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arXiv2026

Minimal Construction of Graphs with Maximum Robustness

The notions of $r$-robustness and $(r,s)$-robustness of a network have been earlier introduced in the literature to achieve resilient consensus in the presence of misbehaving agents. However, while higher robustness levels enable networks to tolerate a higher number of misbehaving agents, they also require dense communication structures, which are not always desirable for systems with limited communication ranges, energy, and resources. Therefore, this paper studies the fundamental structures behind $r$-robustness and $(r,s)$- robustness properties in two ways. (a) We first establish tight necessary conditions on the number of edges that an undirected graph with an arbitrary number of nodes must have to achieve maximum $r$- and $(r,s)$-robustness. (b) We then use these conditions to construct two classes of undirected graphs, referred to as $γ$- and $(γ,γ)$-Minimal Edge Robust Graphs (MERGs), that provably achieve maximum robustness with minimal numbers of edges. We demonstrate the effectiveness of our method via comparison against existing robust graph structures and a set of simulations.

eess.SY↗

arXiv2026

Risk-Aware Optimal Control with Rulebooks

We consider safety-critical control problems involving multiple requirements with different priorities and uncertainty in their evaluation. We represent these requirements using risk-aware rulebooks, where each requirement is assigned a risk measure and an acceptable threshold, and a priority relation is defined among the requirements. Each requirement induces a risk-evaluation function that maps a policy to the risk associated with its violation. We formulate risk-aware optimal control with rulebooks as a lexicographic optimization problem over excess risks and develop an anytime filtering and branch-and-bound algorithm that progressively tightens the certified optimality gap while characterizing the corresponding set of policies at each priority level. The algorithm returns a policy together with these gaps, which bound its suboptimality. We prove that these gaps are valid for any finite computational budget and, under additional assumptions, converge to zero as the computational budget increases. We evaluate the algorithm on a synthetic benchmark with a known optimum and a realistic highway-merging simulation with CVaR-based collision, rear-braking, headway, and comfort rules.

eess.SY↗

arXiv2026

Integrated Transmission and Distribution Expansion Planning Considering Customer Actions and Distributed Energy Resources

The continued integration of distributed energy resources (DERs) motivates research into integrated system planning. While existing literature shows that DERs can reduce system costs, it often overlooks customer behaviour, particularly DER adoption driven by cost savings and incentives. System cost allocation can influence these decisions, affecting DER uptake, grid injections, and overall system efficiency. Therefore, integrated system planning should consider both system- and customer-level benefits of DERs. This paper proposes a multi-step framework that combines an integrated planning model with cost allocation and retailer business models. The integrated planning model minimizes total system costs subject to network constraints, while the cost allocation and retailer models capture customer responses to costs and DER opportunities. By coordinating these models, the framework represents how customer behaviour influences planning outcomes. The proposed approach is demonstrated on a 36-bus system, with results showing that incorporating customer decision-making reduces overall system costs, lowers reliance on transmission-connected generation, and supports more realistic system planning.

eess.SY↗

arXiv2026

Control of Decommissioned Satellites and Space Debris Using CubeSats with Ion Electrospray Engines

The emergence of the New Space era has led to a rapidly increasing number of satellites in Low Earth Orbit (LEO). Consequently, more stringent deorbiting requirements have recently been imposed to avoid the Kessler syndrome in LEO. This has resulted in the proposal of new concepts for space debris removal, including attaching CubeSats to space debris as a promising mitigation strategy. The initial phase of this strategy involves stabilizing and controlling the debris' attitude. This paper proposes an attitude control design for decommissioned satellites using attached CubeSats with staged ion electrospray engines (iESE). The compact design of iESE combined with staging provides increased reliability and mission durations. The large uncertainty in the dynamics of the combined system, i.e. satellite and attached CubeSats, poses a significant challenge to the control design. The approach taken here uses the robust control framework, specifically $μ$-synthesis, to tackle this challenge. The feasibility of the approach is demonstrated on a decommissioned satellite with multiple flexile appendages.

eess.SY↗

arXiv2025

Intelligent Road Anomaly Detection with Real-time Notification System for Enhanced Road Safety

This study aims to improve transportation safety, especially traffic safety. Road damage anomalies such as potholes and cracks have emerged as a significant and recurring cause for accidents. To tackle this problem and improve road safety, a comprehensive system has been developed to detect potholes, cracks (e.g. alligator, transverse, longitudinal), classify their sizes, and transmit this data to the cloud for appropriate action by authorities. The system also broadcasts warning signals to nearby vehicles warning them if a severe anomaly is detected on the road. Moreover, the system can count road anomalies in real-time. It is emulated through the utilization of Raspberry Pi, a camera module, deep learning model, laptop, and cloud service. Deploying this innovative solution aims to proactively enhance road safety by notifying relevant authorities and drivers about the presence of potholes and cracks to take actions, thereby mitigating potential accidents arising from this prevalent road hazard leading to safer road conditions for the whole community.

cs.CV↗

arXiv2026

Structural Compatibility and Uniform Stability of Temporally Degenerate Parabolic Systems

Modern feedback design for distributed parameter systems presupposes that the closed-loop dynamics define a well-posed evolution problem. This presupposition becomes nontrivial for temporally degenerate parabolic systems, where temporal degeneracy affects not only the analytical properties of the evolution equation but also the mathematical formulation of the feedback interconnection itself. It is shown that admissible feedback interconnections for temporally degenerate parabolic systems are completely characterized by an operator compatibility condition linking the singular reaction operator with the actuator and observation operators. This characterization removes the singular component of the closed-loop dynamics and reduces the degenerate evolution equation to a regular evolution equation. Building upon this regularized formulation, a critical--residual decomposition yields a uniform exponential stability certificate, which is subsequently extended to the original infinite-dimensional evolution through a finite-to-infinite lifting theorem. A constructive static output feedback synthesis is finally obtained as a consequence of these results. Numerical experiments illustrate the regularization mechanism, validate the stability certificate, and confirm the finite-to-infinite lifting.

math.OC↗

arXiv2026

Learning-based Adaptive Safety-Critical Control With Evolving Unsafe Regions

Control barrier functions (CBFs) provide a principled framework for safety-critical control, but their construction typically requires an explicit and differentiable description of the safe or unsafe region. It becomes challenging for data-defined unsafe regions that may evolve over time. This paper proposes SafeLink, a data-driven CBF construction and adaptation method based on a cost-sensitive random vector functional link (RVFL) network. SafeLink introduces asymmetric misclassification costs to promote conservative unsafe-region representation while preserving a closed-form solution. We establish the Lipschitz continuity of the learned CBF and its derivatives, and derive sufficient conditions for conservative unsafe-region coverage and the corresponding interval-wise safety guarantees. Analytical updates are further developed for adjusting the misclassification cost and for incrementally adding or decrementally removing samples, avoiding full retraining when the unsafe region changes. Experiments on a two-link manipulator demonstrate that SafeLink rapidly adapts to evolving unsafe regions, enables collision-free target reaching, and achieves substantially lower update runtimes than baselines.

cs.RO↗

arXiv2026

AI-Powered CPS-Enabled Vulnerable-User-Aware Urban Transportation Digital Twin: Methods and Applications

We present methods and applications for the development of digital twins (DT) for urban traffic management. While the majority of studies on the DT focus on its ``eyes," which is the emerging sensing and perception like object detection and tracking, what really distinguishes the DT from a traditional simulator lies in its ``brain," the prediction and decision making capabilities of extracting patterns and making informed decisions from what has been seen and perceived. In order to add value to urban transportation management, DTs need to be powered by artificial intelligence and complement with low-latency high-bandwidth sensing and networking technologies, in other words, cyberphysical systems. This paper can be a pointer to help researchers and practitioners identify challenges and opportunities for the development of DTs; a bridge to initiate conversations across disciplines; and a road map to exploiting potentials of DTs for diverse urban transportation applications.

eess.SY↗

arXiv2026

Risk and Anomaly Identification for Distribution Network Optimal Operation Based on Reinforcement Learning and Uncertainty Quantification

Reliable operation of modern distribution networks requires timely identification of operational risks and anomalous events under pervasive uncertainty. In practice, operators must identify risks that are inherent in stochastic yet in-distribution conditions, and anomalies that correspond to out-of-distribution behaviors such as unusual load patterns, extreme weather or cyber-physical attacks. This paper addresses this joint risk and anomaly identification problem for optimal distribution network operation and proposes a deep reinforcement learning framework that is explicitly uncertainty aware. We integrate distributional and Bayesian deep reinforcement learning to realize a second- order uncertainty quantification scheme that decomposes total uncertainty into aleatoric and epistemic components, which are respectively used to characterize inherent risk and out-of- distribution anomalies. The resulting epistemic estimates drive both exploration during training and out-of-distribution detec- tion with fallback control during deployment, whereas aleatoric estimates are used to characterize intrinsic operational risk. Simulation results demonstrate the performance of our DRL agent and the effectiveness of the uncertainty quantification.

cs.LG↗

arXiv2026

A Constraint-Aware Generative Framework for Synthetic Origin-Destination Demand in Logistics Networks

Large-scale logistics networks require synthetic data generation capabilities to support scenario-based planning under novel conditions-such as network reconfiguration and demand shocks. Existing approaches, which rely primarily on historical observations, lack the ability to generate demand patterns that adapt to changes in network topology while respecting operational constraints. We propose a constraint-aware conditional generative framework for synthetic origin-destination demand generation in hierarchical logistics networks. The framework models demand as a conditional distribution over destinations given each origin, enabling topology-aware synthesis that is both topologically realistic and operationally feasible. Operational guidance is incorporated directly into the generative objective via differentiable constraints, while a flexible conditioning mechanism supports various operational contexts and adaptation to evolving network configurations. We instantiate the proposed framework based on a conditional generative model. Experimental validation on industrial real fulfillment and transportation network demonstrates 16% improvement over graph neural network baselines, 87% operational compliance, and efficient cold-start adaptation, enabling applications in capacity planning, network design evaluation, and routing optimization.

eess.SY↗

arXiv2026

Biased Backpressure Routing for Multihop Wireless Networks with Heterogeneous Interfaces

Heterogeneous-interface multihop wireless networks (Het-MuNets) are emerging as a promising paradigm for tactical networks and for infrastructure-light applications such as vehicular communications, wireless backhaul, and non-terrestrial connectivity. To exploit the diverse profiles of heterogeneous communication technologies in penetration, interference, and bandwidth, packet-to-interface assignment must be determined on a per-hop basis, making routing and scheduling highly complex. In this work, we develop a unified framework for joint packet routing, link scheduling, and interface assignment in Het-MuNets with multiple concurrent flows. By modeling packet-to-interface assignment as transmission between virtual subnodes, we transform interface assignment into intra-device virtual routing, which is solved jointly with physical routing and scheduling under a unified multi-layer shortest path-biased Backpressure (SP-BP) scheme. Numerical results demonstrate that the proposed framework outperforms SP-BP operating on other baseline graph models and non-backpressure routing schemes in goodput, latency, and packet delivery rate.

cs.NI↗

arXiv2026

Observability Analysis for Fusion of Doppler Measurements in Multistatic Radar Near the Tx-Rx Baseline

This paper studies multistatic measurement fusion when a target lies within the Tx--Rx (Transmitter-Receiver) baseline ambiguity zone, with particular emphasis on configurations involving two closely spaced stationary Tx--Rx pairs. Such configurations provide overlapping detectable regions and extend the effective detection range compared with sparsely spaced multistatic systems. However, in this region, the accuracy of range and bearing measurements degrades rapidly, and Doppler measurements often remain the only reliable information source. As a result, target trajectory estimation becomes highly challenging, with observability being marginal or even completely lost. To address this problem, the observability of target trajectories is analyzed under various conditions, enabling system designers to assess system performance in advance. A Doppler-only measurement fusion approach is then developed, employing a multiple-initial-point Maximum Likelihood (ML) nonlinear estimator for initial state estimation, followed by dynamic state updates using an Extended Kalman Filter (EKF). Simulation results are presented and shown to be consistent with the observability analysis.

eess.SY↗

arXiv2026

Importance and methods to control, vary, and characterize mud strength for studying locomotion

Animals and robots encounter mud at the water-land interface. Like sand, mud can stay solid or flow like a fluid. Unlike sand, the yield strength of mud at which solid-fluid transitions occur depends on not only the amount of solid relative to fluid (water in mud, air in dry sand), but also how much coarse grains and fine clay are within the solid. Despite understanding of locomotion on/within dry sand dominated by coarse grains with repulsive normal forces and friction, little is known for mud dominated by fine clay with strong cohesion. Here, we developed methods to prepare uniform mud of controlled, variable yield strength and characterize and track its drift from water evaporation. Compared to other flowable substrates, mud strength measured by upward force during penetration is weaker and can vary more, and mud sticks more during extraction to pull downward, making it more challenging for locomotion.

physics.bio-ph↗

arXiv2026

On the Degree of Safety: Beyond Safe or Unsafe with Control Barrier Functions

A valid control barrier function (CBF) certifies if its represented safe set can be rendered forward invariant, and the sign of its value indicates whether a state is safe or not, but it does not quantify a degree of safety beyond the binary indication. In this paper, we show that among valid CBFs representing the same safe set, interior values and gradients can be changed arbitrarily, so neither quantity determines a degree of safety that is independent of how the set is represented. We also show that whether a candidate CBF-based inequality constraint is feasible does not by itself quantify a degree of safety. In particular, infeasibility can occur either because the safe set is not controlled invariant or because the candidate CBF representation fails. This motivates our distinction between intrinsic and representational infeasibility. Finally, we introduce the invariance authority demand (IAD), a representation-independent degree of safety that quantifies the control authority required for controlled invariance and can be used to guide set or actuator repair.

eess.SY↗

arXiv2026

Context-Enriched Performance Boosting via Operator Decomposition

Performance Boosting (PB) is a control framework that, for a pre-stabilized system subject to $\mathcal L_p$ process disturbances, parametrizes the controllers that preserve closed-loop $\mathcal L_p$-stability through a causal $\mathcal L_p$-stable operator mapping reconstructed disturbances to corrective control actions. Although this permits optimization over expressive stability-preserving controllers, learning a desired policy from disturbance information alone can be difficult. We introduce a structured factorization for context-enriched, multi-input PB operators. The proposed architecture combines an $\mathcal L_p$-stable dynamical module that processes reconstructed disturbances with a uniformly bounded matrix-valued mixer depending on disturbances and contextual signals. Under the standard PB assumptions, this factorization preserves closed-loop $\mathcal L_p$-stability by construction. Moreover, on a weighted-envelope disturbance domain, we prove that the factorization is necessary and sufficient for causal operators satisfying a context-uniform envelope-preservation property. A numerical moving-gate navigation experiment demonstrates the advantages of the proposed architecture over context-agnostic PB, MAD, and reference-aware PB baselines.

eess.SY↗

arXiv2026

D-RADI: A Low-rank ADI Algorithm for Solving Large-scale Discrete-time Algebraic Riccati Equations

The low-rank alternating direction implicit (ADI) method is an efficient numerical technique for solving several types of large-scale matrix equations that admit low-rank solutions. The discrete-time algebraic Riccati equation (DARE) is an important matrix equation with applications in state estimation, controller design, and filter design. In the literature, the low-rank Cholesky factor ADI method for Stein equations has been used within Newton iterations to solve large-scale DAREs. However, no dedicated low-rank ADI solver is available for such DAREs. To address this gap, this paper presents a low-rank ADI solver for large-scale DAREs. We also propose an efficient approach to generate ADI shifts automatically, which makes the proposed solver fully autonomous for solving DAREs. The effectiveness of the proposed solver is compared with MATLAB's \texttt{idare} on a moderate-order problem. Efficiency and accuracy are further demonstrated on large-scale DAREs of order $10^6$. Numerical results confirm that the solver is efficient, accurate, and fully autonomous.

math.NA↗

arXiv2026

Proof of a Conjecture of De Cock and De Moor

De Cock and De Moor proposed a conjecture connecting two seemingly different viewpoints in stochastic subspace identification, one based on Lyapunov equations and the other on principal angles and canonical correlations. The conjecture was recorded as Problem 9.1 of \emph{Unsolved Problems in Mathematical Systems and Control Theory}. We give a direct finite-dimensional proof under the natural nonresonance condition, without requiring stability or diagonalizability. The key mechanism is the rank-one perturbation, which exposes a hidden Cauchy-matrix structure and reduces the problem to rational interpolation. A density and continuity argument then removes the generic spectral assumptions. The result strengthens the original statement. The eigenvalues agree with algebraic multiplicity, a nonsingularity assumption of the original formulation becomes automatic, and on a dense open set of parameters the two matrices are similar rather than merely cospectral. While this manuscript was being prepared, Gillberg and Löfberg independently posted a proof based on a Lyapunov-kernel identity and the classical $AB$--$BA$ principle. The proof given here was developed independently and follows a different route.

math.OC↗

arXiv2026

Multi-Domain Graph-Based Modeling of Energy Systems with Applications to Lithium-Ion Batteries

Graph-based models have been shown to provide a structured representation for complex multi-domain energy systems but face limitations when edge power flows depend on non-adjacent states or when a single edge carries multiple power-flow types driven by different inputs. This paper proposes two general extensions to address these limitations: a recursive state-to-input feedback scheme that embeds non-adjacent state dependencies into edge inputs without altering the graph structure, and a parallel edge decomposition method that represents composite interactions using sets of single-input edges while preserving energy conservation at the vertices. The extended framework is demonstrated on a lithium-ion battery module consisting of 36 parallel cells, and the resulting model predicts module temperatures with errors below 1°C. Validation on this electro-thermal battery system demonstrates the effectiveness of the extended framework for multi-domain systems that cannot be represented by previously established graph-based formulations, and indicates its potential for broader application to complex energy systems in control and design studies.

eess.SY↗