Papers

We develop a structure-specific fidelity-threshold robustness margin for finite-dimensional closed quantum systems under piecewise-constant coherent control. A scalar physical parameter may perturb the drift, a control Hamiltonian, or another declared Hamiltonian component across the control horizon. A differential sensitivity bound for trace-amplitude gate fidelity yields a threshold-dependent Lipschitz constant on the connected safe parameter component and hence a certified finite perturbation radius. Recentering this certificate produces an iterative one-dimensional method that takes certified safe steps toward the first fidelity-threshold boundary in either parameter direction. A three-qubit gate-control example shows that these finite margins vary by up to a factor of three across controllers of comparable nominal fidelity and contain structure-dependent information not captured by nominal differential sensitivity alone.

Supportive continuum robots (SCRs) enhance the load-bearing capability of an operative continuum robot by mechanically coupling it with a supportive arm. However, their passive stiffness is determined by the mechanical configuration and cannot be adjusted online for varying payloads or interaction forces. Active stiffness control is therefore needed to regulate the load response and maintain positioning accuracy. Meanwhile, the closed-chain structure introduces kinematic constraints that complicate task-space regulation and stiffness control. This paper presents an active task-space stiffness control framework for a tendon-driven SCR. An existing geometric variable strain model describes the closed-chain dynamics, which are projected onto the constraint-consistent motion subspace. A projected sliding mode controller regulates the operative arm tip while preserving the constraints, and closed-loop stability is established through Lyapunov analysis. After position regulation, active apparent stiffness is introduced through a virtual Cartesian spring based on position-error feedback to shape the force–displacement response. The framework is evaluated in simulation and experimentally validated under prescribed external loads and different desired configurations. Results show that increasing the commanded stiffness gain reduces load-induced tip deflection and increases apparent directional stiffness, thereby improving load resistance and positioning robustness under external loading.

Electron microscopy requires nanometer-scale specimen positioning over a long stroke. Piezo-stepper actuators are well suited for this task, but their accuracy is limited by hysteresis, mechanical misalignments, and non-collocated sensing. Prior work has addressed these limitations on simplified lab setups. However, extending to a full electron microscope stage introduces coupled nonlinear kinematics and, importantly, the absence of a dedicated point-of-interest (POI) sensor. This paper presents an integrated feedforward framework for precision positioning on such a stage inside an operational electron microscope. Per-element hysteresis compensation first linearizes the actuator response. In the absence of a dedicated POI sensor, a POI measurement is constructed from EM images through cross-correlation-based image tracking. From this measurement, we construct an encoder-based proxy for the POI position. Commutation-angle-domain iterative learning control then uses this proxy as its error signal to cancel the repeatable disturbances of stepping. Because the learned corrections are parameterized in the commutation angle, they transfer across the quasi-static range of drive frequencies. The framework reduces the POI tracking error by over 13x on the lab setup and by 7 to 12x on an operational transmission electron microscope.

The increasing penetration of converter-interfaced resources is making power-system stability assessment more challenging, particularly in heterogeneous grids containing both grid-forming and grid-following converters. Existing decentralized mixed small-gain and small-phase criteria provide scalable stability certificates, but they require all converters to satisfy the same type of condition at a given frequency. As a result, they cannot simultaneously exploit the low gain of grid-following converters and the favorable phase properties of grid-forming converters, leading to unnecessary conservatism. This paper proposes a partitioned mixed gain-phase decentralized stability criterion that allows distinct subsets of converters to satisfy different local requirements at the same frequency. Specifically, one subset can be certified through small-gain bounds, while the complementary subset is certified through small-phase bounds. The admissible trade-off between gain and phase margins is determined by a network-dependent quadratic constraint, yielding a technology-aware stability certificate that remains local at the converter level. The paper characterizes the admissible set of gain and phase bounds, establishes useful convexity and boundedness properties, and develops a practical procedure for selecting these bounds. The proposed method is demonstrated on heterogeneous systems containing grid-forming and grid-following converters, including a two-converter system and the IEEE 39-bus system, outperforming the standard decentralized small-gain and small-phase conditions.

Autonomous robots are moving rapidly from research labs into everyday life - on roads, in the air, in warehouses, and in space. Robot autonomy is no longer solely an academic pursuit, but a collection of mature, field-tested methods and tools that practitioners rely on in real-world deployments. This book offers a clear, unified introduction to the methods that make this possible. Built on decades of teaching at Stanford, the text develops the core elements of modern autonomy stacks within a single conceptual framework, bridging classical robotics and modern physical AI. Every major topic is paired with hands-on Jupyter notebooks and implementation-driven exercises, so readers build practical intuition alongside theoretical understanding. The result is a principled, accessible, and deployment-aware foundation for anyone seeking to design, analyze, or contribute to the next generation of autonomous systems. This is a comprehensive resource for students, engineers, and researchers entering one of today's fastest-growing fields.

The development and testing of advanced aerial robots require experiments in controlled environments with tailored airflow profiles. This paper presents an online learning algorithm for controlling the complex airflow field in a multi-fan vertical wind tunnel. Our method combines a simplified physical model with iterative, measurement-based learning, enabling sample-efficient convergence to desired airflow distributions. We demonstrate the method's versatility by generating complex airflow, such as uniform, Gaussian, and parabolic profiles. Crucially, we show that our algorithm can produce an airflow profile specifically designed for passive soaring, greatly enhancing flight performance of a soaring robot. Variability, practical utility, and robustness of our approach are further highlighted by successful operation with a varying number of fans.

We study cutting planes for nonconvex quadratically constrained quadratic programs (QCQPs) through a project-then-lift approach inspired by mixed-integer rounding (MIR) inequalities. Given two base valid inequalities for the extended QCQP formulation, we project the associated two-row relaxation into a two-dimensional set and analyze the joint range of quadratic functions in two base inequalities. For the nonconvex joint range, we give a closed-form convex hull description of the projected set; for the convex joint range, we give its semidefinite representation. This yields a new family of joint-range inequalities, which can be lifted back to the extended QCQP formulation. MIR inequalities can handle “mixed” terms: continuous variables or fractional linear combinations of integer variables. Similarly, we propose more flexible secant mixed-joint-range inequalities, which better expose and exploit the nonconvex joint range. The proposed approach preserves sparsity, since the support of each lifted inequality is controlled by that of the base inequalities. In preliminary geometric experiments, the joint-range inequalities yield substantial area reduction of the projected relaxation constructed via reformulation-linearization-technique.

Local Flexibility Markets (LFMs) require Distribution System Operators (DSOs) to determine both the quantity of flexibility to procure and the corresponding willingness to pay during market clearing. Existing approaches typically rely on unrealistic centralized AC-OPF clearing algorithms or strictly localized, static flexibility requests driven primarily by congestion management, while the economic value of flexibility is largely neglected. This paper proposes a dynamic flexibility-request methodology in which the DSO's willingness to pay is embedded directly into the market-clearing objective by monetizing transformer and cable aging, network losses, and voltage congestion. To enable computationally efficient clearing, exact convex piecewise-linear epigraph reformulations of the IEEE C57.91 transformer aging model and an Arrhenius-based cable aging model are developed and formally proven to preserve exactness. The proposed framework is validated on a modified CIGRE MV benchmark and compared with a recent state-of-the-art flexibility-request methodology. The results demonstrate significantly higher market liquidity, more efficient flexibility procurement, and improved network operations while preserving the market's transparency and non-discrimination principles.

Parameter-dependent linear matrix inequalities (PD-LMIs) require holding over a continuous domain. When the scheduling parameters vary with time, derivatives of parameter-dependent decisions may also enter the conditions. Since semidefinite programming solvers require finitely many constraints, we introduce GriD-LMIA, the Gridding-based Differentiable PD-LMI Assembler. It converts the conditions that need to hold on a continuous domain into finitely many sufficient LMIs in MATLAB. It first partitions the domain with a hyper-rectangular grid and represents known data and decisions on each cell with tensor Bernstein polynomials. The package exports direct Bernstein, Pólya-elevated, and sum-of-squares-based certificates through YALMIP. Examples are given to examine the balance among grid density, decision degree, and certificate choice.

We introduce an approach for derivation and smoothing of macroscopic densities and velocities from people trajectories, obtained from microscopic position data of individuals within a football stadium. We compute macroscopic densities specifically for susceptible, infected, and exposed individuals, via detection of exposed individuals based on the duration of critical contacts between susceptible and infected. We then present and numerically solve a crowd flow - epidemic spreading PDE model using a finite volume scheme. Finally, we calibrate the model using the smoothed densities computed.

Steelmaking process loads (SPLs) are flexible resources that enhance local renewable-energy utilization and reduce electricity procurement costs in industrial microgrids. However, strong multistage coupling makes current decisions affect subsequent feasibility, challenging conventional deep reinforcement learning to reduce costs while maintaining process feasibility throughout production. This paper proposes a process-knowledge-embedded safe deep reinforcement learning framework for the real-time dispatch of SPLs in industrial microgrids. Specifically, a lossless active-frontier action space is constructed, and a process-distance-guided action-processing mechanism reallocates excluded-action probabilities according to process distance and the actor's safe-action preference. Recursive process feasibility is established to guarantee admissible execution and feasible continuation. Furthermore, the expected process-correction distance is incorporated into PPO through a correction budget and a primal-dual update to internalize process knowledge into the raw policy, while a derived bound quantifies the raw policy's dependence on safety processing. Case studies using real-world data demonstrate zero process losses, electricity-cost reductions of 49.2% and 25.9% relative to rule-based scheduling and rolling MILP, respectively, within an acceptable computation time.

Motion retargeting approaches often prioritize kinematic similarity over whole-body dynamics, contact consistency, and actuation limits, yielding references that are difficult for reinforcement learning (RL) policies to reproduce, particularly for contact-rich behaviors. We present a contact-implicit, direct simulation-based multiple shooting (DSMS) framework that transforms kinematically feasible references into dynamically feasible whole-body trajectories. By embedding a differentiable simulator within a nonlinear program, DSMS resolves contact, friction, impacts, self-collision, and joint limits internally while enforcing tracking, actuation, and task constraints without prescribing a contact schedule or introducing explicit contact constraints. Compared with existing retargeting methods, DSMS accelerates motion-imitation RL training and yields policies with high success rates and low tracking error. We further demonstrate zero-shot sim-to-real transfer on the Unitree G1 through command-conditioned contact-rich crawling and a highly dynamic 180-degree jump-turn.

Model Predictive Control (MPC) delivers constraint-aware control, but its reliance on online optimization limits its use on systems with fast dynamics, high-dimensional models, or long horizons. Existing GPU implementations typically treat the device as a linear-algebra accelerator, leaving the optimization loop dependent on repeated kernel launches and high-latency memory transfers. This paper introduces CUDA MPC, a GPU-native MPC framework that co-designs the optimization algorithm, execution model, and memory architecture for CUDA hardware. CUDA MPC pairs a parallel-in-horizon alternating direction method of multipliers (ADMM) splitting with a fused CUDA kernel that runs the entire iterative solve on the device. Intermediate optimization variables stay in low-latency, on-chip shared memory, and a localized atomic-flag protocol synchronizes only adjacent horizon blocks, minimizing host intervention, kernel-dispatch overhead, and global-memory traffic. Across six nonlinear robotics benchmarks spanning increasing state dimension and constraint density, CUDA MPC sustains real-time rates at horizons one to two orders of magnitude longer than CPU solvers: it solves an optimization-based collision-avoidance parking problem with 100 s of lookahead within a 0.1 s sampling interval, and is the only solver evaluated that achieves both real-time execution and collision-free coordination for a centralized 10-agent swarm, where acados and CasADi return no feasible solution and require 3.5 s and 4.5 s per solve. Against tensor-framework implementations of the same ADMM splitting, the fused kernel is up to $965\times$ faster.

This paper proposes a new automated decision-making framework to enhance the resilience of electrical systems against wildfires by applying operational strategies that account for decision-dependent uncertainty (DDU). The proposed framework incorporates both preventive and corrective measures, enabling adaptive and automated decision-making throughout the course of evolving wildfire scenarios. First, a baseline multistage optimization model is presented as a foundation to support wildfire-driven operational decision-making. The model then incorporates DDU, wherein Public Safety Power Shutoff (PSPS) decisions made in earlier stages influence the probabilities and parameters of future wildfire scenarios. To efficiently solve the resulting complex optimization problem, a mathematical decomposition algorithm is employed. The effectiveness of the proposed approach is demonstrated through case studies on the IEEE 30-bus system. Simulation results confirm that incorporating the impact of DDU into the optimization process provides more realistic, and operationally resilient solutions in the face of evolving wildfire threats.

This paper proposes a novel automated decision-support framework aimed at enhancing the resilience of power systems and operational resilience against wildfires by formulating the decision-making process as a stochastic multi-stage programming during a progressive wildfire. The paper develops a framework that takes into account both preventive and corrective actions, enabling automated and adaptive decisions based on potential scenarios over the course of a wildfire's progression. This approach considers the evolving nature of the wildfire threat and seeks to optimize the response strategies accordingly throughout its duration. The objective is to minimize wildfire risk and operational costs while reducing load curtailment. The framework accounts for potential contingencies caused by progressive wildfires. A novel algorithm is proposed to construct a decision tree based on wildfire progression and system geographical information. Additionally, a novel stochastic dual dynamic programming approach is deployed to solve the proposed optimization problem, achieving a global optimum for the framework. The effectiveness of the proposed method is demonstrated on the IEEE 30-bus system under various wildfire impact scenarios and is then applied to the IEEE 300-bus system to illustrate the scalability of the proposed approach. The results highlight the advantages of the proposed automated framework over a single-stage operational optimization strategy in enhancing power grid resilience under wildfire conditions.

The inertia constant H[s] is a fundamental indicator of power system resilience, linking power imbalance between generation and load to frequency deviation. It is essential in frequency reserve dispatch under stability-constrained optimal power flow (OPF), demand response (DR) in ancillary service, system decoupling and frequency control in modern power system. While the inertia constant is traditionally defined as the intrinsic kinetic energy of synchronous generators on bar normalized to the power base, this neglects the releasable power under nonlinear dynamics and control inside HVDC and Inverter-based Resources (IBRs). Accurate real-time inertia estimation is therefore essential to perform proper frequency control and to indicate the risks of failure in frequency restoration. It, however, is challenging with noisy frequency measurement under event-driven parameter jumps and locational transient responses. This paper presents a systematic comparative analysis on inertia estimation algorithms (IEAs) for frequency response applications. Classical methods such as filtering and fitting under measurement-based methods are benchmarked against data-based parameter estimation techniques such as recursive least squares (RLS) and model-based methods such as Kalman filtering (KF). The main contributions are: (i) a holistic review of model- and data-based inertia estimation methods, (ii) exploration on the effect of IEA to wind-based inertia emulation strategies. The findings underscore the need for robust, adaptive, and data-driven estimation frameworks to ensure secure operation of future low-inertia grids.

Magnetic components in high-frequency, high-power-density converters are increasingly driven by non-sinusoidal flux-density waveforms with fast transitions, minor-loop operation, dc bias, and temperature variation. Under these conditions, steady-state core-loss formulas and single-valued material curves cannot fully capture transient magnetization responses. This work proposes the Physics-Informed Hybrid Neural Operator (PI-HNO), a compact material-specific neural model with B-H energy-consistency regularization for core-loss-oriented transient magnetization prediction. Given the measured B(t)-H(t) history, the input B(t) series over the prediction interval and operating-condition information, PI-HNO predicts the H(t) series and the corresponding reconstructed B-H trajectory. The model integrates a local recurrent branch for boundary-state representation and rate-dependent response evolution with a Preisach-inspired global branch that extracts waveform-level hysteresis context. Evaluation on the MagNetX transient database using material-specific models for 14 ferrite materials demonstrates that PI-HNO achieves a compact trade-off between sequence accuracy and B(t)-H(t) energy consistency, with the mean and 95th percentile B(t)-H(t) energy consistency errors of 1.92% and 7.60%, respectively, using only 4777 trainable parameters per model. Ablation studies further demonstrate that the local, global, and energy-aware regularized components provide distinct contributions to transient magnetization prediction.

Safely navigating polytopic environments while respecting the dynamics, control, and exact geometry of the underlying system is a challenge in robotics. Control barrier functions (CBFs) synthesize safe control policies by rendering the safe set forward invariant, but many existing CBF-based methods approximate polytopes using conservative smooth shapes, such as spheres or ellipsoids, to obtain explicit differentiable distance functions. In this article, we propose an exact Signed Distance Function (SDF) formulation for a polytopic robot and polytopic obstacles and integrate it with nonsmooth CBFs. Leveraging Minkowski operations, the proposed method computes the exact SDF via companion convex programs in both the collision-free (positive-sign) and in-collision (negative-sign) cases. Furthermore, by exploiting the convenient geometric properties of 2D Minkowski operations and the optimality conditions of the two companion convex programs, we derive a unified analytical expression for the gradient of the exact SDF via sensitivity analysis. The exact rotational gradient further reveals a previously masked class of local minima induced by the coupling between geometry and nonholonomic kinematics. We demonstrate the effectiveness of the proposed framework through a pure-translation case and three scenarios with unicycle models involving recovery from an unsafe initialization and single- and multiple-obstacle avoidance. Comparisons with baseline methods highlight how the proposed framework enables non-conservative maneuvers and safety recovery.

This paper considers boundary stabilization problems for a first-order hyperbolic partial integro-differential equation (PIDE) subject to concurrent input and state delays. The coexistence of these two types of delays complicates control design, especially under the case of large input delay that requires to predict more state information. A backstepping-based boundary controller is developed to achieve stabilization and delay compensation. The design relies on two affine Volterra transformations involving both Fredholm- and Volterra-type integral terms, which results in a four-PIDE kernel equations. To establish their well-posedness, the kernel domain is partitioned along characteristic lines into a finite number of triangular subregions, and the kernel solution is constructed successively in the preceding subregion to the next one. The finite-time stability of the resulting closed-loop system is established. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.

We present a biconvex approach for minimum-time motion planning around convex obstacles that is guaranteed to converge, is anytime, and supports derivative constraints to arbitrary order. We jointly convexify the minimum-time objective and all derivative constraints through a change of variables, and handle collision avoidance via time-varying separating planes, reducing the problem to a biconvex program. This program is solved by alternating between computing maximum-margin separating planes and optimizing the trajectory. By only adding planes for obstacles that the current iterate collides with, the trajectory can jump around obstacles and escape local minima. The method is guaranteed to converge starting from a simple collision-free polygonal curve. In our experiments on drone navigation and dual-arm bin unloading, we find that the proposed method reliably produces high-quality trajectories with computation times comparable to state-of-the-art decomposition-based motion planners, while handling a larger class of problems and being substantially more robust to bad initialization. Project page:https://wernerpe.github.io/bmtp-website/

Conventional grid-forming (GFM) control strategies often treat the DC source as an unconstrained link, creating mismatches when applied to the wind turbine generators (WTGs). Focusing on primary frequency regulation, this paper systematically investigates the mismatch between the GFM-WTGs behavior and the droop-based primary frequency regulation. To address this issue, a novel coordination strategy between WTG primary frequency regulation and GFM control is proposed. By establishing well-designed relationships among the power-tracking coefficient, power set-point, and frequency deviation, the proposed strategy enables GFM-WTGs to participate consistently in primary frequency regulation within predefined frequency limits while maintaining appropriate power points and effectively utilizing the allowable power reserve. Furthermore, the proposed method preserves the control structure and dynamic performance of conventional GFM control and inherently adapts to varying wind-speed conditions. Comparative case studies under different operating scenarios demonstrate the effectiveness and superiority of the proposed strategy.

Robotic systems must operate under uncertainty while satisfying complex task and safety specifications. Monitoring such specifications under uncertainty remains challenging, as existing formulations typically require extensive data or explicit uncertainty distributions. In this paper, we propose a real-time monitoring framework that reduces data requirements by leveraging data-driven reachable sets for specification evaluation. We instantiate the framework for maritime navigation, where complex specifications arise from traffic rules. We develop a data-efficient pipeline for constructing reachable sets and derive a monitoring formulation suitable for real-time deployment. Simulation and hardware experiments demonstrate robust monitoring under realistic disturbances, achieving improved risk detection compared to state-of-the-art metrics.

Increasing renewable-energy penetration heightens power-system variability and complicates disturbance containment. Controlled islanding mitigates cascading failures by partitioning a stressed network to limit disrupted power transfer while preserving each island's operational integrity, but this constrained partitioning problem is NP-hard. Although QAOA offers a complementary search strategy, limited near-term qubit capacity restricts conventional formulations. This paper presents a qubit-efficient hybrid quantum framework combining a physics-informed compact encoding with Lagrangian constraint handling and classical feasibility refinement. The encoding exploits grid structure while formally preserving the original feasible solution space and objective. For a fixed island count on sparse working graphs, the formulation reduces phase-separator and per-layer gate complexity from quadratic to linear scaling with system size. Tests on eight IEEE systems ranging from 9 to 89 buses and multiple quantum-provider backends produce feasible, high-quality islanding solutions under practical circuit and sampling budgets. Factorial ablation attributes resource and runtime improvements to the complementary effects of compact encoding and qubit-efficient constraint handling. Noise analysis shows stable solution quality under tested device noise, while landscape diagnostics reveal smoother, more consistently scaled QAOA cost surfaces and improved parameter-optimization behavior. These results offer a transferable approach for scaling constrained quantum optimization toward larger real-world applications on near-term hardware.

Artificial intelligence (AI) is increasingly central to power and energy systems, supporting modeling, forecasting, optimization, and control. Yet most existing works emphasize specialized applications and offer little reusable material for newcomers or interdisciplinary learners, who increasingly rely on large language models rather than building their own. This gap points to a need for engineering-grounded AI (EGAI), in which AI workflows follow established engineering and power-system domain rules rather than acting as task-agnostic black boxes. Motivated by a community survey of researchers and practitioners, which shows 92% report at least one barrier before running an AI model and 94% want a power-specific hands-on course. This paper presents a framework consisting of open, executable module library that lowers the entry barrier for AI in power systems. The modules follow a progressive difficulty ladder that maps core AI concepts onto representative power-system tasks: (i) foundational deep neural network (DNN) templates for function approximation and load-curve fitting; (ii) a domain-coupled convolutional neural network (CNN) power-flow surrogate for a 5-bus system; and (iii) frontier modules on DNN-assisted optimization, deep reinforcement learning (DRL) for battery storage control, and physics-informed neural networks (PINNs) for the swing equation. All modules are released as Jupyter notebooks that run locally or on Google Colab and are delivered through an IEEE online course and IEEE Power & Energy Society (PES) webinar series. The webinar drew more than 590 live attendees, which is among the ten most-attended IEEE PES webinars, and over 344 repository visits within two weeks, reinforcing the survey-based motivation.

Parameter drift remains a practical limitation of adaptive vibration control systems, particularly when persistence of excitation diminishes after disturbance attenuation or when measurement disturbances render the adaptation problem ill-conditioned. This issue is especially relevant in flexible structures, where adaptive controllers may continue updating parameters even after satisfactory vibration suppression has been achieved. This paper proposes a computationally efficient root-mean-square (RMS)-based stopping criterion that mitigates parameter drift by freezing adaptation once satisfactory vibration attenuation has been sustained over a prescribed interval. The criterion is implemented by recursively computing an exponentially weighted moving RMS of the performance variable and requires negligible additional computational effort. The proposed mechanism is integrated with retrospective cost adaptive control (RCAC) and validated through both numerical simulations and closed-loop experiments on a cantilever-beam vibration-suppression platform with a noncollocated actuator configuration. Without the proposed stopping criterion, continued adaptation after disturbance rejection leads to gradual parameter drift and degradation of vibration suppression performance. When the RMS-based threshold is enabled, controller parameters remain bounded, and the achieved vibration attenuation is preserved. The results demonstrate that a simple performance-based monitoring mechanism can effectively prevent parameter drift in adaptive vibration control, retain the transient benefits of adaptation, and incur minimal computational overhead.

In this paper, we propose a new robust navigation framework for path following tasks in robots operating within unknown, cluttered environments. Our approach ensures reactive safety through obstacle avoidance and guaranteed convergence to a target path, while simultaneously mitigating the impact of unknown-but-bounded disturbances using a tube-based control strategy. The methodology integrates key aspects in the robot navigation: (i) a nominal Integrated Guidance and Control scheme for path-following employing Artificial Vector Fields guidance and Backstepping control; (ii) a smooth distance function that enables a continuous control law formulation for seamless obstacle avoidance; (iii) a unified control objective that balances collision avoidance with path-following; and (iv) an adaptive control component to provide robustness against external disturbances. We provide formal proofs of safety and stability using barrier functions and Lyapunov stability theory. The effectiveness of the proposed framework is validated through extensive numerical simulations.

We study policy optimization for gain-scheduled linear quadratic regulation, where one schedule of gains, interpolated through fixed weighting functions, is optimized against a family of plants. The resulting cost can develop spurious local minima, and existing convergence certificates are either local or severely conservative. We establish an exact identity: when the gradient of the cost is evaluated with the minimizer's closed-loop covariances, the scheduled cost is star-convex about the minimizer. The identity holds on the entire feasible set, for any parametrization of the schedule. Convergence is governed by a single dimensionless ratio. Wherever the ratio satisfies a threshold condition, gradient descent converges linearly to the optimum on entire sublevel regions at an explicit rate; at every spurious stationary point the condition necessarily fails. Experiments that maximize the ratio directly show the threshold to be an active boundary of the landscape. This extended version contains the complete proofs and additional numerical studies omitted from the letter for space.

Timescale separation is a powerful tool for analyzing interconnected dynamical systems. Meanwhile, operator theory provides a general framework for studying the convergence of iterative methods formulated as fixed-point iterations, including algorithms arising in optimization, learning, and control. In this paper, we bridge these two areas by establishing timescale separation results for fixed-point iterations induced by both deterministic and stochastic operators. As customary in timescale separation, our results involve auxiliary systems that arise from the original interconnection in the limit as the timescale parameter tends to zero and separately capture the dynamics induced by the slow and fast operators. The proposed operator-theoretic framework yields explicit and readily checkable bounds on this tunable parameter, expressed in terms of standard operator constants. To illustrate the applicability of our results, we employ them to prove the convergence properties of a feedback optimization scheme in both deterministic and stochastic settings.

This paper studies the distributed online control problem over a network of linear time-invariant (LTI) systems in the presence of adversarial disturbances and time-varying convex costs. The network cost is characterized by the summation of local cost functions, where each local function is sequentially revealed only to the corresponding agent. The goal of each agent is to generate a control sequence, using only local observations and neighbor communication, that competes with the best centralized linear policy in hindsight. We extend the recently proposed Online Spectral Control framework from the centralized setting to the distributed setting. In particular, each agent applies a spectral controller obtained by convolving past disturbances with the leading eigenvectors of a Hankel matrix, while the controller parameters are updated through a distributed online gradient descent step over the local surrogate costs. We formulate this problem this problem as a regret minimization problem based on the spectral parameterization, and under standard assumptions, we establish a sublinear regret bound of $O(\frac{\sqrt{T}\text{poly}(\log T)}{\gamma^3})$, where $T$ is the time horizon and $\gamma$ denotes the stability margin. The resulting bound also captures the dependence on the network size and connectivity.

External inputs to local flexibility markets, network models, demand scenarios, flexibility offers, and asset thermal, economic parameters do not change the clearing methodology, yet they are routinely defined under heterogeneous assumptions, which hinders reproducible benchmarking. This paper provides a complete, methodology-agnostic input set built around a modified CIGRE MV network with prescribed base-load and stress-load conditions, synthetic flexibility offers, wholesale prices, and transformer and cable parameters. Baseline AC operating points (voltages, loadings, and aging) are reported for both days so that alternative flexibility-request and clearing methods can be applied to the same inputs and compared fairly. The associated data are released openly on Zenodo.