arXiv subjects

Emiliano Dall'Anese

Publications and source records attributed to Emiliano Dall'Anese.

At least 19 recordsLinked to original sources

arXiv2026

On the Stability of Power Systems with AI Data Centers: A Multi-Equilibrium Switched DAE Framework

The rapid growth of Artificial Intelligence (AI) data centers is introducing dynamic loads into power transmission systems as GPU clusters switch between computational phases with distinct power demands. These dynamics are naturally modeled by switched affine differential-algebraic equations (DAEs), where each mode induces a different equilibrium and consistency space. We study their stability using control and hybrid systems tools. Differential projectors derived from the quasi-Weierstrass form yield an equivalent hybrid representation, from which we characterize the $ω$-limit set and establish Lyapunov conditions for practical stability with an explicit $\mathcal{KL}$ bound accounting for switching-induced resets. For stochastic inference workloads, we use Foster--Lyapunov techniques to establish probabilistic uniform global recurrence under mode-dependent dwell times and transition probabilities. The framework is validated on the IEEE 39-bus transmission network with co-located AI data centers using high-fidelity electromagnetic transient simulations of deterministic training and stochastic inference workloads.

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arXiv2026

Omega-Limit Sets and Input-to-State Stability in Power Grids With Switching Equilibria

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields -- or modes--, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of $Ω$-limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

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arXiv2026

Online Feedback Optimization for Constrained Stochastic Problems with Decision-Dependent Distributions: Extended Version

Online feedback optimization (OFO) leverages real-time output measurements to optimize the operation of networked systems without requiring full knowledge of system dynamics or disturbances. We develop an OFO approach for constrained stochastic optimization problems in which the distribution of the system's random parameters shifts in response to the control actions. We propose a projected primal-dual algorithm where the true dual constraint sets are replaced by surrogate sets. Our main result is an upper bound on the mean-square tracking error, which decomposes into four interpretable terms reflecting: (i) the stochasticity of the problem, (ii) output measurement errors, (iii) time-variability of the problem, and (iv) the mismatch between surrogate and true dual constraint sets. The theory is illustrated in a numerical experiment for power grids with price-responsive assets.

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arXiv2026

Reachability Analysis for Power Systems with Heterogeneous Resources via Jordan Transformation

This paper develops a computationally efficient framework for reachability analysis of transmission-level power system dynamics with synchronous generators, grid-forming and grid-following inverters, and uncertain power injections/withdrawals. Starting from reduced-order device models and a frequency-divider representation, we derive a linear ordinary-differential-equation model suitable for efficient reachable-set computation under bounded disturbances across network buses. The proposed reachability method combines interval reachability and contraction-based bounds to construct certified over-approximations for the linear ordinary-differential-equation model. A real Jordan transformation separates non-oscillatory modes, handled through a linear embedding system, from oscillatory modes, enclosed using contraction-based ball bounds. Numerical experiments on a modified IEEE 39-bus system validate the reachable tubes against high-fidelity electromagnetic-transient (EMT) simulations, and demonstrate multi-second reachable sets computed in sub-second time.

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arXiv2026

Sampled-data Systems: Stability, Contractivity and Single-iteration Suboptimal MPC

This paper analyzes the stability of interconnected continuous-time (CT) and discrete-time (DT) systems coupled through sampling and zero-order hold mechanisms. The DT system updates its output at regular intervals $T>0$ by applying an $n$-fold composition of a given map. This setup is motivated by online and sampled-data implementations of optimization-based controllers - particularly model predictive control (MPC) - where the DT system models $n$ iterations of an algorithm approximating the solution of an optimization problem. We introduce the concept of a reduced model, defined as the limiting behavior of the sampled-data system as $T \to 0^+$ and $n \to +\infty$. Our main theoretical contribution establishes that when the reduced model is contractive, there exists a threshold duration $T(n)$ for each iteration count $n$ such that the CT-DT interconnection achieves exponential stability for all sampling periods $T < T(n)$. Finally, under the stronger condition that both the CT and DT systems are contractive, we show exponential stability of their interconnection using a small-gain argument. Our theoretical results provide new insights into suboptimal MPC stability, showing that convergence guarantees hold even when using a single iteration of the optimization algorithm - a practically significant finding for real-time control applications.

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arXiv2026

Independence of Closed-Loop Equilibria and Stability from the Choice of Control Barrier Function for a Given Safe Set

Control barrier functions (CBFs) play a critical role in the design of safe optimization-based controllers for control-affine systems. Given a CBF associated with a given, predefined ``safe'' set, the typical approach consists in embedding CBF-based constraints into the optimization problem defining the control law to enforce forward invariance of the safe set. While this approach effectively guarantees safety for a given CBF, the CBF-based control law can introduce undesirable equilibrium points (i.e., points that are not equilibria of the original system). Given that there exist many different CBFs associated with a given fixed safe set, open questions remain on how the choice of CBF influences the number and locations of undesirable equilibria and, in general, the dynamics of the closed-loop system. This paper investigates how the choice of CBF impacts the dynamics of the closed-loop system and shows that: (i) The choice of CBF does not affect the number, location, and (local) stability properties of the equilibria in the interior of the safe set; (ii) undesirable equilibria only appear on the boundary of the safe set; and, (iii) the number and location of undesirable equilibria for the closed-loop system do not depend of the choice of the CBF. Additionally, for the well-established \textit{safety filters}, we show that the stability properties of equilibria of the closed-loop system are independent of the choice of the CBF and of the associated extended class-K function, provided that the CBFs are chosen from the same equivalence class.

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arXiv2026

Local Safety Filters for Networked Systems via Two-Time-Scale Design

Safety filters based on Control Barrier Functions (CBFs) provide formal guarantees of forward invariance, but are often difficult to implement in networked dynamical systems. This is due to global coupling and communication requirements. This paper develops locally implementable approximations of networked CBF safety filters that require no coordination across subsystems. The proposed approach is based on a two-time-scale dynamic implementation inspired by singular perturbation theory, where a small parameter $ε$ separates fast filter dynamics from the plant dynamics; then, a local implementation is enabled via derivative estimation. Explicit bounds are derived to quantify the mismatch between trajectories of the systems with dynamic filter and with the ideal centralized safety filter. These results characterize how safety degradation depends on the time-scale parameter $ε$, estimation errors, and filter activation time, thereby quantifying trade-offs between safety guarantees and local implementability.

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arXiv2026

Safe Policy Optimization via Control Barrier Function-based Safety Filters

Control barrier function (CBF)-based safety filters provide a systematic way to enforce state constraints, but they can significantly alter the closed-loop dynamics induced by a nominal, stabilizing controller. In particular, the resulting safety-filtered system may exhibit undesirable behaviors including limit cycles, unbounded trajectories, and undesired equilibria. This paper develops a policy optimization framework to maximally enhance the stability properties of safety-filtered controllers. Focusing on linear systems with linear nominal controllers, we jointly parameterize the nominal feedback gain and safety-filter components, and optimize them using trajectory-based objectives computed from closed-loop rollouts. To ensure that the nominal controller remains stabilizing throughout training, we encode Lyapunov-based stability conditions as smooth scalar constraints and enforce them using robust safe gradient flow. This guarantees feasibility of the stability constraints along the optimization iterates and therefore avoids instability during training. Numerical experiments on obstacle-avoidance problems show that the proposed approach can remove asymptotically stable undesired equilibria and improve convergence behavior while maintaining forward invariance of the safe set.

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arXiv2026

Demand Response Under Stochastic, Price-Dependent User Behavior

This paper focuses on price-based residential demand response implemented through dynamic adjustments of electricity prices during DR events. It extends existing DR models to a stochastic framework in which customer response is represented by price-dependent random variables, leveraging models and tools from the theory of stochastic optimization with decision-dependent distributions. The inherent epistemic uncertainty in the customers' responses renders open-loop, model-based DR strategies impractical. To address this challenge, the paper proposes to employ stochastic, feedback-based pricing strategies to compensate for estimation errors and uncertainty in customer response. The paper then establishes theoretical results demonstrating the stability and near-optimality of the proposed approach and validates its effectiveness through numerical simulations.

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arXiv2026

Learning to Pursue AC Optimal Power Flow Solutions with Feasibility Guarantees

This paper focuses on an AC optimal power flow (OPF) problem for distribution feeders equipped with controllable distributed energy resources (DERs). We consider a solution method that is based on a continuous approximation of the projected gradient flow - referred to as the safe gradient flow - that incorporates voltage and current information obtained either through real-time measurements or power flow computations. These two setups enable both online and offline implementations. The safe gradient flow involves the solution of convex quadratic programs (QPs). To enhance computational efficiency, we propose a novel framework that employs a neural network approximation of the optimal solution map of the QP. The resulting method has two key features: (a) it ensures that the DERs' setpoints are practically feasible, even for an online implementation or when an offline algorithm has an early termination; (b) it ensures convergence to a neighborhood of a strict local optimizer of the AC OPF. The proposed method is tested on a 93-node distribution system with realistic loads and renewable generation. The test shows that our method successfully regulates voltages within limits during periods with high renewable generation.

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arXiv2025

Online convex optimization for robust control of constrained dynamical systems

This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex optimization framework with tools from robust model predictive control to propose an algorithm that is able to guarantee robust constraint satisfaction. The performance of the closed loop emerging from application of our framework is studied in terms of its dynamic regret, which is proven to be bounded linearly by the variation of the cost functions and the magnitude of the disturbances. We corroborate our theoretical findings and illustrate implementational aspects of the proposed algorithm by a numerical case study on a tracking control problem of an autonomous vehicle.

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arXiv2025

High Probability Convergence Bounds for Non-convex Stochastic Gradient Descent with Sub-Weibull Noise

Stochastic gradient descent is one of the most common iterative algorithms used in machine learning and its convergence analysis is a rich area of research. Understanding its convergence properties can help inform what modifications of it to use in different settings. However, most theoretical results either assume convexity or only provide convergence results in mean. This paper, on the other hand, proves convergence bounds in high probability without assuming convexity. Assuming strong smoothness, we prove high probability convergence bounds in two settings: (1) assuming the Polyak-Łojasiewicz inequality and norm sub-Gaussian gradient noise and (2) assuming norm sub-Weibull gradient noise. In the second setting, as an intermediate step to proving convergence, we prove a sub-Weibull martingale difference sequence self-normalized concentration inequality of independent interest. It extends Freedman-type concentration beyond the sub-exponential threshold to heavier-tailed martingale difference sequences. We also provide a post-processing method that picks a single iterate with a provable convergence guarantee as opposed to the usual bound for the unknown best iterate. Our convergence result for sub-Weibull noise extends the regime where stochastic gradient descent has equal or better convergence guarantees than stochastic gradient descent with modifications such as clipping, momentum, and normalization.

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arXiv2025

Online Learning with Probing for Sequential User-Centric Selection

We formalize sequential decision-making with information acquisition as the probing-augmented user-centric selection (PUCS) framework, where a learner first probes a subset of arms to obtain side information on resources and rewards, and then assigns $K$ plays to $M$ arms. PUCS covers applications such as ridesharing, wireless scheduling, and content recommendation, in which both resources and payoffs are initially unknown and probing is costly. For the offline setting with known distributions, we present a greedy probing algorithm with a constant-factor approximation guarantee $ζ= (e-1)/(2e-1)$. For the online setting with unknown distributions, we introduce OLPA, a stochastic combinatorial bandit algorithm that achieves a regret bound $\mathcal{O}(\sqrt{T} + \ln^{2} T)$. We also prove a lower bound $Ω(\sqrt{T})$, showing that the upper bound is tight up to logarithmic factors. Experiments on real-world data demonstrate the effectiveness of our solutions.

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arXiv2025

A Distributed Optimization Framework to Regulate the Electricity Consumption of a Residential Neighborhood with Renewables

Demand response services at the distribution level are emerging as enabling strategies for improving grid reliability in the presence of intermittent renewable generation and grid congestion. For residential loads, space heating and cooling, water heating, electric vehicle charging, and routine appliances make up the bulk of the electricity consumption. Controlling these loads is essential to effectively partake into grid operations and provide services such as peak shaving and demand response. However, maintaining user comfort is important for ensuring user participation to such a program. This paper formulates a novel mixed integer linear programming problem to control the overall electricity consumption of a residential neighborhood by considering the users' comfort and preferences. To efficiently solve the problem for communities involving a large number of homes, a distributed optimization framework based on the Dantzig-Wolfe decomposition technique is developed. We demonstrate the load shaping capacity and the computational performance of the proposed optimization framework in a simulated environment.

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arXiv2025

Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers

Control Barrier Functions (CBFs) have been widely utilized in the design of optimization-based controllers and filters for dynamical systems to ensure forward invariance of a given set of safe states. While CBF-based controllers offer safety guarantees, they can compromise the performance of the system, leading to undesirable behaviors such as unbounded trajectories and emergence of locally stable spurious equilibria. Computing reachable sets for systems with CBF-based controllers is an effective approach for runtime performance and stability verification, and can potentially serve as a tool for trajectory re-planning. In this paper, we propose a computationally efficient interval reachability method for performance verification of systems with optimization-based controllers by: (i) approximating the optimization-based controller by a pre-trained neural network to avoid solving optimization problems repeatedly, and (ii) using mixed monotone theory to construct an embedding system that leverages state-of-the-art neural network verification algorithms for bounding the output of the neural network. Results in terms of closeness of solutions of trajectories of the system with the optimization-based controller and the neural network are derived. Using a single trajectory of the embedding system along with our closeness of solutions result, we obtain an over-approximation of the reachable set of the system with optimization-based controllers. Numerical results are presented to corroborate the technical findings.

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arXiv2024

Incremental Volt/Var Control for Distribution Networks via Chance-Constrained Optimization

This paper considers an incremental Volt/Var control scheme for distribution systems with high integration of inverter-interfaced distributed generation (such as photovoltaic systems). The incremental Volt/Var controller is implemented with the objective of minimizing reactive power usage while maintaining voltages within safe limits sufficiently often. To this end, the parameters of the incremental Volt/Var controller are obtained by solving a chance-constrained optimization problem, where constraints are designed to ensure that voltage violations do not occur more often than a pre-specified probability. This approach leads to cost savings in a controlled, predictable way, while still avoiding significant over- or under-voltage issues. The proposed chance-constrained problem is solved using a successive convex approximation method. Once the gains are broadcast to the inverters, no additional communication is required since the controller is implemented locally at the inverters. The proposed method is successfully tested on a low-voltage single-phase 42-nodes network and on the three-phase unbalanced IEEE 123-node test system.

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arXiv2024

k-Dimensional Agreement in Multiagent Systems

Given a network of agents, we study the problem of designing a distributed algorithm that computes k independent weighted means of the network's initial conditions (namely, the agents agree on a k-dimensional space). Akin to average consensus, this problem finds applications in distributed computing and sensing, where agents seek to simultaneously evaluate k independent functions at a common point by running a single coordination algorithm. We show that linear algorithms can agree on quantities that are oblique projections of the vector of initial conditions, and we provide techniques to design protocols that are compatible with a pre-specified communication graph. More broadly, our results show that a single agreement algorithm can solve $k$ consensus problems simultaneously at a fraction of the complexity of classical approaches but, in general, it requires higher network connectivity.

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arXiv2024

Optimal Power Flow Pursuit via Feedback-based Safe Gradient Flow

This paper considers the problem of controlling inverter-interfaced distributed energy resources (DERs) in a distribution grid to solve an AC optimal power flow (OPF) problem in real time. The AC OPF includes voltage constraints, and seeks to minimize costs associated with the economic operation, power losses, or the power curtailment from renewables. We develop an online feedback optimization method to drive the DERs' power setpoints to solutions of an AC OPF problem based only on voltage measurements (and without requiring measurements of the power consumption of non-controllable assets). The proposed method - grounded on the theory of control barrier functions - is based on a continuous approximation of the projected gradient flow, appropriately modified to accommodate measurements from the power network. We provide results in terms of local exponential stability, and assess the robustness to errors in the measurements and in the system Jacobian matrix. We show that the proposed method ensures anytime satisfaction of the voltage constraints when no model and measurement errors are present; if these errors are present and are small, the voltage violation is practically negligible. We also discuss extensions of the framework to virtual power plant setups and to cases where constraints on power flows and currents must be enforced. Numerical experiments on a 93-bus distribution system and with realistic load and production profiles show a superior performance in terms of voltage regulation relative to existing methods.

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