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At least 163 records · Page 9Linked to original sources
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

SPARC: Spine with Prismatic And Revolute Compliance for Faster Quadrupedal Bounding

Quadruped mammals coordinate sagittal spinal bending with axial extension and compression during dynamic locomotion. Yet most robotic quadrupeds use rigid trunks, passively compliant spines with fixed properties, or actively controlled spines that track prescribed trajectories. Whether actively regulated spinal compliance can support faster dynamic locomotion remains unclear. We present SPARC, a compact 1.26-kg, 3-DoF sagittal-plane spine that combines revolute and prismatic motion with independently tunable task-space stiffness and damping. A floating-base impedance controller renders the desired task-space compliance, and benchtop tests show that the fitted axial stiffness matches commanded values within 1.5%. We integrate SPARC into an 8-DoF quadruped and evaluate it across 97 bounding trials under three spine configurations: impedance-controlled SPARC, the same SPARC module held near a fixed pose using position control, and a lightweight rigid spine. Impedance-controlled SPARC reaches 1.029 m/s, compared with 0.769 m/s for position-controlled SPARC and 0.673 m/s for the rigid spine. Impedance-controlled SPARC reaches higher speeds with larger axial motion and greater mechanical power exchange, while at matched speed it has a higher electrical cost of transport than the rigid spine, revealing an energetic trade-off. Code and hardware are available at: https://github.com/YueWang996/sparc

cs.RO↗
arXiv2026

BESS Siting and Sizing to Mitigate EV Charging-Induced Voltage Violations: A Planning Space Reduction Approach

The rapid growth of electric vehicle (EV) charging can cause persistent voltage violations in distribution networks and increase the need for grid-side voltage support. This paper develops a proactive voltage management framework for planning battery energy storage systems (BESS) to mitigate EV charging-induced voltage violations. Annual EV charging profiles are generated through Monte Carlo simulation using probability distributions derived from real charging events and are incorporated into an annual voltage assessment to identify stressed operating conditions. An optimal expansion planning model then determines installation locations and capacities at minimum investment cost. To improve computational tractability, a planning space reduction (PSR) strategy combines critical period selection to reduce the chronological horizon with candidate bus screening to reduce the BESS siting space. The resulting investment decisions are evaluated through full-year operational validation on the IEEE 33-bus, IEEE 69-bus, and a 240-bus distribution system. Results show that PSR reduces solution time by up to 99.2% while matching the exhaustive benchmark in the 33-bus and 69-bus systems and limiting the objective deviation to 0.55% in the 240-bus system. The optimized BESS deployments eliminate the identified annual voltage violations and further reduce electricity purchase costs and network energy losses under increasing EV penetration.

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arXiv2026

Extragradient methods with complexity guarantees for hierarchical variational inequalities

In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under equilibrium constraints, constrained min-max problems, hierarchical game problems, optimal control under VI constraints, and simple bilevel optimization problems. For this general problem formulation, we establish rates of convergence in terms of suitably constructed gap functions, measuring feasibility gaps and optimality gaps. We present worst-case iteration complexity results on both levels of the variational problem, as well as weak convergence under a geometric weak sharpness condition on the lower level solution set. Our results match and improve the state of the art in terms of their iteration complexity and the generality of the problem formulation.

math.OC↗
arXiv2026

State-space fading memory

The fading-memory (FM) property captures the progressive loss of influence of past inputs on a system's current output and has originally been formalized by Boyd and Chua in an operator-theoretic framework. Despite its importance for systems approximation, reservoir computing, and recurrent neural networks, its connection with state-space notions of nonlinear stability, especially incremental ones, remains understudied. This paper introduces a state-space definition of FM. In state-space, FM can be interpreted as an extension of incremental input-to-output stability ($δ$IOS) that explicitly incorporates a memory kernel upper-bounding the decay of past input differences. It is also closely related to Boyd and Chua's FM definition, with the sole difference of requiring uniform, instead of general, continuity of the memory functional with respect to an input-fading norm. We demonstrate that incremental input-to-state stability ($δ$ISS) implies FM semi-globally for time-invariant systems under an equibounded input assumption. Notably, Boyd and Chua's approximation theorems apply to $δ$ISS state-space models. As a closing application, we show that, under mild assumptions, the state-space model of a current-driven memristive device possesses the FM property.

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arXiv2026

Distributed Sum-of-Squares Programming for Local Stability Analysis of Polynomial PDEs

It has recently been shown that the evolution of a state, described by a Partial Differential Equation (PDE), can be more conveniently represented as the evolution of the state's highest spatial derivative (the ``fundamental state''), which lies in L_2 and has no boundary conditions or continuity constraints. For linear PDEs, this yields a Partial Integral Equation (PIE) parametrized by Partial Integral (PI) operators mapping the fundamental state to the PDE state. In this paper, we show that for polynomial PDEs, the dynamics of the fundamental state can be compactly expressed as a distributed polynomial in the fundamental state, parametrized by a new tensor algebra of PI operators acting on the tensor product of the fundamental state. We further define a sum-of-squares (SOS) parameterization of the distributed polynomial and use this to construct a distributed SOS program, for testing local stability of polynomial PDEs.

eess.SY↗
arXiv2026

Observation-Aligned Two-Stage Domain Decomposition for Physics-Informed Traffic State Estimation with Sparse Fixed Sensors

Traffic state estimation from sparse fixed sensors is challenging because physics-informed neural networks (PINNs) tend to over-smooth sharp transitions admitted by the Lighthill-Whitham--Richards (LWR) model. This study proposes Two-Stage Domain Decomposition Physics-Informed Neural Networks (TSDD-PINN), an observation-aligned framework for LWR-based offline speed-field reconstruction. The framework supports spatial, temporal, and space--time refinement. Matched direction analysis shows that spatial refinement has the lowest mean error and less than half the training time of space--time refinement in the tested setting, while temporal refinement is faster. A global parent PINN is first trained. In the controlled spatial implementation, its residual profile guides a deterministic partition for warm-started child networks. An optional operational safeguard retains Stage~1 when the prespecified screen does not activate. The primary I-24 MOTION evaluation spans five days, five sensor configurations, and ten seeds per configuration, yielding 1{,}500 runs. Controlled TSDD-PINN attains the lowest relative $L_2$ error in 18 of 25 configurations and 14 of 15 sparse-sensing cases, while training 2.4 times faster than the extended PINN (XPINN) baseline under the evaluated implementations and training budgets. Non-neural comparisons show that the advantage over interpolation is concentrated under sparse sensing, whereas dense sensing often favors interpolation. A separate 250-run operational evaluation finds infrequent activation and motivates the Stage-1-preserving safeguard. The residual is treated as an indicator of model difficulty rather than a validated shock detector. The evidence supports a sensing-density-dependent operating range rather than uniform improvement.

cs.LG↗
arXiv2026

Multi-Robot Bearing-based Pose Estimation via Angle Rigidity

This letter proposes a novel distributed pose estimator for multi-robot systems evolving on $\mathrm{SE}(3)$. The robots' positions are estimated in $\mathbb{R}^3$ using angles computed from body-frame bearings, without requiring orientation knowledge. The robots' orientations are then recovered in $\mathrm{SO}(3)$ from the estimated positions, together with bearing and bearing-rate measurements. The estimator accommodates directed sensing topologies and requires only infinitesimal angle rigidity (IAR), thereby relaxing the requirement, common in bearing-based approaches, that every robot acquire at least two bearings. Unlike existing angle-based schemes, the proposed method also estimates the robots' orientations. We prove local uniform exponential stability of the observer, assuming that a subset of robots executes persistently exciting motions. These theoretical results are corroborated through numerical simulations.

cs.RO↗
arXiv2026

Variable-Step Time-Delay Control for Proactive Aperiodic Spacecraft Attitude Control

This paper addresses proactive aperiodic spacecraft attitude control under model uncertainty, environmental disturbances, and actuator degradation. To this end, we develop Variable step Time Delay Control (VTDC), which jointly designs robust feedback control and control-update scheduling rather than treating them as separate components. Inspired by adaptive stepsize regulation in Runge Kutta integration, VTDC structures the local control error to scale with the realized timestep. Using sliding manifold based Time Delay Control, the resulting System Time Delay Error (TDE), which reflects local model and uncertainty variations, is shown to be quadratically bounded by the control interval. This relation yields a closed form feedback law that enlarges or reduces the subsequent interval to regulate the TDE magnitude. The next update time is therefore determined algebraically without continuous trigger monitoring, future state prediction, or iterative search. The resulting variable step closed loop admits bounded timesteps and step ratios, excludes Zeno behavior, and renders the sliding variable uniformly ultimately bounded. Nonlinear spacecraft attitude control simulations demonstrate accurate tracking with low scheduling cost under representative uncertainties and disturbances.

eess.SY↗
arXiv2026

On Global Regulatability of Robot Manipulators by Classical PID

A long-standing open problem in robot manipulator control is whether global regulation can be achieved by classical PID control. This paper provides an answer to this question for classical PID controllers with triple parameters (k_p,k_i,k_d) in R^3. We find and prove that for one-degree-of-freedom manipulators, the classical PID control guarantees global stability and asymptotic regulation under standard structural assumptions, and further derive explicit quantitative design conditions for the PID gains. However, for multi-degree-of-freedom cases, we can construct a robot manipulator satisfying the same structural assumptions for which no choice of PID gains (k_p,k_i,k_d) can achieve global asymptotic regulation. These results provide a fundamental understanding of the abovementioned open problem, revealing both the fundamental capability and intrinsic limitation of the classical PID control for robot manipulator dynamics.

cs.RO↗
arXiv2026

Locating Power System Oscillation Sources by Extracting Interharmonics from Synchrophasor Data

Recent studies have shown that oscillating phasors arise from beating waves caused by interharmonics. This finding has led to an interharmonic-based oscillation source-location method. But waveform data needed for the method are less available than PMU synchrophasor data. This paper investigates whether interharmonics can be extracted directly from phasor data for similar applications. The results show that, for certain oscillation phenomena, phasor data can support interharmonic extraction and oscillation source location. Sensitivity studies have identified the requirements, and a cloud-based software tool is developed for PMU-based source location.

eess.SY↗
arXiv2026

Trajectory-Based Co-Optimization of Arrival Scheduling and Descent Path Design in the Terminal Maneuvering Area

Terminal arrival scheduling and descent procedure design are studied in two largely separate literatures. Scheduling models reduce each aircraft to a travel time and deliver target landing times, and fuel-efficient descent procedures are designed one aircraft at a time with the schedule taken as given, although both decide where an arriving aircraft absorbs delay before final approach. Existing formulations therefore cannot trade a slower, earlier-configuring descent against level track miles, a schedule that is efficient in time can be expensive in fuel, and autonomous or reduced-crew operations will need a single trajectory plan that ground automation and the flight management system both accept. To close this gap, we propose a four-dimensional terminal arrival scheduler that selects each aircraft's lateral path extension, glideslope-capture distance, and flap-deployment trigger speeds in one decision. We evaluate every candidate idle-thrust descent offline with a wind-aware backward plan and a six-degree-of-freedom forward simulation that returns descent time, fuel burn, minimum track length, and stabilized-approach feasibility, and a rolling-horizon scheduler commits one verified descent and one extension per aircraft under wake-separation constraints and observed entry winds. Two Atlanta terminal airspace case studies quantify the benefit. We show that co-optimized continuous descents save about 15\% of fleet fuel below saturation in a free-descent environment and that delayed deceleration saves about 23\%, while on the six published Runway 8L arrival flows the charted altitude floors remove 31\% of the design lattice and reduce the savings to 9--10\% and 20--21\%, respectively. We also find that wind moves single-aircraft descent fuel by 34--81\% yet explains at most 4\% of fleet fuel variance, because aircraft-specific wind effects average out across a scenario.

eess.SY↗
arXiv2026

Preference-Oriented Aggregation of Heterogeneous Distributed Energy Resources for Reserve Dispatch

Aggregating distributed energy resources (DERs) aims to encode their collective flexibility into a single set for efficient grid dispatch. However, existing aggregation methods are overly conservative for heterogeneous DERs due to two main challenges: 1) dimensional heterogeneity, which complicates the combination of flexibilities across different time dimensions, and 2) type heterogeneity, where diverse and irregular DER profiles hinder accurate approximations, resulting in significant flexibility loss. To resolve these challenges, this paper propose a novel preference-oriented aggregation method for reserve dispatch. For dimensional heterogeneity, we extend existing techniques by reformulating the Minkowski sum as a polytope projection problem using a matrix transformation technique. By unifying DERs in a higher-dimensional space and projecting them back into the aggregate feasible region, the proposed technique effectively aggregates dimensionally heterogeneous DERs. For type heterogeneity, we further develop a distributed aggregation-dispatch coordination framework that incorporates reserve dispatch preferences into aggregation. This framework effectively captures the critical, active aggregate flexibility prioritized in optimal reserve dispatch, thereby significantly reducing the flexibility loss when aggregating type-heterogeneous DERs. Numerical tests validate the effectiveness of our method in addressing both heterogeneities and highlight its promising potential for power systems with high reserve requirements.

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arXiv2026

Coupling-Aware Aggregation of Multi-Zone HVAC Loads under Uncertainty: A Two-level Framework

Aggregating building heating, ventilation, and air-conditioning (HVAC) loads unlocks substantial demand-side flexibility for power systems. Yet multi-zone coupling creates intricate interdependencies and uncertainty propagation, complicating the quantification of aggregate flexibility. To address this issue, this paper proposes a coupling-aware two-level aggregation framework. At the building level, tailored Gaussian elimination and coordinate transformation techniques are employed to recast the high-dimensional thermal dynamics as an equivalent lower-dimensional analytical expression. This expression streamlines the subsequent aggregator-level stage by (i) clarifying the propagation of zone-level uncertainties to the building-level interface, (ii) decoupling intra-building multi-zone coupling from inter-building aggregation, and (iii) providing full-dimensional building-level flexibility sets that enable tractable reformulation. At the aggregator level, existing geometric aggregation approaches are generalized by a newly developed matrix-transformation technique. This technique effectively constructs inner approximations between polytopes of different dimensions, producing closed-form images of high-dimensional multi-zone HVAC flexibility in power subspace. The resulting inner approximation is then recast as a customized separatable linear program that efficiently determines the optimal aggregate parameters. Case studies validate the effectiveness of our framework, highlighting its accuracy, reliability, and scalability.

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

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

Traffic Congestion Control for ARZ Model with an Arbitrarily Large Input Delay

This paper addresses the stabilization problem for Aw-Rascle-Zhang (ARZ) traffic model in the presence of an arbitrarily large input delay. The linearized ARZ model is a $2 \times 2$ hyperbolic partial differential equation (PDE) system with proximal reflection, which introduces significant analytical challenges when combined with input delays. To tackle this problem, we propose a backstepping-based boundary controller capable of stabilizing the linearized ARZ model under these conditions. The input delay is modeled as a transport PDE, which reformulates the entire system into a $3 \times 3$ hyperbolic PDE system. A backstepping transformation is designed to map the original system into a stable target system, enabling the design of a delay-compensated controller. A key technical contribution of this work is that for hyperbolic PDEs with delays, we develop a characteristic-region-wise construction for kernel functions subject to two boundary constraints and close the proof via successive approximation. Another contribution is that we utilize the small-gain theorem for input-to-state stability (ISS) of hyperbolic PDEs. Two simulations are provided to illustrate the effectiveness of the proposed delay-compensated controller: one compares it with a controller without compensation, and the other employs real traffic vehicle data to validate its effectiveness.

eess.SY↗
arXiv2026

Taylor-Informed Indirect Adaptive Predictive Control Using Jacobian-Frozen Affine Predictors

This paper develops a Taylor-informed indirect adaptive predictive control framework for nonlinear sampled-data systems using Jacobian-frozen affine predictors. A finite Taylor expansion approximates the sampled nonlinear dynamics, and recursive least squares (RLS) identifies its polynomial coefficients online. At each sampling instant, the Jacobian of the identified map is evaluated at the current operating point and frozen over the prediction horizon, yielding an affine predictor for model predictive control. In contrast to generic nonlinear feature dictionaries, the implemented polynomial dictionary is a forward-Euler/Taylor-structure-informed reduced dictionary. Exact joint-odd symmetry eliminates even-total-degree monomials, whereas additional forward-Euler-informed pruning constitutes a deliberate model reduction. Numerical simulations on an unstable nonlinear benchmark compare different Taylor degrees. The results show that higher-order models improve tracking accuracy as the operating point moves farther from the expansion point while maintaining comparable control effort. The complete MATLAB implementation is publicly available to facilitate reproducibility.

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