Scott Moura

Shida Jiang, Junzhe Shi, Scott Moura

The Kalman filter (KF) is an optimal linear state estimator for linear systems, and numerous extensions, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF), have been developed for nonlinear systems. Although these nonlinear KFs differ in how they approximate nonlinear transformations, they all retain the same update framework as the linear KF. In this paper, we show that, under nonlinear measurements, this conventional framework inherently tends to underestimate the true posterior covariance, leading to overconfident covariance estimates. To the best of our knowledge, this is the first work to provide a mathematical proof of this systematic covariance underestimation in a general nonlinear KF framework. Motivated by this analysis, we propose a covariance-recalibrated framework that re-approximates the measurement model after the state update to better capture the actual effect of the Kalman gain on the posterior covariance; when recalibration indicates that an update is harmful, the update can be withdrawn. The proposed framework can be combined with essentially any existing nonlinear KF, and simulations across four nonlinear KFs and five applications show that it substantially improves both state and covariance estimation accuracy, often reducing errors by several orders of magnitude. The code and supplementary material are available at https://github.com/Shida-Jiang/A-new-framework-for-nonlinear-Kalman-filters.

Shida Jiang, Jaewoong Lee, Shengyu Tao et al.

Nonlinear extensions of the Kalman filter (KF), such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are indispensable for state estimation in complex dynamical systems, yet the conditions for a nonlinear KF to provide robust and accurate estimations remain poorly understood. This work proposes a theoretical framework that identifies the causes of failure and success in certain nonlinear KFs and establishes guidelines for their improvement. Central to our framework is the concept of covariance compensation: the deviation between the covariance predicted by a nonlinear KF and that of the EKF. With this definition and detailed theoretical analysis, we derive three design guidelines for nonlinear KFs: (i) invariance under orthogonal transformations, (ii) sufficient covariance compensation beyond the EKF baseline, and (iii) selection of compensation magnitude that favors underconfidence. Both theoretical analysis and empirical validation confirm that adherence to these principles significantly improves estimation accuracy, whereas fixed parameter choices commonly adopted in the literature are often suboptimal. The codes and the proofs for all the theorems in this paper are available at https://github.com/Shida-Jiang/Guidelines-for-Nonlinear-Kalman-Filters.

Upadhi Vijay, Soomin Woo, Scott J. Moura et al.

This research provides a novel framework to estimate the economic, environmental, and social values of electrifying public transit buses, for cities across the world, based on open-source data. Electric buses are a compelling candidate to replace diesel buses for the environmental and social benefits. However, the state-of-art models to evaluate the value of bus electrification are limited in applicability because they require granular and bespoke data on bus operation that can be difficult to procure. Our valuation tool uses General Transit Feed Specification, a standard data format used by transit agencies worldwide, to provide high-level guidance on developing a prioritization strategy for electrifying a bus fleet. We develop physics-informed machine learning models to evaluate the energy consumption, the carbon emissions, the health impacts, and the total cost of ownership for each transit route. We demonstrate the scalability of our tool with a case study of the bus lines in the Greater Boston and Milan metropolitan areas.

Sangjae Bae, Yeojun Kim, Jacopo Guanetti et al.

This paper presents the design and implementation results of an ecological adaptive cruise controller (ECO-ACC) which exploits driving automation and connectivity. The controller avoids front collisions and traffic light violations, and is designed to reduce the energy consumption of connected automated vehicles by utilizing historical and real-time signal phase and timing data of traffic lights that adapt to the current traffic conditions. We propose an optimization-based generation of a reference velocity, and a velocity-tracking model predictive controller that avoids front collisions and violations. We present an experimental setup encompassing the real vehicle and controller in the loop, and an environment simulator in which the traffic flow and the traffic light patterns are calibrated on real-world data. We present and analyze simulation and experimental results, finding a significant potential for energy consumption reduction, even in the presence of traffic.

Shida Jiang, Shengyu Tao, Vincent Molina et al.

A conventional electric vehicle (EV) powertrain relies on a centralized high-voltage DC-AC inverter, thereby limiting cell-level control and potentially reducing overall driving range and battery lifetime. This paper studies an H-bridge-based cell-level inverter topology that performs power conversion at the cell level, enabling independent control of individual cells and expanding the design space for battery management. Leveraging these additional degrees of freedom, we propose a model-agnostic energy-throughput control strategy that extends EV range while improving battery-pack lifetime. Because usable energy (and thus driving range) and lifetime are governed by the cells with the lowest state-of-charge (SOC) and state-of-health (SOH), respectively, the proposed controller preferentially routes energy throughput to healthier cells. Specifically, during charging, it permits cell SOCs to diverge to promote SOH equalization; during discharging, it rebalances SOC to maximize usable capacity under per-cell constraints. The proposed SOC-SOH-aware control strategy is evaluated on two aging models representing lithium manganese oxide and lithium iron phosphate chemistries, using a Tesla Model 3 charge-discharge profile across 14 different parameter settings. Simulations show a 7-38% improvement in lifetime relative to a conventional SOC-only balancing baseline. More broadly, the results suggest a software-defined pathway to extend EV pack life through routine charging, with minimal reliance on specific degradation models or discharge profiles.

Caroline Le Floch, Somil Bansal, Claire J. Tomlin et al.

This paper presents a predictive controller for handling plug-and-play (P&P) charging requests of flexible loads in a distribution system. We define two types of flexible loads: (i) deferrable loads that have a fixed power profile but can be deferred in time and (ii) shapeable loads that have flexible power profiles but fixed energy requests, such as Plug-in Electric Vehicles (PEVs). The proposed method uses a hierarchical control scheme based on a model predictive control (MPC) formulation for minimizing the global system cost. The first stage computes a reachable reference that trades off deviation from the nominal voltage with the required generation control. The second stage uses a price-based objective to aggregate flexible loads and provide load shaping services, while satisfying system constraints and users' preferences at all times. It is shown that the proposed controller is recursively feasible under specific conditions, i.e. the flexible load demands are satisfied and bus voltages remain within the desired limits. Finally, the proposed scheme is illustrated on a 55 bus radial distribution network.

Chao Sun, Xinwei Shen, Scott Moura

This paper proposes a robust optimal eco-driving control strategy considering multiple signalized intersections with uncertain traffic signal timing. A spatial vehicle velocity profile optimization formulation is developed to minimize the global fuel consumption, with driving time as one state variable. We introduce the concept of effective red-light duration (ERD), formulated as a random variable, to describe the feasible passing time through signalized intersections. A chance constraint is appended to the optimal control problem to incorporate robustness with respect to uncertain signal timing. The optimal eco-driving control problem is solved via dynamic programming (DP). Simulation results demonstrate that the optimal eco-driving can save fuel consumption by 50-57% while maintaining arrival time at the same level, compared with a modified intelligent driver model as the benchmark. The robust formulation significantly reduces traffic intersection violations, in the face of uncertain signal timing, with small sacrifice on fuel economy compared to a non-robust approach.

Dimitris M. Vlachogiannis, Hua Wei, Scott Moura et al.

Single occupancy vehicles are the most attractive transportation alternative for many commuters, leading to increased traffic congestion and air pollution. Advancements in information technologies create opportunities for smart solutions that incentivize ridesharing and mode shift to higher occupancy vehicles (HOVs) to achieve the car lighter vision of cities. In this study, we present HumanLight, a novel decentralized adaptive traffic signal control algorithm designed to optimize people throughput at intersections. Our proposed controller is founded on reinforcement learning with the reward function embedding the transportation-inspired concept of pressure at the person-level. By rewarding HOV commuters with travel time savings for their efforts to merge into a single ride, HumanLight achieves equitable allocation of green times. Apart from adopting FRAP, a state-of-the-art (SOTA) base model, HumanLight introduces the concept of active vehicles, loosely defined as vehicles in proximity to the intersection within the action interval window. The proposed algorithm showcases significant headroom and scalability in different network configurations considering multimodal vehicle splits at various scenarios of HOV adoption. Improvements in person delays and queues range from 15% to over 55% compared to vehicle-level SOTA controllers. We quantify the impact of incorporating active vehicles in the formulation of our RL model for different network structures. HumanLight also enables regulation of the aggressiveness of the HOV prioritization. The impact of parameter setting on the generated phase profile is investigated as a key component of acyclic signal controllers affecting pedestrian waiting times. HumanLight's scalable, decentralized design can reshape the resolution of traffic management to be more human-centric and empower policies that incentivize ridesharing and public transit systems.

Yi Ju, Jiaman Wu, Zhihan Su et al.

Electric vehicle (EV) charging infrastructure is crucial for advancing EV adoption, managing charging loads, and ensuring equitable transportation electrification. However, there remains a notable gap in comprehensive accessibility metrics that integrate the mobility of the users. This study introduces a novel accessibility metric, termed Trajectory-Integrated Public EVCS Accessibility (TI-acs), and uses it to assess public electric vehicle charging station (EVCS) accessibility for approximately 6 million residents in the San Francisco Bay Area based on detailed individual trajectory data in one week. Unlike conventional home-based metrics, TI-acs incorporates the accessibility of EVCS along individuals' travel trajectories, bringing insights on more public charging contexts, including public charging near workplaces and charging during grid off-peak periods. As of June 2024, given the current public EVCS network, Bay Area residents have, on average, 7.5 hours and 5.2 hours of access per day during which their stay locations are within 1 km (i.e. 10-12 min walking) of a public L2 and DCFC charging port, respectively. Over the past decade, TI-acs has steadily increased from the rapid expansion of the EV market and charging infrastructure. However, spatial disparities remain significant, as reflected in Gini indices of 0.38 (L2) and 0.44 (DCFC) across census tracts. Additionally, our analysis reveals racial disparities in TI-acs, driven not only by variations in charging infrastructure near residential areas but also by differences in their mobility patterns.

Thibaud Cambronne, Samuel Bobick, Wente Zeng et al.

Demand charge, a utility fee based on an electricity customer's peak power consumption, often constitutes a significant portion of costs for commercial electric vehicle (EV) charging station operators. This paper explores control methods to reduce peak power consumption at workplace EV charging stations in a joint price and power optimization framework. We optimize a menu of price options to incentivize users to select controllable charging service. Using this framework, we propose a model predictive control approach to reduce both demand charge and overall operator costs. Through a Monte Carlo simulation, we find that our algorithm outperforms a state-of-the-art benchmark optimization strategy and can significantly reduce station operator costs.

Hao Tu, Scott Moura, Yebin Wang et al.

Mathematical modeling of lithium-ion batteries (LiBs) is a primary challenge in advanced battery management. This paper proposes two new frameworks to integrate physics-based models with machine learning to achieve high-precision modeling for LiBs. The frameworks are characterized by informing the machine learning model of the state information of the physical model, enabling a deep integration between physics and machine learning. Based on the frameworks, a series of hybrid models are constructed, through combining an electrochemical model and an equivalent circuit model, respectively, with a feedforward neural network. The hybrid models are relatively parsimonious in structure and can provide considerable voltage predictive accuracy under a broad range of C-rates, as shown by extensive simulations and experiments. The study further expands to conduct aging-aware hybrid modeling, leading to the design of a hybrid model conscious of the state-of-health to make prediction. The experiments show that the model has high voltage predictive accuracy throughout a LiB's cycle life.

Mathilde D. Badoual, Scott J. Moura

Load serving entities with storage units reach sizes and performances that can significantly impact clearing prices in electricity markets. Nevertheless, price endogeneity is rarely considered in storage bidding strategies and modeling the electricity market is a challenging task. Meanwhile, model-free reinforcement learning such as the Actor-Critic are becoming increasingly popular for designing energy system controllers. Yet implementation frequently requires lengthy, data-intense, and unsafe trial-and-error training. To fill these gaps, we implement an online Supervised Actor-Critic (SAC) algorithm, supervised with a model-based controller -- Model Predictive Control (MPC). The energy storage agent is trained with this algorithm to optimally bid while learning and adjusting to its impact on the market clearing prices. We compare the supervised Actor-Critic algorithm with the MPC algorithm as a supervisor, finding that the former reaps higher profits via learning. Our contribution, thus, is an online and safe SAC algorithm that outperforms the current model-based state-of-the-art.

Sangjae Bae, David Isele, Kikuo Fujimura et al.

This paper proposes a discretionary lane selection algorithm. In particular, highway driving is considered as a targeted scenario, where each lane has a different level of traffic flow. When lane-changing is discretionary, it is advised not to change lanes unless highly beneficial, e.g., reducing travel time significantly or securing higher safety. Evaluating such "benefit" is a challenge, along with multiple surrounding vehicles in dynamic speed and heading with uncertainty. We propose a real-time lane-selection algorithm with careful cost considerations and with modularity in design. The algorithm is a search-based optimization method that evaluates uncertain dynamic positions of other vehicles under a continuous time and space domain. For demonstration, we incorporate a state-of-the-art motion planner framework (Neural Networks integrated Model Predictive Control) under a CARLA simulation environment.

Hao Tu, Scott Moura, Huazhen Fang

Mathematical modeling of lithium-ion batteries (LiBs) is a central challenge in advanced battery management. This paper presents a new approach to integrate a physics-based model with machine learning to achieve high-precision modeling for LiBs. This approach uniquely proposes to inform the machine learning model of the dynamic state of the physical model, enabling a deep integration between physics and machine learning. We propose two hybrid physics-machine learning models based on the approach, which blend a single particle model with thermal dynamics (SPMT) with a feedforward neural network (FNN) to perform physics-informed learning of a LiB's dynamic behavior. The proposed models are relatively parsimonious in structure and can provide considerable predictive accuracy even at high C-rates, as shown by extensive simulations.

Aaron Kandel, Scott J. Moura

This paper presents a distributionally robust Q-Learning algorithm (DrQ) which leverages Wasserstein ambiguity sets to provide idealistic probabilistic out-of-sample safety guarantees during online learning. First, we follow past work by separating the constraint functions from the principal objective to create a hierarchy of machines which estimate the feasible state-action space within the constrained Markov decision process (CMDP). DrQ works within this framework by augmenting constraint costs with tightening offset variables obtained through Wasserstein distributionally robust optimization (DRO). These offset variables correspond to worst-case distributions of modeling error characterized by the TD-errors of the constraint Q-functions. This procedure allows us to safely approach the nominal constraint boundaries. Using a case study of lithium-ion battery fast charging, we explore how idealistic safety guarantees translate to generally improved safety relative to conventional methods.

Sangjae Bae, Dhruv Saxena, Alireza Nakhaei et al.

This paper presents a real-time lane change control framework of autonomous driving in dense traffic, which exploits cooperative behaviors of other drivers. This paper focuses on heavy traffic where vehicles cannot change lanes without cooperating with other drivers. In this case, classical robust controls may not apply since there is no safe area to merge to without interacting with the other drivers. That said, modeling complex and interactive human behaviors is highly non-trivial from the perspective of control engineers. We propose a mathematical control framework based on Model Predictive Control (MPC) encompassing a state-of-the-art Recurrent Neural network (RNN) architecture. In particular, RNN predicts interactive motions of other drivers in response to potential actions of the autonomous vehicle, which are then systematically evaluated in safety constraints. We also propose a real-time heuristic algorithm to find locally optimal control inputs. Finally, quantitative and qualitative analysis on simulation studies are presented to illustrate the benefits of the proposed framework.

Abhishek Halder, Kenneth F. Caluya, Bertrand Travacca et al.

We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN). The ordinary and stochastic differential equations associated with the HNN were introduced in the literature as analog optimizers, and were reported to exhibit good performance in numerical experiments. In this work, we point out that the deterministic HNN can be transcribed into Amari's natural gradient descent, and thereby uncover the explicit relation between the underlying Riemannian metric and the activation functions. By exploiting an equivalence between the natural gradient descent and the mirror descent, we show how the choice of activation function governs the geometry of the HNN dynamics. For the stochastic HNN, we show that the so-called "diffusion machine", while not a gradient flow itself, induces a gradient flow when lifted in the space of probability measures. We characterize this infinite dimensional flow as the gradient descent of certain free energy with respect to a Wasserstein metric that depends on the geodesic distance on the ground manifold. Furthermore, we demonstrate how this gradient flow interpretation can be used for fast computation via recently developed proximal algorithms.