arXiv subjects

Laurent El Ghaoui

Publications and source records attributed to Laurent El Ghaoui.

At least 19 recordsLinked to original sources

arXiv2026

Implicit Neural Networks as Static Controllers: Certificates and Performance Separation

Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller as a trainable linear interconnection closed through a known static activation map, thereby making well-posedness and Lyapunov/IQC analysis mathematically easy to handle. For finite-dimensional LTI plants, we first develop a rigorous analysis theory for a given INC, including Perron--Frobenius and norm conditions for well posedness, LMI/IQC certificates for exponential stability, and LMIs for discounted infinite-horizon quadratic performance. We then formulate synthesis as a certification-compatible heuristic search: training is carried out under explicit well-posedness constraints, implicit-differentiation formulas provide gradients, and the resulting controller is accepted only after independent post-training LMIs or regional admissibility checks are feasible. Finally, we establish constrained-control separation results: for a specific scalar unstable plant with hard actuator bounds, an INC achieves a strictly smaller discounted infinite-horizon cost than any admissible finite-order dynamic linear controller. Additional results cover quadratic state-input costs, comparison with linear static output feedback, and computable upper/lower-bound certificates. Numerical examples illustrate the mechanism and the resulting certified performance.

eess.SY↗

arXiv2026

A Distributionally Robust Reinforcement Learning Framework for Constrained Urban EV Dispatch

We study city-scale control of electric-vehicle (EV) ride-hailing fleets where dispatch, repositioning, and charging decisions must respect charger and feeder limits under uncertain, spatially correlated demand and travel times. We formulate the problem as a hex-grid semi-Markov decision process (semi-MDP) with mixed actions -- discrete actions for serving, repositioning, and charging, together with continuous charging power -- and variable action durations. To guarantee physical feasibility during both training and deployment, the policy learns over high-level intentions produced by a masked, temperature-annealed actor. These intentions are projected at every decision step through a time-limited rolling mixed-integer linear program (MILP) that strictly enforces state-of-charge, port, and feeder constraints. To mitigate distributional shifts, we optimize a Soft Actor-Critic (SAC) agent against a Wasserstein-1 ambiguity set with a graph-aligned Mahalanobis ground metric that captures spatial correlations. The robust backup uses the Kantorovich-Rubinstein dual, a projected subgradient inner loop, and a primal-dual risk-budget update. Our architecture combines a two-layer Graph Convolutional Network (GCN) encoder, twin critics, and a value network that drives the adversary. Experiments on a large-scale EV fleet simulator built from NYC taxi data show that PD-RSAC achieves the highest net profit, reaching \$1.22M, compared with \$0.58M-\$0.70M for strong heuristic, single-agent RL, and multi-agent RL baselines, including Greedy, SAC, MAPPO, and MADDPG, while maintaining zero feeder-limit violations.

cs.AI↗

arXiv2026

Class-Based Smart Charging Control for Electric Vehicles

This paper proposes a stochastic control framework for the operation of electric-vehicle (EV) charging stations equipped with on-site photovoltaic (PV) generation and battery storage. To preserve scalability for large fleets, vehicles are aggregated into a finite number of classes according to their residual charging demand, yielding a compact state description and avoiding vehicle-level optimization. The charging-station dynamics are modeled in discrete time and capture stochastic arrivals, charging-induced class transitions, stochastic departures, PV generation, battery operation, and power exchange with the grid. Based on the corresponding expectation model, we formulate a finite-horizon smart-charging problem that jointly optimizes class-wise charging actions and energy-management variables to balance electricity-purchase cost and transitions toward lower residual-demand classes. The resulting stage problem is a linear program, solved in shrinking-horizon form and implemented online after integer discretization of the first charging action. We also derive a robust counterpart that preserves feasibility under interval uncertainty on the first moments of arrivals, departures, and PV generation. To validate scalability and robustness, we conduct an extensive simulation campaign across nine configurations, combining three real-world electricity price patterns with three EV-arrival profiles. Numerical results show that, at comparable but slightly lower service levels, the proposed controller reduces the cost per kWh by up to 17.5% relative to a service-greedy First-In-First-Out baseline; the total daily cost decreases even more substantially because the controller avoids economically unattractive charging. Overall, the results demonstrate a tunable Pareto trade-off between economic efficiency and charging-service quality for large-scale charging hubs.

math.OC↗

arXiv2026

A Digital Twin Framework for Decision-Support and Optimization of EV Charging Infrastructure in Localized Urban Systems

As Electric Vehicle (EV) adoption accelerates in urban environments, optimizing charging infrastructure is vital for balancing user satisfaction, energy efficiency, and financial viability. This study advances beyond static models by proposing a digital twin framework that integrates agent-based decision support with embedded optimization to dynamically simulate EV charging behaviors, infrastructure layouts, and policy responses across scenarios. Applied to a localized urban site (a university campus) in Hanoi, Vietnam, the model evaluates operational policies, EV station configurations, and renewable energy sources. The interactive dashboard enables seasonal analysis, revealing a 20% drop in solar efficiency from October to March, with wind power contributing under 5% of demand, highlighting the need for adaptive energy management. Simulations show that dynamic notifications of newly available charging slots improve user satisfaction, while gasoline bans and idle fees enhance slot turnover with minimal added complexity. Embedded metaheuristic optimization identifies near-optimal mixes of fast (30kW) and standard (11kW) solar-powered chargers, balancing energy performance, profitability, and demand with high computational efficiency. This digital twin provides a flexible, computation-driven platform for EV infrastructure planning, with a transferable, modular design that enables seamless scaling from localized to city-wide urban contexts.

eess.SY↗

arXiv2026

A Multi-Criterion Approach to Smart EV Charging with CO2 Emissions and Cost Minimization

We study carbon-aware smart charging in a fossil-dominated grid by coupling a simplified hydro-thermal-renewable dispatch model with a tractable linear charging scheduler. The case study is informed by Vietnam's regional data. Thermal units remain dominant, renewables are time-varying, and hydropower is modeled through a single reservoir budget. From the day-ahead dispatch we derive hourly carbon intensity and a corresponding carbon-cost signal; these are combined with a local time-of-use tariff in the EV charging problem. The resulting weighted-sum linear program is multi-objective: by sweeping the trade-off coefficient, we recover the supported Pareto frontier between electricity cost and charging-associated emissions. In a 300-EV public-charging scenario with a 0.8 MW feeder cap, the proposed carbon-aware scheduler preserves the 19.8% bill reduction of a cost-only optimizer while lowering charging-associated emissions by 7.3%; a more carbon-focused tuning still remains 12.6% cheaper and 9.3% cleaner than a FIFO baseline. A hydro-sensitivity study shows that changing the reservoir budget by +/- 20% moves the mean grid carbon intensity from 360 to 466 g/kWh, yet the carbon-aware scheduler remains consistently cheaper and cleaner than FIFO. The dispatch and charging LPs solve in few milliseconds on a standard desktop computer, showing that the framework is lightweight enough for repeated day-ahead studies.

eess.SY↗

arXiv2025

Electric Vehicle Routing Problem with Time Windows and Station-based or Route-based Charging Options

The Electric Vehicle Routing Problem with Time Windows and Station-based or Route-based Charging Options addresses fleet optimization incorporating both conventional charging stations and continuous wireless charging infrastructure. This paper extends Schneider et al.'s foundational EVRP-TW model with arc-based dynamic wireless charging representation, partial coverage modeling, and hierarchical multi-objective optimization prioritizing fleet minimization. Computational experiments on Schneider benchmark instances demonstrate substantial operational benefits, with distance and time improvements ranging from 0.7% to 35.9% in secondary objective components. Analysis reveals that 20% wireless coverage achieves immediate benefits, while 60% coverage delivers optimal performance across all test instances for infrastructure investment decisions.

eess.SY↗

arXiv2025

Tree-Sliced Wasserstein Distance with Nonlinear Projection

Tree-Sliced methods have recently emerged as an alternative to the traditional Sliced Wasserstein (SW) distance, replacing one-dimensional lines with tree-based metric spaces and incorporating a splitting mechanism for projecting measures. This approach enhances the ability to capture the topological structures of integration domains in Sliced Optimal Transport while maintaining low computational costs. Building on this foundation, we propose a novel nonlinear projectional framework for the Tree-Sliced Wasserstein (TSW) distance, substituting the linear projections in earlier versions with general projections, while ensuring the injectivity of the associated Radon Transform and preserving the well-definedness of the resulting metric. By designing appropriate projections, we construct efficient metrics for measures on both Euclidean spaces and spheres. Finally, we validate our proposed metric through extensive numerical experiments for Euclidean and spherical datasets. Applications include gradient flows, self-supervised learning, and generative models, where our methods demonstrate significant improvements over recent SW and TSW variants.

cs.LG↗

arXiv2025

Naive Feature Selection: a Nearly Tight Convex Relaxation for Sparse Naive Bayes

Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This leads to a combinatorial maximum-likelihood problem, for which we provide an exact solution in the case of binary data, or a bound in the multinomial case. We prove that our convex relaxation bounds becomes tight as the marginal contribution of additional features decreases, using a priori duality gap bounds dervied from the Shapley-Folkman theorem. We show how to produce primal solutions satisfying these bounds. Both binary and multinomial sparse models are solvable in time almost linear in problem size, representing a very small extra relative cost compared to the classical naive Bayes. Numerical experiments on text data show that the naive Bayes feature selection method is as statistically effective as state-of-the-art feature selection methods such as recursive feature elimination, $l_1$-penalized logistic regression and LASSO, while being orders of magnitude faster.

cs.LG↗

arXiv2025

A Robust Optimization Model for Cost-Efficient and Fast Electric Vehicle Charging with L2-norm Uncertainty

In this paper, we propose a robust optimization model that addresses both the cost-efficiency and fast charging requirements for electric vehicles (EVs) at charging stations. By combining elements from traditional cost-minimization models and a fast charging objective, we construct an optimization model that balances user costs with rapid power allocation. Additionally, we incorporate L2-norm uncertainty into the charging cost, ensuring that the model remains resilient under cost fluctuations. The proposed model is tested under real-world scenarios and demonstrates its potential for efficient and flexible EV charging solutions.

eess.SY↗

arXiv2024

Optimizing electric vehicles charging through smart energy allocation and cost-saving

As the global focus on combating environmental pollution intensifies, the transition to sustainable energy sources, particularly in the form of electric vehicles (EVs), has become paramount. This paper addresses the pressing need for Smart Charging for EVs by developing a comprehensive mathematical model aimed at optimizing charging station management. The model aims to efficiently allocate the power from charging sockets to EVs, prioritizing cost minimization and avoiding energy waste. Computational simulations demonstrate the efficacy of the mathematical optimization model, which can unleash its full potential when the number of EVs at the charging station is high.

math.OC↗

arXiv2024

The Extrapolation Power of Implicit Models

In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer depth and incorporation of feedback within their computational graph, are put to the test across various extrapolation scenarios: out-of-distribution, geographical, and temporal shifts. Our experiments consistently demonstrate significant performance advantage with implicit models. Unlike their non-implicit counterparts, which often rely on meticulous architectural design for each task, implicit models demonstrate the ability to learn complex model structures without the need for task-specific design, highlighting their robustness in handling unseen data.

cs.LG↗

arXiv2022

State-driven Implicit Modeling for Sparsity and Robustness in Neural Networks

Implicit models are a general class of learning models that forgo the hierarchical layer structure typical in neural networks and instead define the internal states based on an ``equilibrium'' equation, offering competitive performance and reduced memory consumption. However, training such models usually relies on expensive implicit differentiation for backward propagation. In this work, we present a new approach to training implicit models, called State-driven Implicit Modeling (SIM), where we constrain the internal states and outputs to match that of a baseline model, circumventing costly backward computations. The training problem becomes convex by construction and can be solved in a parallel fashion, thanks to its decomposable structure. We demonstrate how the SIM approach can be applied to significantly improve sparsity (parameter reduction) and robustness of baseline models trained on FashionMNIST and CIFAR-100 datasets.

cs.LG↗

arXiv2022

Stochastic Frank-Wolfe for Constrained Finite-Sum Minimization

We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization with sparse, low-rank, or other structured constraints. The proposed method is simple to implement, does not require step-size tuning, and has a constant per-iteration cost that is independent of the dataset size. Furthermore, as a byproduct of the method we obtain a stochastic estimator of the Frank-Wolfe gap that can be used as a stopping criterion. Depending on the setting, the proposed method matches or improves on the best computational guarantees for Stochastic Frank-Wolfe algorithms. Benchmarks on several datasets highlight different regimes in which the proposed method exhibits a faster empirical convergence than related methods. Finally, we provide an implementation of all considered methods in an open-source package.

math.OC↗

arXiv2022

Sparse Optimization for Unsupervised Extractive Summarization of Long Documents with the Frank-Wolfe Algorithm

We address the problem of unsupervised extractive document summarization, especially for long documents. We model the unsupervised problem as a sparse auto-regression one and approximate the resulting combinatorial problem via a convex, norm-constrained problem. We solve it using a dedicated Frank-Wolfe algorithm. To generate a summary with $k$ sentences, the algorithm only needs to execute $\approx k$ iterations, making it very efficient. We explain how to avoid explicit calculation of the full gradient and how to include sentence embedding information. We evaluate our approach against two other unsupervised methods using both lexical (standard) ROUGE scores, as well as semantic (embedding-based) ones. Our method achieves better results with both datasets and works especially well when combined with embeddings for highly paraphrased summaries.

cs.CL↗

arXiv2021

Data-Driven Reachability analysis and Support set Estimation with Christoffel Functions

We present algorithms for estimating the forward reachable set of a dynamical system using only a finite collection of independent and identically distributed samples. The produced estimate is the sublevel set of a function called an empirical inverse Christoffel function: empirical inverse Christoffel functions are known to provide good approximations to the support of probability distributions. In addition to reachability analysis, the same approach can be applied to general problems of estimating the support of a random variable, which has applications in data science towards detection of novelties and outliers in data sets. In applications where safety is a concern, having a guarantee of accuracy that holds on finite data sets is critical. In this paper, we prove such bounds for our algorithms under the Probably Approximately Correct (PAC) framework. In addition to applying classical Vapnik-Chervonenkis (VC) dimension bound arguments, we apply the PAC-Bayes theorem by leveraging a formal connection between kernelized empirical inverse Christoffel functions and Gaussian process regression models. The bound based on PAC-Bayes applies to a more general class of Christoffel functions than the VC dimension argument, and achieves greater sample efficiency in experiments.

eess.SY↗

arXiv2021

Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems

Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many cases, requires controllers to retain and process long-term memories of the past. We consider the important class of recurrent neural networks (RNN) as dynamic controllers for nonlinear uncertain partially-observed systems, and derive convex stability conditions based on integral quadratic constraints, S-lemma and sequential convexification. To ensure stability during the learning and control process, we propose a projected policy gradient method that iteratively enforces the stability conditions in the reparametrized space taking advantage of mild additional information on system dynamics. Numerical experiments show that our method learns stabilizing controllers while using fewer samples and achieving higher final performance compared with policy gradient.

eess.SY↗

arXiv2021

Learning-based Initialization Strategy for Safety of Multi-Vehicle Systems

Multi-vehicle collision avoidance is a highly crucial problem due to the soaring interests of introducing autonomous vehicles into the real world in recent years. The safety of these vehicles while they complete their objectives is of paramount importance. Hamilton-Jacobi (HJ) reachability is a promising tool for guaranteeing safety for low-dimensional systems. However, due to its exponential complexity in computation time, no reachability-based methods have been able to guarantee safety for more than three vehicles successfully in unstructured scenarios. For systems with four or more vehicles,we can only empirically validate their safety performance.While reachability-based safety methods enjoy a flexible least-restrictive control strategy, it is challenging to reason about long-horizon trajectories online because safety at any given state is determined by looking up its safety value in a pre-computed table that does not exhibit favorable properties that continuous functions have. This motivates the problem of improving the safety performance of unstructured multi-vehicle systems when safety cannot be guaranteed given any least-restrictive safety-aware collision avoidance algorithm while avoiding online trajectory optimization. In this paper, we propose a novel approach using supervised learning to enhance the safety of vehicles by proposing new initial states in very close neighborhood of the original initial states of vehicles. Our experiments demonstrate the effectiveness of our proposed approach and show that vehicles are able to get to their goals with better safety performance with our approach compared to a baseline approach in wide-ranging scenarios.

cs.RO↗

arXiv2021

Reachability-based Safe Planning for Multi-Vehicle Systems withMultiple Targets

Recently there have been a lot of interests in introducing UAVs for a wide range of applications, making ensuring safety of multi-vehicle systems a highly crucial problem. Hamilton-Jacobi (HJ) reachability is a promising tool for analyzing safety of vehicles for low-dimensional systems. However, reachability suffers from the curse of dimensionality, making its direct application to more than two vehicles intractable. Recent works have made it tractable to guarantee safety for 3 and 4 vehicles with reachability. However, the number of vehicles safety can be guaranteed for remains small. In this paper, we propose a novel reachability-based approach that guarantees safety for any number of vehicles while vehicles complete their objectives of visiting multiple targets efficiently, given any K-vehicle collision avoidance algorithm where K can in general be a small number. We achieve this by developing an approach to group vehicles into clusters efficiently and a control strategy that guarantees safety for any in-cluster and cross-cluster pair of vehicles for all time. Our proposed method is scalable to large number of vehicles with little computation overhead. We demonstrate our proposed approach with a simulation on 15 vehicles. In addition, we contribute a more general solution to the 3-vehicle collision avoidance problem from a past recent work, show that the prior work is a special case of our proposed generalization, and prove its validity.

cs.RO↗