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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

LeWRON: Learning ElectroWeak phase tRansitiON with agentic architecture

An agent to analyze electroweak phase transition. LeWRON turns a BSM model description or a reproduction target into a structured run: symbolic setup, effective-potential artifacts, finite-temperature machinery, generated model code, a scientific report, and an interactive exploration session. It keeps both machine-readable artifacts and human-readable notes, so a run can be resumed, audited, revised, and shared.

Wang, Isaac [Fermi National Accelerator Laboratory↗
DOE OSTI2026

AutoLabs: cognitive multi-agent systems with self-correction for autonomous chemical experimentation

The automation of chemical research through self-driving laboratories (SDLs) promises to accelerate scientific discovery, yet the reliability and granular performance of the underlying AI agents remain critical, under-examined challenges. In this work, we introduce AutoLabs, a self-correcting, multi-agent architecture designed to autonomously translate natural-language instructions into executable protocols for a high-throughput liquid handler. The system engages users in dialogue, decomposes experimental goals into discrete tasks for specialized agents, performs tool-assisted stoichiometric calculations, and iteratively self-corrects its output before generating a hardware-ready file. We present a comprehensive evaluation framework featuring five benchmark experiments of increasing complexity, from simple sample preparation to multi-plate timed syntheses. Through a systematic ablation study of 20 agent configurations, we assess the impact of reasoning capacity, architectural design (single- vs. multi-agent), tool use, and self-correction mechanisms. Our results demonstrate that agent reasoning capacity is the most critical factor for success, reducing quantitative errors in chemical amounts (nRMSE) by over 85% in complex tasks. When combined with a multi-agent architecture and iterative self-correction, AutoLabs approaches expert-authored reference procedures on the benchmark (F1-score > 0.89) on challenging multi-plate syntheses. These findings establish a clear blueprint for developing robust and trustworthy AI partners for autonomous laboratories, highlighting the synergistic effects of modular design, advanced reasoning, and self-correction to ensure both performance and reliability in high-stakes scientific applications. Code: https://github.com/pnnl/autolabs

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Topology-Dependent Performance of Free-Space Photonic Quantum Networks Under Noise

Photonic quantum communication enables secure and high-fidelity information transfer beyond classical limits, with direct relevance to emerging quantum networks operating in free-space environments. While physical-layer models of depolarizing noise, Gamma–Gamma turbulence statistics, entanglement swapping, and decoy-state QKD security bounds are individually well established, prior work typically treats these components in isolation or under fixed network assumptions. In this work, we develop a unified topology-aware analytical framework that simultaneously integrates free-space optical link budgets, turbulence-induced visibility degradation, depolarizing qubit noise, multi-hop entanglement cascade dynamics, teleportation fidelity thresholds, CHSH nonlocality certification, and asymptotic decoy-state secret key rate bounds across star, mesh, and ring graph structures. Rather than introducing new physical channel models, we demonstrate that identical physical links exhibit fundamentally different end-to-end performance once embedded within different network topologies. Mesh architectures minimize visibility cascade through hop-count reduction but incur quadratic hardware scaling. Star topologies minimize link count but concentrate noise and synchronization overhead at the hub. Ring configurations offer linear hardware scaling with multiplicative fidelity degradation. The results establish topology as a first-order design parameter in near-term free-space quantum networks operating without full quantum repeater infrastructures. While motivated by distributed multi-agent architectures, the framework applies broadly to terrestrial, airborne, and satellite-assisted photonic quantum communication systems.

QKD↗
DOE OSTI2026

Agentic traffic intelligence: Augmented human-in-the-loop scenario generation for microscopic traffic simulation

Traditional microscopic traffic simulation generation often relies on static datasets and manual design, limiting its ability to simulate complex conditions easily. This paper presents a novel framework, Agentic Traffic Intelligence, which combines human approval large language models (LLMs), the Real-Twin tool, and multi-agent systems to perform realistic microscopic traffic simulation scenario generation. The proposed framework incorporates human-in-the-loop (HIL) control, retrieval-augmented generation (RAG), and multi-agent control mechanisms. HIL mechanisms are used to guide multiple LLMs focused on attributes for microscopic simulation generation and to improve the interpretability and transparency of LLM execution for users. RAG enhances context extraction by dynamically integrating external knowledge sources for traffic scenario generation foundations. A multi-agent architecture with supervisory control coordinates the interaction of simulation components, including traffic simulators, control logic, and calibration tools. This enables the synthesis of simulation-ready scenarios that reflect dynamic demand profiles and behavior controls. Furthermore, the framework fuses multisource traffic data with unstructured context and supports iterative refinement through interactive user feedback. Validated through microscopic simulation using Simulation of Urban Mobility, the generated scenarios demonstrate high-fidelity network generation with inflow and turn movement and behavioral calibration, offering a robust and efficient tool for stress-testing and optimizing urban mobility systems.

Hierarchical multi-agent control↗
DOE OSTI2025

Surrogate Modelling of 3rd Integer Resonant Extraction at Fermilab Delivery Ring

We present an ongoing work in which a surrogate model is being developed to reproduce the response dynamics of the third-integer resonant extraction process in the Delivery Ring (DR) at Fermilab. This effort is in pursuit of smoothly extracting circulating beam to the Mu2e Experiment s production target, wherein the goal is to extract a uniform slice of the circulating $1e12$ protons in the DR over 25,000 turns (43~ms). The DR contains 3 harmonic sextupoles which excite a third-integer resonance as well as three fast, tune-ramping quadrupole magnets which drive the horizontal tune towards the $29/3$ resonance. In our initial work the surrogate model trains on a semi-analytical simulation provided in the same format as live data. Using Reinforcement Learning (and other potential ML methods), the trained surrogate acts as the environment in which a simple ML control agent could learn to dynamically adjust the quadrupole ramp at 430 break points within the 43 microsecond spill window. The control agent will be hosted on a dedicated Arria 10 FPGA, introducing its own requirements on control agent architecture. In this work we report the accuracy and fidelity of surrogate models in comparison to the response dynamics of the physics simulator.

Narayanan, Aakaash [Fermilab] (ORCID:0000000157944↗
DOE OSTI2025

Comprehensive assessment of deep reinforcement learning approaches for economic dispatch in nuclear-driven microgrids

As the electrical grid integrates more variable renewable energy sources such as wind and solar, the demand for distributed and flexible systems to address this increased variability becomes critical. Nuclear-driven microgrids provide a promising solution by offering stable generation to complement intermittent renewables, ensuring grid reliability and operating efficiency. This paper proposes a recurrent deep reinforcement learning framework for optimal economic dispatch in a nuclear-powered microgrid integrating renewable energy sources, small modular reactors, battery storage systems, and balance-of-plant dynamics. A three-agent control architecture is developed, where demand and renewable energy agents act as forecasters, and a reinforcement learning-based dispatch agent performs real-time energy allocation. A nonlinear programming formulation is first used to generate an optimal baseline for benchmarking. The proposed dispatch controller, based on Proximal Policy Optimization enhanced with Long Short-Term Memory networks, exploits temporal correlations in system dynamics by taking advantage of the time series used as inputs to improve policy robustness under uncertainty. Comparative analysis against established deep reinforcement learning methods, including Proximal Policy Optimization with a feedforward architecture, Soft Actor-Critic, and Twin Delayed Deep Deterministic Policy Gradient, demonstrates superior performance. Numerical results indicate that the proposed controller achieves a 0.39% cost reduction relative to the nonlinear programming benchmark and outperforms other learning-based methods by generating additional revenue of up to 0.35%. All reinforcement learning controllers compute dispatch actions in less than 0.3 s, resulting in a computational speedup of more than three orders of magnitude over the nonlinear programming baseline. The findings of this paper highlight their applicability for real-time operation and control in nuclear-integrated microgrids under volatile operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

LC-Opt: Benchmarking Reinforcement Learning and Agentic AI for End-to-End Liquid Cooling Optimization in Data Centers

Liquid cooling is critical for thermal management in high-density data centers with the rising AI workloads. However, machine learning-based controllers are essential to unlock greater energy efficiency and reliability, promoting sustainability. We present LC-Opt, a Sustainable Liquid Cooling (LC) benchmark environment, for reinforcement learning (RL) control strategies in energy-efficient liquid cooling of high-performance computing (HPC) systems. Built on the baseline of a high-fidelity digital twin of Oak Ridge National Lab's Frontier Supercomputer cooling system, LC-Opt provides detailed Modelica-based end-to-end models spanning site-level cooling towers to data center cabinets and server blade groups. RL agents optimize critical thermal controls like liquid supply temperature, flow rate, and granular valve actuation at the IT cabinet level, as well as cooling tower (CT) setpoints through a Gymnasium interface, with dynamic changes in workloads. This environment creates a multi-objective real-time optimization challenge balancing local thermal regulation and global energy efficiency, and also supports additional components like a heat recovery unit (HRU). We benchmark centralized and decentralized multi-agent RL approaches, demonstrate policy distillation into decision and regression trees for interpretable control, and explore LLM-based methods that explain control actions in natural language through an agentic mesh architecture designed to foster user trust and simplify system management. LC-Opt democratizes access to detailed, customizable liquid cooling models, enabling the ML community, operators, and vendors to develop sustainable data center liquid cooling control solutions.

Naug, Avisek [Hewlett Packard Enterprise]↗
DOE OSTI2026

Multi-Agent Control Planes for Quantum Networks: A Scalable Architecture for Autonomous Quantum Internet Management

Quantum networks are expected to enable distributed quantum computing, secure communication, and global entanglement distribution. However, operating such networks presents significant challenges, including stochastic quantum processes, fragile entanglement resources, dynamic topology, and cross-layer control requirements. Current quantum network control architectures largely rely on centralized or hierarchical controllers inspired by classical software-defined networking (SDN). While effective for small testbeds, these approaches face scalability, latency, and reliability limitations as quantum networks grow. This paper proposes a multi-agent control plane architecture for quantum networks. In this design, intelligent software agents operate at quantum nodes, repeaters, and orchestration layers, collectively managing entanglement generation, routing, purification, and scheduling. The distributed intelligence of the agent system allows the network to adapt dynamically to quantum hardware variability and environmental noise. We argue that multi-agent systems provide significant advantages over centralized control approaches, including scalability, resilience, local autonomy, and real-time adaptation. The paper discusses architectural design principles, agent coordination mechanisms, and research challenges in deploying multi-agent control planes for the emerging quantum Internet.

Alnajjar, Anees [ORNL] (ORCID:0000000237101601)↗
DOE OSTI2025

OR-AGENT framework – Architecting electrified heavy-duty drayage applications

The widespread adoption of zero-emission vehicles in heavy-duty (HD) commercial freight transportation faces considerable technoeconomic challenges. For heavy-duty trucks, ensuring high uptime, cost parity with diesel, and safety standards is especially critical as these vehicles operate over long distances with heavy loads, where any downtime or off-nominal behaviors significantly impacts logistics, productivity, and the total cost of ownership. Unlike traditional diesel refueling, BEV charging infrastructure must be co-optimized with vehicle deployment, operational demands, and grid capacity to ensure cost-effective and reliable freight operations. However, the lack of a standardized ownership and service model has led to a fragmented approach—where commercial vehicle operators may invest in, own, and maintain both vehicle/batteries and charging/energy infrastructure. This disconnect may exclude energy service providers from the equation, forcing fleet operators to explore ‘behind-the-fence’ energy solutions that increase capital investment, operational downtime, overhead costs, and, in some cases, net carbon emissions. To address these issues, this study introduces OR-AGENT (Optimal Regional Architecture Generation for Efficient National Transport), a comprehensive modeling framework that integrates powertrain architectures, charging infrastructures, and energy backbone systems into a cohesive strategy. In this paper, OR-AGENT is applied to develop an interconnected systems architecture for energy efficiency and resiliency enhancement of heavy-duty drayage vehicles at the Port of Savannah, GA. This framework showcases an interconnected systems approach to electrifying heavy-duty drayage vehicles at the Port of Savannah, GA. The study assessed BEVs with 400–1200 kWh battery capacities, accounting for seasonal variations in weather and freight routing. A diverse charging mix (150 kW–1250 kW) was evaluated alongside grid capacity constraints, cost, and carbon intensity analysis, leading to the development of a strategic microgrid/Distributed Energy Resources (DER) deployment architecture to ensure a reliable and sustainable transition. However, the findings also highlight the need for alternative zero-emission solutions for remaining trips, such as larger batteries, electrified roadways, hydrogen powertrains, or net-zero emission fuels. In conclusion, the findings are incorporated into a Total Cost of Ownership (TCO) model to identify optimal architectures for an interconnected electrified ecosystem.

Commercial vehicles↗
DOE OSTI2025

Osprey Framework v0.2.2

The Alpha Berkeley Framework is a software architecture for building agentic AI systems that coordinate multi-step workflows in scientific and industrial environments. It is based on a plan-first orchestration model, where natural language requests are translated into execution plans with explicit dependencies and optional human approval. The framework includes capability classification, which selects relevant tools on a per-task basis to keep orchestration efficient as the number of available tools grows. It incorporates task extraction methods that compress conversational context and integrate external resources such as databases, APIs, and knowledge bases into structured, machine-readable tasks. Execution is supported by modular services with checkpointing, artifact management, and error handling, allowing workflows to be paused, inspected, and resumed. The system is designed for deployment in production environments, supporting both local and containerized execution as well as integration with HPC clusters. Interfaces include command-line tools, browser-based workflows, and containerized services. The framework has been demonstrated in tutorial examples and deployed at the Advanced Light Source, where it coordinates accelerator control and analysis workflows.

Hellert, Thorsten [Lawrence Berkeley National Labo↗
DOE OSTI2025

Hydrogen and Electric Charging Infrastructure for Heavy-Duty Trucks: A Nationally Scalable Megaregion Assessment

Decarbonizing regional and long-haul freight is challenging due to the limitations of battery-electric commercial vehicles and infrastructure constraints. Hydrogen fuel cell medium- and heavy-duty vehicles (MHDVs) offer a viable alternative, aligning with the decarbonization goals of the Department of Energy and commercial entities. Historically, alternative fuels like compressed natural gas and liquefied propane gas have faced slow adoption due to barriers like infrastructure availability. To avoid similar issues, effective planning and deploying zero-emission hydrogen fueling infrastructure is crucial. This research develops deployment plans for affordable, accessible, and sustainable hydrogen refueling stations, supporting stakeholders in the decarbonized commercial vehicle freight system. It aims to benefit underserved and rural energy-stressed communities by improving air quality, reducing noise pollution, and enhancing energy resiliency. This research also provides a blueprint for replacing diesel in over-the-road Class 8 freight truck applications with hydrogen fueling solutions. The study focuses on the Texas Triangle Megaregion (I-45, I-35, and I-10), the I-10 corridor between San Antonio, TX, and Los Angeles, CA, and the I-5/CA-99 corridors between Los Angeles, CA, and San Francisco, CA. This area represents a significant portion of U.S. heavy-duty freight movement, carrying ~8.5% of the national freight volume. Using the OR-AGENT (Optimal Regional Architecture Generation for Efficient National Transport) modeling framework, the study conducts an advanced assessment of commercial vehicles, road and freight networks, and energy systems. The framework integrates data on freight mobility, traffic, weather, and energy pathways to deliver a region-specific, optimized vehicles powertrain architectures, infrastructure deployment solutions, operational logistics, and energy pathways. By considering all vehicle origin-destination pairs utilizing these corridors and all feasible fueling station location options, the framework's genetic algorithm identifies the minimum number and optimal locations of hydrogen refueling stations, ensuring no vehicle is stranded. It also determines fuel schedules and quantities at each station. A roadmap for station deployment based on multiple adoption trajectories ensures a strategic rollout of hydrogen refueling infrastructure.

Sujan, Vivek [ORNL] (ORCID:0000000269882342)↗
DOE OSTI2025

Complexing Agent-Assisted Membraneless Zinc–Iodine Aqueous Batteries

A membrane is required for conventional zinc–iodine aqueous batteries, since soluble polyiodides cross over to the anode side and react with zinc metal spontaneously. Making the battery membraneless increases ion transport and reduces its cost and overall footprint. In this paper, a membraneless Zn–I 2 aqueous battery is demonstrated, employing a complexing agent, 1-butyl-1-methylpyrrolidinium iodide (MBPI), to promote the formation of I 5 – -containing, phase-separated polyiodides upon charging, to minimize self-discharge and suppress Zn dendrite growth. With an additional 0.3 M MBPI in 4 M ZnI 2 electrolyte, the membraneless battery achieved 65 cycles with >85% Coulombic efficiency, whereas the MBPI-free control failed immediately. Additionally, a volumetric capacity of 14.3 Ah L –1 was achieved, surpassing those of most membraneless batteries reported to date regardless of redox chemistry, and underscores the potential of complexing agents in simplifying the architecture of conventional Zn–I 2 flow batteries.

25 ENERGY STORAGE↗
DOE OSTI2026

Development and Implementation of a New AI-Based Tool to Support Fast Reactor Software Model Generation and Validation

This report summarizes FY26 work to develop Maggie, an artificial intelligence-based assistant designed to support software model generation and validation activities for fast reactor analysis codes. The project established a modular, code-agnostic software architecture that separates reusable agent capabilities from code-specific knowledge and tools, with initial implementation focused on the FRP-supported fast reactor safety analysis code SAS4A/SASSYS1 (SAS). A curated SAS-specific knowledge base was assembled from the code manual, training materials, historical analysis reports, and representative input files, and was integrated through retrieval-augmented generation to ground Maggie’s responses in authoritative sources. Maggie was deployed on the internal Argonne network, where it demonstrated practical user-facing capability as a chatbot for answering natural language questions about SAS and retrieving relevant technical information. Demonstration cases also showed that Maggie can generate useful snippets of SAS input for selected modeling tasks, while highlighting current limitations in reliability and consistency for more complex input generation tasks. Overall, the FY26 effort established the technical foundation for an AI-assisted capability intended to improve the efficiency, consistency, and accessibility of fast reactor software model development at Argonne and, with further improvements, to support eventual use by the broader fast reactor community, including industry users of FRP-supported analysis tools.

Thomas, Rachel [Argonne National Laboratory (ANL),↗
DOE OSTI2026

Agentic Diagrammatica: Towards Autonomous Symbolic Computation in High Energy Physics

We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge for LLM agents, as correctness is governed by implicit mathematical conventions that are not encoded in a form that can be easily checked in the computational backend. We identify two complementary remedies, tool-constrained computation and targeted knowledge grounding, and pursue the first as the primary architecture. Concretely, we concentrate the agent's action distribution onto tool calls with convention-fixing semantics, in which the agent specifies a compact, human-auditable diagram specification and a trusted backend performs the symbolic or numerical manipulations exactly. The toolkit provides two complementary calculation paths consuming a shared diagram specification: Naive Dimensional Analysis (NDA) for order-of-magnitude rate estimates and Exact Diagrammatic Analysis (EDA) for tree-level symbolic calculations via automatic FeynCalc code generation, both supplemented by automatic Feynman diagram enumeration and a navigable theory knowledge base. The architecture is validated on two benchmarks: (1) an exhaustive catalog of all tree-level, single-vertex $1\to 2$ partial decay widths across scalar, fermion, and vector parents, with complete massless and threshold limits and Standard Model validation; and (2) an NDA sensitivity study of the muon decay multiplicity $μ^+ \to ν_μ\barν_e + n(e^+e^-) + e^-$, determining the maximum observable $n$ at current and planned muon experiments.

Menzo, Tony [Alabama U.; Fermilab] (ORCID:00000002↗
DOE OSTI2025

Surrogate modeling of Cellular-Potts agent-based models as a segmentation task using the U-Net neural network architecture

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Wolf

The Workflow Orchestration Language Framework (WOLF) is an agentic framework grounded in natural language with an architecture inspired by reinforcement learning (RL)—designed to orchestrate, scale, and accelerate complex workflows. The concept of WOLF was born out of the very successful ASC Tri-lab Multi-Agent Design Assistant (MADA) project, but extends beyond its domain-specific design agents to provide a more general and extensible architecture. WOLF capitalizes on the lessons learned from MADA and is fully aligned with Sutton’s The Bitter Lesson—that the most enduring progress in AI comes from general-purpose methods that scale with computation, rather than narrow techniques built on domain-specific human knowledge. In this spirit, WOLF enables agents to autonomously learn workflows, capture strategies as reusable playbooks, and build a growing corpus of interpretable, auditable “wisdom artifacts.” These artifacts, expressed in natural language, bridge human and machine understanding while preserving adaptability and scalability as computational power continues to expand.

Boureima, Ismaeal↗
DOE OSTI2025

ADEPT: A Pedagogical Framework for Integrating Agentic AI with Deterministic Scientific Workflows

The integration of Large Language Models (LLMs) into scientific research promises to accelerate discovery, yet a significant gap remains between the dynamic reasoning of Artificial Intelligence (AI) agents and the static, deterministic nature of canonical scientific workflows. This paper introduces ADEPT (Agentic Discovery and Exploration Platform for Tools), a reference architecture and pedagogical framework explicitly designed to bridge this gap. ADEPT's primary mission is to provide a transparent, "glass-box" environment where researchers and engineers can learn to effectively wrap established scientific software (e.g., BLAST, Nextflow pipelines) and compose it into reliable, agent-driven workflows. We describe its modular, multi-server architecture, which leverages the Model Context Protocol (MCP) for tool serving, LangGraph for robust agentic orchestration, and a secure nsjail-based sandbox for safe code execution. By prioritizing architectural clarity, safety, and modularity, ADEPT serves as an extensible blueprint for building trustworthy AI-augmented systems and fosters the collaborative development necessary to responsibly employ agentic AI for science. We provide practical examples of how to adapt and extend this framework, highlighting its utility in workforce development and AI-readiness capabilities across research and development projects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Optimization-based approaches to control of connected and automated vehicles: Principles, complexities, applications, challenges, and outlook

Safe and optimal motion control for connected and automated vehicles (CAVs) poses a fundamental optimization challenge at the intersection of system complexity, environmental uncertainty, and stringent real-time constraints. Existing surveys address this challenge in isolation – focusing either on specific control techniques or individual uncertainty sources – without providing a unified framework that characterizes the trade-offs among computational tractability, performance verifiability, and adaptive generalization across paradigms. This review addresses that gap by presenting a cohesive analytical framework concentrated on the decision-making and trajectory optimization layers of the CAV autonomy stack. We systematically analyze three major optimization paradigms – first-principles model-based optimization, data-driven methods, and hybrid synergistic architectures – evaluating each against four core complexity axes: problem formulation, constraint handling, optimality guarantees, and robustness. Key applications including platooning, trajectory planning, collision avoidance, and cooperative control are examined to reveal recurring methodological patterns and critical operational constraints that limit real-world performance. Our synthesis identifies verifiable hybrid architectures, incentive-aligned multi-agent cooperation, and hardware-algorithm co-design as the defining research frontiers, and distills a targeted agenda for developing CAV control systems that are simultaneously safe, computationally efficient, and deployable in the full complexity of real-world traffic environments.

Muzahid, Abu Jafar Md [University of Tennessee, Kn↗