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We propose a Model Predictive Control (MPC) with a single-step prediction horizon to solve infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems. The proposed method relies on two techniques. First, we estimate the expected values of the convex costs using a computationally tractable approximation, achieved by sampling across the space of disturbances. Second, we implement a data-driven approach to approximate the optimal value function and its corresponding domain, through systematic exploration of the system's state space. These estimates are subsequently used as the terminal cost and terminal set within the proposed MPC. We prove recursive feasibility, robust constraint satisfaction, and convergence in probability to the target set. Furthermore, we prove that the estimated value function converges to the optimal value function in a local region. The effectiveness of the proposed MPC is illustrated with detailed numerical simulations and comparisons with a value iteration method and a Learning MPC that minimizes a certainty equivalent cost., Comment: Submitted to the IEEE Transactions on Automatic Control more...

We study the problem of stereo singing voice cancellation, a subtask of music source separation, whose goal is to estimate an instrumental background from a stereo mix. We explore how to achieve performance similar to large state-of-the-art source separation networks starting from a small, efficient model for real-time speech separation. Such a model is useful when memory and compute are limited and singing voice processing has to run with limited look-ahead. In practice, this is realised by adapting an existing mono model to handle stereo input. Improvements in quality are obtained by tuning model parameters and expanding the training set. Moreover, we highlight the benefits a stereo model brings by introducing a new metric which detects attenuation inconsistencies between channels. Our approach is evaluated using objective offline metrics and a large-scale MUSHRA trial, confirming the effectiveness of our techniques in stringent listening tests. more...

We study a two-dimensional Pauli operator describing a charged quantum particle with spin $1/2$ moving on a plane in presence of an orthogonal Aharonov-Bohm magnetic flux. We classify all the admissible self-adjont realizations and give a complete picture of their spectral and scattering properties. Symmetries of the resulting Hamiltonians are also discussed, as well as their connection with the Dirac operator perturbed by an Aharonov-Bohm singularity., Comment: 33 pages, pdfLaTeX, slightly enlarged and updated with respect to the previous version, to appear in J. Spectr. Theory. Prop. 2.26 corrected and Remark 2.27 added. Additional minor modifications more...

Motivated by various geometric problems, we study the nodal set of solutions to Dirac equations on manifolds, of general form. We prove that such set has Hausdorff dimension less than or equal to $n-2$, $n$ being the ambient dimension. We extend this result, previously known only in the smooth case or in specific cases, working with locally Lipschitz coefficients. Under some additional, but still quite general, structural assumptions we provide a stratification result for the nodal set, which appears to be new already in the smooth case. This is achieved by exploiting the properties of a suitable Almgren-type frequency function, which is of independent interest., Comment: 34 pages more...

We propose a Stochastic MPC (SMPC) formulation for path planning with autonomous vehicles in scenarios involving multiple agents with multi-modal predictions. The multi-modal predictions capture the uncertainty of urban driving in distinct modes/maneuvers (e.g., yield, keep speed) and driving trajectories (e.g., speed, turning radius), which are incorporated for multi-modal collision avoidance chance constraints for path planning. In the presence of multi-modal uncertainties, it is challenging to reliably compute feasible path planning solutions at real-time frequencies ($\geq$ 10 Hz). Our main technological contribution is a convex SMPC formulation that simultaneously (1) optimizes over parameterized feedback policies and (2) allocates risk levels for each mode of the prediction. The use of feedback policies and risk allocation enhances the feasibility and performance of the SMPC formulation against multi-modal predictions with large uncertainty. We evaluate our approach via simulations and road experiments with a full-scale vehicle interacting in closed-loop with virtual vehicles. We consider distinct, multi-modal driving scenarios: 1) Negotiating a traffic light and a fast, tailgating agent, 2) Executing an unprotected left turn at a traffic intersection, and 3) Changing lanes in the presence of multiple agents. For all of these scenarios, our approach reliably computes multi-modal solutions to the path-planning problem at real-time frequencies., Comment: The first three authors contributed equally more...

We present a novel method to measure the arrival time statistics of continuous electron beams with sub-ps resolution, based on the combination of an RF deflection cavity and fast single electron imaging. We observe Poissonian statistics within time bins from 100~ns to 2~ns and increasingly pronounced sub-Poissonian statistics as the time bin decreases from 2~ps to 340~fs. This 2D streak-camera in principle enables femtosecond-level arrival time measurements, paving the way to observing Pauli blocking effects in electron beams and thus serving as an essential diagnostic tool towards degenerate electron beam sources for free electron quantum optics. more...

This work presents a novel Learning Model Predictive Control (LMPC) strategy for autonomous racing at the handling limit that can iteratively explore and learn unknown dynamics in high-speed operational domains. We start from existing LMPC formulations and modify the system dynamics learning method. In particular, our approach uses a nominal, global, nonlinear, physics-based model with a local, linear, data-driven learning of the error dynamics. We conducted experiments in simulation and on 1/10th scale hardware, and deployed the proposed LMPC on a full-scale autonomous race car used in the Indy Autonomous Challenge (IAC) with closed loop experiments at the Putnam Park Road Course in Indiana, USA. The results show that the proposed control policy exhibits improved robustness to parameter tuning and data scarcity. Incremental and safety-aware exploration toward the limit of handling and iterative learning of the vehicle dynamics in high-speed domains is observed both in simulations and experiments., Comment: Accepted by ICRA 2024 more...

We present two quadrotor raceline optimization approaches which differ in using Euclidean or non-Euclidean geometry to describe vehicle position. Both approaches use high-fidelity quadrotor dynamics and avoid the need to approximate gates using waypoints. We demonstrate both approaches on simulated racetracks with realistic vehicle parameters where we demonstrate 100x faster compute time than comparable published methods and improved solver convergence. We then extend the non-Euclidean approach to compute racelines in the presence of numerous static obstacles. more...

Challenges drive the state-of-the-art of automated medical image analysis. The quantity of public training data that they provide can limit the performance of their solutions. Public access to the training methodology for these solutions remains absent. This study implements the Type Three (T3) challenge format, which allows for training solutions on private data and guarantees reusable training methodologies. With T3, challenge organizers train a codebase provided by the participants on sequestered training data. T3 was implemented in the STOIC2021 challenge, with the goal of predicting from a computed tomography (CT) scan whether subjects had a severe COVID-19 infection, defined as intubation or death within one month. STOIC2021 consisted of a Qualification phase, where participants developed challenge solutions using 2000 publicly available CT scans, and a Final phase, where participants submitted their training methodologies with which solutions were trained on CT scans of 9724 subjects. The organizers successfully trained six of the eight Final phase submissions. The submitted codebases for training and running inference were released publicly. The winning solution obtained an area under the receiver operating characteristic curve for discerning between severe and non-severe COVID-19 of 0.815. The Final phase solutions of all finalists improved upon their Qualification phase solutions.HSUXJM-TNZF9CHSUXJM-TNZF9C more...

We present a data-driven optimization approach for robotic controlled deposition with a degradable tool. Existing methods make the assumption that the tool tip is not changing or is replaced frequently. Errors can accumulate over time as the tool wears away and this leads to poor performance in the case where the tool degradation is unaccounted for during deposition. In the proposed approach, we utilize visual and force feedback to update the unknown model parameters of our tool-tip. Subsequently, we solve a constrained finite time optimal control problem for tracking a reference deposition profile, where our robot plans with the learned tool degradation dynamics. We focus on a robotic drawing problem as an illustrative example. Using real-world experiments, we show that the error in target vs actual deposition decreases when learned degradation models are used in the control design., Comment: To be published in the proceedings of IFAC World Congress 2023 more...

This work presents a novel hierarchical approach to increase Battery Electric Buses (BEBs) utilization in transit fleets. The proposed approach relies on three key components. A learning-based BEB digital twin cloud platform is used to accurately predict BEB charge consumption on a per vehicle, per driver, and per route basis, and accurately predict the time-to-charge BEB batteries to any level. These predictions are then used by a Predictive Block Assignment module to maximize the BEB fleet utilization. This module computes the optimal BEB daily assignment and charge management strategy. A Depot Parking and Charging Queue Management module is used to autonomously park and charge the vehicles based on their charging demands. The paper discusses the technical approach and benefits of each level in architecture and concludes with a realistic simulations study. The study shows that if our approach is employed, BEB fleet utilization can increase by 50% compared to state-of-the-art methods., Comment: Accepted at the 35th IEEE Intelligent Vehicles Symposium (IV 2023) more...

Current-induced bond rupture is a fundamental process in nanoelectronic architectures such as molecular junctions and in scanning tunneling microscopy measurements of molecules at surfaces. The understanding of the underlying mechanisms is important for the design of molecular junctions that are stable at higher bias voltages and is a prerequisite for further developments in the field of current-induced chemistry. In this work, we analyse the mechanisms of current-induced bond rupture employing a recently developed method, which combines the hierarchical equations of motion approach in twin space with the matrix product state formalism, and allows accurate, fully quantum mechanical simulations of the complex bond rupture dynamics. Extending previous work [J. Chem. Phys. 154, 234702 (2021)], we consider specifically the effect of multiple electronic states and multiple vibrational modes. The results obtained for a series of models of increasing complexity show the importance of vibronic coupling between different electronic states of the charged molecule, which can enhance the dissociation rate at low bias voltages profoundly. more...

This paper presents a novel energy-efficient motion planning algorithm for Connected Autonomous Vehicles (CAVs) on urban roads. The approach consists of two components: a decision-making algorithm and an optimization-based trajectory planner. The decision-making algorithm leverages Signal Phase and Timing (SPaT) information from connected traffic lights to select a lane with the aim of reducing energy consumption. The algorithm is based on a heuristic rule which is learned from human driving data. The optimization-based trajectory planner generates a safe, smooth, and energy-efficient trajectory toward the selected lane. The proposed strategy is experimentally evaluated in a Vehicle-in-the-Loop (VIL) setting, where a real test vehicle receives SPaT information from both actual and virtual traffic lights and autonomously drives on a testing site, while the surrounding vehicles are simulated. The results demonstrate that the use of SPaT information in autonomous driving leads to improved energy efficiency, with the proposed strategy saving 37.1% energy consumption compared to a lane-keeping algorithm., Comment: IEEE Intelligent Vehicle Symposium, Anchorage, Alaska, June 4-7, 2023 more...

We build an explicit $C^1$ isometric embedding $f_{\infty}:\mathbb{H}^2\to\mathbb{E}^3$ of the hyperbolic plane whose image is relatively compact. Its limit set is a closed curve of Hausdorff dimension 1. Given an initial embedding $f_0$, our construction generates iteratively a sequence of maps by adding at each step $k$ a layer of $N_{k}$ corrugations. To understand the behavior of $df_\infty$ we introduce a $formal$ $corrugation$ $process$ leading to a $formal$ $analogue$ $\Phi_{\infty}:\mathbb{H}^2\to \mathcal{L}(\mathbb{R}^2,\mathbb{R}^3)$. We show a self-similarity structure for $\Phi_{\infty}$. We next prove that $df_\infty$ is close to $\Phi_{\infty}$ up to a precision that depends on the sequence $N_*:= (N_{k})_k$. We then introduce the $pattern$ $maps$ $\boldsymbol{\nu}_{\infty}^\Phi$ and $\boldsymbol{\nu}_{\infty}$, of respectively $\Phi_{\infty}$ and $df_\infty$, that together with $df_0$ entirely describe the geometry of the Gauss maps associated to $\Phi_{\infty}$ and $df_\infty$. For well chosen sequences of corrugation numbers, we finally show an asymptotic convergence of $\boldsymbol{\nu}_{\infty}$ towards $\boldsymbol{\nu}_{\infty}^\Phi$ over circles of rational radii., Comment: 51 pages, 8 figures more...

We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions. Inspired by Branch-and-Bound techniques, the key idea is to train a Neural Network/Random Forest, which for a given parameter, predicts a strategy consisting of (1) a set of Linear Programs (LPs) such that their feasible sets form a partition of the feasible set of the MILP and (2) a candidate integer solution. For control computation and sub-optimality quantification, we solve a set of LPs online in parallel. We demonstrate our approach for a motion planning example and compare against various commercial and open-source mixed-integer programming solvers., Comment: First two authors contributed equally more...

We propose an iterative approach for designing Robust Learning Model Predictive Control (LMPC) policies for a class of nonlinear systems with additive, unmodelled dynamics. The nominal dynamics are assumed to be difference flat, i.e., the state and input can be reconstructed using flat output sequences. For the considered class of systems, we synthesize Robust MPC policies and show how to use historical trajectory data collected during iterative tasks to 1) obtain bounds on the unmodelled dynamics and 2) construct a convex value function approximation along with a convex safe set in the space of output sequences for designing terminal components in the Robust MPC design. We show that the proposed strategy guarantees robust constraint satisfaction, asymptotic convergence to a desired subset of the state space, and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on a minimum time control problem using a constrained nonlinear and uncertain vehicle model. more...

We present an output feedback stochastic model predictive controller (SMPC) for constrained linear time-invariant systems. The system is perturbed by additive Gaussian disturbances on state and additive Gaussian measurement noise on output. A Kalman filter is used for state estimation and an SMPC is designed to satisfy chance constraints on states and hard constraints on actuator inputs. The proposed SMPC constructs bounded sets for the state evolution and a tube-based constraint tightening strategy where the tightened constraints are time-invariant. We prove that the proposed SMPC can guarantee an infeasibility rate below a user-specified tolerance. We numerically compare our method with a classical output feedback SMPC with simulation results which highlight the efficacy of the proposed algorithm., Comment: IEEE American Control Conference (ACC) 2023, May 31 - June 2, San Diego, CA, USA more...

This work presents a distributed algorithm for resolving cooperative multi-vehicle conflicts in highly constrained spaces. By formulating the conflict resolution problem as a Multi-Agent Reinforcement Learning (RL) problem, we can train a policy offline to drive the vehicles towards their destinations safely and efficiently in a simplified discrete environment. During the online execution, each vehicle first simulates the interaction among vehicles with the trained policy to obtain its strategy, which is used to guide the computation of a reference trajectory. A distributed Model Predictive Controller (MPC) is then proposed to track the reference while avoiding collisions. The preliminary results show that the combination of RL and distributed MPC has the potential to guide vehicles to resolve conflicts safely and smoothly while being less computationally demanding than the centralized approach. more...

A distributed coordination method for solving multi-vehicle lane changes for connected autonomous vehicles (CAVs) is presented. Existing approaches to multi-vehicle lane changes are passive and opportunistic as they are implemented only when the environment allows it. The novel approach of this paper relies on the role of a facilitator assigned to a CAV. The facilitator interacts with and modifies the environment to enable lane changes of other CAVs. Distributed MPC path planners and a distributed coordination algorithm are used to control the facilitator and other CAVs in a proactive and cooperative way. We demonstrate the effectiveness of the proposed approach through numerical simulations. In particular, we show enhanced feasibility of a multi-CAV lane change in comparison to the simultaneous multi-CAV lane change approach in various traffic conditions generated by using a data-set from real-traffic scenarios., Comment: 8 pages, 4 figures. Accepted at IFAC World Congress 2023 more...