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Sergio Grammatico

Publications and source records attributed to Sergio Grammatico.

At least 19 recordsLinked to original sources
arXiv2026

Hybrid Sequential Feedback Optimization for Wind Farm Power Maximization

This paper considers feedback optimization for optimal steady-state operation of nonlinear discrete-time systems when the steady-state input-output map and its sensitivity are expensive to compute. We propose a hybrid extension of sequential feedback optimization (SFO) that augments the model-based SFO gradient with correction terms through a convex combination with summable diminishing weights. Two variants are studied: one based on recursive least-squares (RLS) sensitivity estimation, and another on extremum seeking control (ESC) gradient estimation. Under contractivity and smoothness assumptions, we show that both hybrid schemes preserve the convergence of SFO to a neighborhood of the optimal steady state. The proposed methods are validated through a wind farm power maximization problem using a medium-fidelity model, demonstrating improved early transient performance compared to pure SFO.

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arXiv2026

A New Lineserach for Accelerated Composite Minimization

The choice of the stepsize in first-order convex optimization is typically based on the smoothness constant and plays a crucial role in the performance of algorithms. Recently, there has been a resurgent interest in introducing adaptive stepsizes that do not explicitly depend on smooth constant. In this paper, we propose a novel linesearch stepsize rule based on function evaluations (i.e., zero-order information) that enjoys provable convergence guarantees for both accelerated and non-accelerated gradient descent. We further discuss the similarities and differences between the proposed stepsize regimes and the existing stepsize rules (including Polyak and Armijo). We numerically benchmark the performance of our proposed algorithms against state-of-the-art methods across three major problems classes of (1) smooth minimization (logistic regression, quadratic programs, log-sum-exponential, and smooth max-cut relaxation) (2) composite minimization ($\ell_1$-regularized least-squares, $\ell_1$-constrained least-squares, and $\ell_1$-regularized logistic regression), and (3) non-convex minimization (cubic minimization). These classes include a wide range of operations research and management applications such as portfolio optimization, discrete choice models, sparse classification and feature selections, high-order optimization and trust-region subproblems.

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arXiv2026

Parallel Branch Model Predictive Control on GPUs

We present a GPU-based solver for trajectory planning problems using branch Model Predictive Control. Building on iterative LQR methods, we adopt a multiple-shooting formulation for the system dynamics and use an augmented Lagrangian method to handle general stage-wise constraints. This design enables straightforward warm-starting. The constraint-handling capability of our solver is validated on two challenging trajectory planning problems. In addition, we develop two tailored inner LQR solvers that exploit the tree-sparse structure. The solvers offer different levels of parallelism, making them appropriate for different tree sizes. The numerical results demonstrate that, compared to a high-performance CPU-based solver, our approach achieves superior performance on large-scale problems.

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arXiv2026

Adaptive Incentive Design in Dynamic Principal-Agent Problem via Kernelized Bandits

We consider the dynamic principal-agent problem under asymmetric information, wherein a principal sequentially designs contracts to incentivize an agent with unknown preferences and hidden actions. A fundamental bottleneck in the existing literature is the assumption of deterministic agent utility, which renders the principal's expected utility discontinuous and forces computationally intractable discretizations of the contract space. In this paper, we address this limitation by introducing a stochastic counterpart into the agent's utility model, capturing the inherent physical and behavioral variations in realistic subsystems. We formally prove that this stochastic formulation restores the continuity of the principal's expected utility. Leveraging this continuous geometric structure, we formulate the interaction as a structured multi-armed bandit problem subject to heteroscedastic noise. We propose a \texttt{Heteroscedastic GP-UCB} algorithm that utilizes a Neural Network (Arcsin) kernel, chosen to capture the non-stationary, sigmoidal geometry of the utility landscape. For an $m$-dimensional compact contract space, we establish a high-probability cumulative regret bound of $O\left(\sqrt{T}(\log T)^{m+1}\right)$. Finally, we demonstrate the practical efficacy of our theoretical framework by formulating the Vehicle-to-Grid (V2G) incentive design problem, proving its equivalence to a dynamic principal-agent problem, and showing superior economic performance for grid aggregators.

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arXiv2026

Parallel Dynamic Programming for Conic Linear Quadratic Control

Linear Quadratic (LQ) control problems are at the heart of linear control theory and Model Predictive Control (MPC). While performant, standard approaches to solving such problems are inherently serial, limiting real-time scalability despite the parallel computing power available on modern multi-core CPUs. Contributing to addressing this challenge and motivated by ``divide and conquer'' strategies, we present a parallel-in-time approach that solves computationally demanding conic optimal control problems through the use of the alternating direction method of multipliers (ADMM). In particular, we formulate the inner primal update of ADMM as an LQ problem and split the reformulated problem along the time horizon. This enables us to derive a variant of the Riccati recursion using dynamic programming to solve each subproblem in parallel. Numerical benchmarks on two real-world applications demonstrate as much as a 5x speedup compared to existing related approaches on multi-core CPU hardware.

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arXiv2026

Benchmarking Sequential Feedback Optimization for Wind Farm Power Maximization

This paper benchmarks sequential feedback optimization (SFO) for wind farm power maximization using a medium-fidelity dynamic flow model. We compare SFO with two well-established approaches, adjoint-based economic model predictive control (AMPC) and extremum seeking control (ESC), under a common nine-turbine layout and identical operating constraints. The comparison focuses on steady-state power production and computational efficiency, both relevant for real-time implementation. The simulation results illustrate that SFO achieves higher steady-state power while preserving real-time feasibility, AMPC provides a better transient performance at a higher online computational cost and without guarantees of convergence to the steady-state optimum, and ESC offers a computationally inexpensive model-free baseline that may converge to locally optimal solutions. These results provide a practical reference for selecting wind farm control strategies and for designing scalable, real-time optimization methods.

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arXiv2026

Fast Newton methods for linear-quadratic dynamic games with application to autonomous vehicle platooning and intersection crossing

We consider constrained linear-quadratic dynamic games arising in autonomous vehicle platooning, intersection crossing and other cooperative driving scenarios. Infinite-horizon Nash equilibria are reformulated as receding-horizon affine variational inequalities with special structure. Exploiting this formulation, we design Newton-type algorithms with local quadratic convergence. The resulting methods achieve extremely fast convergence, making them well suited for real-time and embedded receding-horizon control in safety-critical traffic applications. Simulations of platooning and intersection crossing demonstrate substantial performance gains over first-order and operator-splitting approaches, hence high application potential.

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arXiv2026

Learning-Based Stackelberg Equilibrium Seeking with Application to Demand-Side Energy Management

Demand-side management (DSM) enables distribution system operators (DSOs) to steer electricity consumption through dynamic price signals or incentive mechanisms, thereby leveraging end-users' flexibility potential for delivering grid services. The resulting hierarchical interaction between the DSO and the end-users can be formulated as a Stackelberg game, where the operator dynamically sets the prices and the end-users optimally respond to them. Efficiently designing these price signals is challenging, as the users' response models are unknown or difficult to estimate. In this paper, we propose a learning-based zeroth-order algorithm for incentive design, in which the iterative update of the incentive signals is efficiently assisted by a data-driven online estimation of the users' responses. The proposed method is then proven to converge to an equilibrium tariff while allowing the DSO to estimate the decision-making problems at the user level. Moreover, the method preserves users' privacy, as the update rule of the DSO is solely based on observations of communicated end-user actions. Numerical simulations employing real-world data illustrate the efficient convergence of our learning-based proposed method, while significantly reducing the number of required interactions between the DSO and the end-users with respect to the state-of-the-art approach.

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arXiv2026

Induced Stackelberg Equilibrium Seeking via Iterative Tikhonov Regularization

Existing methods for learning Stackelberg equilibria typically assume that the followers' (variational, generalized) Nash equilibrium is unique. However, in the presence of multiple equilibria, without a selection convention, the problem may become ill-posed, thus leading standard algorithms to potentially fail to converge. This paper addresses this issue by introducing an optimal selection at the lower-level game, hereby defining a Stackelberg game with induced equilibrium selection. To this end, we enable the leader to augment the followers' game with an additional vanishing term that acts as an incentive. We then propose a follower-agnostic zeroth-order method, whereby the leader converges to a solution of the resulting problem by iteratively probing the followers and jointly updating its decision variable and the incentive term.

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arXiv2026

A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games

This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a solution algorithm with linear convergence rate. The fast convergence of the method enables receding-horizon control architectures. Furthermore, we demonstrate that {the associated VI admits a closed-form solution within a neighborhood of the attractor, thus allowing for a further reduction in computation time.} Finally, we benchmark the proposed method via numerical experiments in an automated driving application.

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arXiv2026

Locally Linear Convergence for Nonsmooth Convex Optimization via Coupled Smoothing and Momentum

We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function is the sum of two nonsmooth functions. With regard to convergence rate, we provide the global (optimal) sublinear convergence guarantees of O(1/k), which is known to be provably optimal for the studied class of functions, along with a local linear rate if the nonsmooth term fulfills a so-call locally strong convexity condition. We validate the performance of our algorithm on several problem classes, including regression with the l1-norm (the Lasso problem), sparse semidefinite programming (the MaxCut problem), Nuclear norm minimization with application in model free fault diagnosis, and l_1-regularized model predictive control to showcase the benefits of the coupling. An interesting observation is that although our global convergence result guarantees O(1/k) convergence, we consistently observe a practical transient convergence rate of O(1/k^2), followed by asymptotic linear convergence as anticipated by the theoretical result. This two-phase behavior can also be explained in view of the proposed smoothing rule.

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arXiv2026

Adversarially and Distributionally Robust Virtual Energy Storage Systems via the Scenario Approach

We study virtual energy storage services based on the aggregation of EV batteries in parking lots under time-varying, uncertain EV departures and state-of-charge limits. We propose a convex data-driven scheduling framework in which a parking lot manager provides storage services to a prosumer community while interacting with a retailer. The framework yields finite-sample, distribution-free guarantees on constraint violations and allows the parking lot manager to explicitly tune the trade-off between economic performance and operational safety. To enhance reliability under imperfect data, we extend the formulation to adversarial perturbations of the training samples and Wasserstein distributional shifts, obtaining robustness certificates against both corrupted data and out-of-distribution uncertainty. Numerical studies confirm the predicted profit-risk trade-off and show consistency between the theoretical certificates and the observed violation levels.

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arXiv2026

A Hybrid Algorithm for Monotone Variational Inequalities

Inspired by the adaptive Golden Ratio Algorithm (aGRAAL), we propose two new methods for solving monotone variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio in aGRAAL, the convergence speed can be improved, which motivates us to study the switching between small and large momentum parameters to accelerate convergence. We validate the performance of our proposed algorithms on several classes of variational inequality problems studied in the machine learning and control literature, including Nash equilibrium seeking, composite minimization, Markov decision processes, and zero-sum games, and compare them to that of existing methods.

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arXiv2026

Contingency Planning for Safety-Critical Autonomous Vehicles: A Review and Perspectives

Contingency planning is the architectural capability that enables autonomous vehicles (AVs) to anticipate and mitigate discrete, high-impact hazards, such as sensor outages and adversarial interactions. This paper presents a comprehensive survey of the field, synthesizing fragmented literature into a unified logic-conditioned hybrid control framework. Within this formalism, we categorize approaches into two distinct paradigms: Reactive Safety, which responds to realized hazards by enforcing safety constraints or executing fail-safe maneuvers; and Proactive Safety, which optimizes for future recourse by branching over potential modal transitions. In addition, we propose a fine-grained taxonomy that partitions the landscape into external contingencies (environmental and interactive hazards) and internal contingencies (system faults). Through a critical comparative analysis, we reveal a fundamental structural divergence: internal faults are predominantly addressed via reactive fail-safe mechanisms, whereas external interaction uncertainties increasingly require proactive branching strategies. Furthermore, we identify a critical methodological divergence: whereas physical hazards are typically managed with formal guarantees, semantic and out-of-distribution anomalies currently rely heavily on empirical validation. We conclude by identifying the open challenges in bridging the gap between theoretical guarantees and practical validation, advocating for hybrid architectures and standardized benchmarking to transition contingency planning from formulation to certifiable real-world deployment.

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arXiv2025

Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach

We study a class of distributionally robust games where agents are allowed to heterogeneously choose their risk aversion with respect to distributional shifts of the uncertainty. In our formulation, heterogeneous Wasserstein ball constraints on each distribution are enforced through a penalty function leveraging a Lagrangian formulation. We then formulate the distributionally robust Nash equilibrium problem and show that under certain assumptions it is equivalent to a finite-dimensional variational inequality problem with a strongly monotone mapping. We then design an approximate Nash equilibrium seeking algorithm and prove convergence of the average regret to a quantity that diminishes with the number of iterations, thus learning the desired equilibrium up to an a priori specified accuracy. Numerical simulations corroborate our theoretical findings.

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arXiv2025

A Frank-Wolfe Algorithm for Strongly Monotone Variational Inequalities

We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links.

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arXiv2025

On data-driven Wasserstein distributionally robust Nash equilibrium problems with heterogeneous uncertainty

We study stochastic Nash equilibrium problems subject to heterogeneous uncertainty on the expected valued cost functions of the individual agents, where we assume no prior knowledge of the underlying probability distributions of the uncertain variables. To account for this lack of knowledge, we consider an ambiguity set around the empirical probability distribution under the Wasserstein metric. We then show that, under mild assumptions, finite-sample guarantees on the probability that any resulting distributionally robust Nash equilibrium is also robust with respect to the true probability distributions with high confidence can be obtained. Furthermore, by recasting the game as a distributionally robust variational inequality, we establish asymptotic consistency of the set of data-driven distributionally robust equilibria to the solution set of the original game. Finally, we recast the distributionally robust Nash game as a finite-dimensional Nash equilibrium problem. We illustrate the proposed distributionally robust reformulation via numerical experiments of stochastic peer-to-peer electricity markets and Nash-Cournot games.

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