theory. By incorporating a weighting matrix, an extended stability condition is derived. Compared to conventional passivity-based stability conditions, the proposed theory significantly reduces conservativeness and is more suited for analyzing grid-inverter interactions and guiding inverter control design. Theoretical analyses, numerical examples, and experimental results are provided to validate the effectiveness of the proposed methods.

This article addresses small-signal stability issues for multi-parallel grid-forming converter systems based on a newly developed extended passivity theory. The proposed methods provide streamlined, decentralized stability conditions that cover the full frequency range with reduced conservativeness, serving as theoretical tools and practical guidelines for assessment, cause localization, and mitigation of small-signal instability risks in such systems. Numerical examples and experimental results are provided to verify the effectiveness of the proposed methods.

A resilient state estimation scheme for uniformly observable nonlinear systems, based on a method for local identification of sensor attacks, is presented. The estimation problem is combinatorial in nature, and so many methods require substantial computational and storage resources as the number of sensors increases. To reduce the complexity, the proposed method performs the attack identification with local subsets of the measurements, not with the set of all measurements. A condition for nonlinear attack identification is introduced as a relaxed version of existing redundant observability condition. It is shown that an attack identification can be performed even when the entire state cannot be recovered from the measurements. As a result, although a portion of measurements are compromised, they can be locally identified and excluded from the state estimation, and thus, the true state can be recovered. Simulation results demonstrate the effectiveness of the proposed scheme.