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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Improved Guarantees for Optimal Nash Equilibrium Seeking and Bilevel Variational Inequalities

We consider a class of hierarchical variational inequality (VI) problems that subsumes VI-constrained optimization and several other problem classes, including the optimal solution selection problem and the optimal Nash equilibrium (NE) seeking problem. Our main contribution is threefold. (i) We consider bilevel VIs with monotone and Lipschitz continuous mappings and devise a single-timescale iteratively regularized extragradient method, named IR-EG 𝚖,𝚖 . We improve the existing iteration complexity results for addressing both bilevel VI and VI-constrained convex optimization problems. (ii) Under the strong monotonicity of the outer-level mapping, we develop a method named IR-EG 𝚜,𝚖 and derive faster guarantees than those in (i). We also study the iteration complexity of this method under a constant regularization parameter. These results appear to be new for both bilevel VIs and VI-constrained optimization. (iii) To our knowledge, complexity guarantees for computing the optimal NE in nonconvex settings do not exist. Motivated by this lacuna, we consider VI-constrained nonconvex optimization problems and devise an inexactly projected gradient method, named IPR-EG, where the projection onto the unknown set of equilibria is performed using IR-EG 𝚜,𝚖 with a prescribed termination criterion and an adaptive regularization parameter. We obtain new complexity guarantees in terms of a residual map and an infeasibility metric for computing a stationary point. Here, we validate the theoretical findings using preliminary numerical experiments for computing the best and the worst NEs.

bilevel optimization↗
DOE OSTI2021

Approximating Nash Equilibrium in Day-ahead Electricity Market Bidding with Multi-agent Deep Reinforcement Learning

In this paper, a day-ahead electricity market bidding problem with multiple strategic generation company (GEN-CO) bidders is studied. The problem is formulated as a Markov game model, where GENCO bidders interact with each other todevelop their optimal day-ahead bidding strategies. Considering unobservable information in the problem, a model-free and data-driven approach, known as multi-agent deep deterministic policy gradient (MADDPG), is applied for approximating the Nash equilibrium (NE) in the above Markov game. The MADDPG algorithm has the advantage of generalization due to the automatic feature extraction ability of the deep neural networks. The algorithm is tested on an IEEE 30-bus system with three competitive GENCO bidders in both an uncongested caseand a congested case. Comparisons with a truthful bidding strategy and state-of-the-art deep reinforcement learning methods including deep Q network and deep deterministic policy gradient (DDPG) demonstrate that the applied MADDPG algorithm can find a superior bidding strategy for all the market participants with increased profit gains. In addition, the comparison with a conventional model-based method shows that the MADDPG algorithm has higher computational efficiency, which is feasible for real-world applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Security Constrained Distributed Transaction Model for Multiple Prosumers

Massive access of renewable energy has prompted demand-side distributed resources to participate in regulation and improve flexibility of power systems. With large-scale access of massive, decentralized, and diverse distributed resources, demand-side market members have transformed from traditional “consumers” to “prosumers”. To explore the distributed transaction model of prosumers, in this paper, a multi-prosumer distributed transaction model is proposed, and the Conditional Value-at-Risk (CVaR) theory is applied to quantify potential risks caused by the stochastic characteristics inherited from renewable energy. First, a prosumer model under constraints of the distribution network including photovoltaic units, fuel cells, energy storage system, central air conditioning and flexible loads is established, and a multi-prosumer distributed transaction strategy is proposed to achieve power sharing among multiple prosumers. Second, a prosumer transaction model based on CVaR is constructed to measure risks inherited from the uncertainty of PV output within the prosumer and ensure safety of system operation in extreme PV output scenarios. Then, the alternating direction multiplier method (ADMM) is utilized to solve the constructed model efficiently. Finally, distributed transaction costs of prosumers are distributed fairly based on the generalized Nash equilibrium to maximize social benefits. Simulation results show the multi-prosumer distributed transaction mechanism established under the proposed generalized Nash equilibrium method can encourage power sharing among prosumers, increasing their own income and social benefits. Also, the CVaR can assist decision making of prosumers in weighting the risks and benefits, improving system resilience through energy management of prosumers.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Entangling Quantum Generative Adversarial Networks

Generative adversarial networks (GANs) are one of the most widely adopted machine learning methods for data generation. In this work, we propose a new type of architecture for quantum generative adversarial networks (an entangling quantum GAN, EQ-GAN) that overcomes limitations of previously proposed quantum GANs. Leveraging the entangling power of quantum circuits, the EQ-GAN converges to the Nash equilibrium by performing entangling operations between both the generator output and true quantum data. In the first multiqubit experimental demonstration of a fully quantum GAN with a provably optimal Nash equilibrium, we use the EQ-GAN on a Google Sycamore superconducting quantum processor to mitigate uncharacterized errors, and we numerically confirm successful error mitigation with simulations up to 18 qubits. Finally, we present an application of the EQ-GAN to prepare an approximate quantum random access memory and for the training of quantum neural networks via variational datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Enhancing Grid Resilience with HIVE: Decentralized V2G Coordination for Black Starts

This paper proposes the HIVE (Harmonized Integration of Vehicle Energy for Grid Support) model, a novel game-theoretic framework for decentralized coordination of electrified vehicles to enable black start and load restoration during grid outages. In the absence of a central controller, HIVE employs a cooperative game to model vehicle interactions, allowing autonomous decision-making while admitting to a Nash equilibrium for grid restoration. The framework addresses the heterogeneity of vehicles and their operational constraints, selecting a lead vehicle for grid-forming and coordinating grid-following vehicles to support prioritized loads. Applied to a hospital blackout scenario, HIVE demonstrates robust performance in forming an islanded microgrid and sustaining critical loads under varying vehicle availability, state of charge, and power constraints. Simulation results highlight the model’s effectiveness in ensuring decentralized coordination of energy allocation and prioritizing loads, offering a scalable solution for resilient grid operations.

32 - ENERGY CONSERVATION, CONSUMPTION, AND UTILIZA↗
NASA NTRS1999

The Conference Proceedings of the 1999 Air Transport Research Group (ATRG) of the WCTR Society

In this paper, we develop a model with which allows us to measure not only the changes in equilibrium outcomes and welfare consequences of liberalizing a bilateral air transport agreement, but also the distribution of the gains and losses to carriers and consumers of each bilateral country and those of the third foreign countries. Our model also allows to measure the effects of changes in a bilateral agreement on the amount of traffic diversion between the direct bilateral routes and the indirect routes via a third country. We also provide an extension of our model to a case of oligopoly market outcome (Coumot Nash equilibrium). In our model, quality aspects are treated in the framework of hedonic price theory by specifying the quality-adjusted price (quantity) as a multiplication of the observed price (quantity) by the reciprocal quality index function (the quality index function). Numerical simulations were conducted to measure the effects of changing the following major policy levers in a bilateral air transport agreement: 1) Removing price regulation while retaining frequency and entry restrictions; 2) Removing price and entry regulation while retaining frequency restrictions; 3) Removing frequency regulations while retaining price and entry regulations; 4) Removing frequency and entry regulations while retaining price regulation; 5) Removing price and frequency regulations while retaining entry restriction; and 6) Removing all price, frequency and entry regulations (de facto, open skies).

Zhang, Anming↗
DOE OSTI2020

A non-cooperative meta-modeling game for automated third-party calibrating, validating and falsifying constitutive laws with parallelized adversarial attacks

The evaluation of constitutive models, especially for high-risk and high-regret engineering applications, requires efficient and rigorous third-party calibration, validation and falsification. While there are numerous efforts to develop paradigms and standard procedures to validate models, difficulties may arise due to the sequential, manual, and often biased nature of the commonly adopted calibration and validation processes, thus slowing down data collections, hampering the progress towards discovering new physics, increasing expenses and possibly leading to misinterpretations of the credibility and application ranges of proposed models. This work attempts to introduce concepts from game theory and machine learning techniques to overcome many of these existing difficulties. Here, we introduce an automated meta-modeling game where two competing AI agents systematically generate experimental data to calibrate a given constitutive model and to explore its weakness such that the experiment design and model robustness can be improved through competitions. The two agents automatically search for the Nash equilibrium of the meta-modeling game in an adversarial reinforcement learning framework without human intervention. In particular, a protagonist agent seeks to find the more effective ways to generate data for model calibrations, while an adversary agent tries to find the most devastating test scenarios that expose the weaknesses of the constitutive model calibrated by the protagonist. By capturing all possible design options of the laboratory experiments into a single decision tree, we recast the design of experiments as a game of combinatorial moves that can be resolved through deep reinforcement learning by the two competing players. Our adversarial framework emulates idealized scientific collaborations and competitions among researchers to achieve a better understanding of the application range of the learned material laws and prevent misinterpretations caused by conventional AI-based third-party validation. Numerical examples are given to demonstrate the wide applicability of the proposed meta-modeling game with adversarial attacks on both human-crafted constitutive models and machine learning models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Dynamic probabilistic risk assessment and game theory for cyber security risk analysis in nuclear power plants

Nuclear Power Plants and energy systems have become more prone to cyber-attacks with their digitalization and the increased use of smart equipment. Hence, it is important to quantify the risk associated with cyber-attacks in such systems. Dynamic Probabilistic Risk Assessment which involves studying the evolution of a system due to random events and operator and attacker actions during a cyber-attack by employing a physics-based model of the system is a suitable framework to quantify cybersecurity risk in nuclear power plants. In addition to the plant dynamics, it is also important to model the strategies of the attackers and plant operators for an effective cybersecurity risk assessment. Game theory provides a set of necessary tools to model such strategic interactions. In this research, a framework that integrates dynamic probabilistic risk assessment with game theory for cybersecurity risk analysis in nuclear power plants is presented. The mathematical formulation is derived based on the theory of continuous event trees. We propose a game theory based action model, that utilizes physics-based rewards to define the strategies of attackers and operators at every decision epoch. As a case study, the risk associated with cyber-attacks on the digital components in the secondary side of a pressurized water reactor is studied using a reduced order model. A set of attacker actions and a set of operator actions are defined for the system. The operator and attacker interactions were modelled using simultaneous game, their action policies were computed using the concept of mixed strategy Nash equilibrium and the evolution of the system was studied.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Non-cooperative Game-based Approach to Distributed Beam Scheduling in Millimeter-Wave Networks

We consider the distributed beam scheduling problem in mm-Wave networks where the base stations may belong to different operators and there is no centralized coordination among them. Our goal is to design distributed beam scheduling algorithms such that the network utility, which is defined as a logarithm function of the average throughput of the user equipment, can be maximized. We propose a non-cooperative game-based scheduling approach where the base stations are modeled as players that greedily maximize their own utilities. The Nash Equilibrium (NE) then provides a distributed solution to the network utility maximization problem. By employing the Lyapunov optimization, the asymptotic optimality of the proposed scheduling can be guaranteed. We prove the existence and provide sufficient conditions which guarantee the uniqueness of the NE by establishing an equivalence to the Variational Inequality (VI) problem. We also propose a parallel power adaptation algorithm which is proved to converge to the NE. Numerical results show the superiority of the proposed scheduling over several distributed baseline schemes.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

A Decentralized Market Mechanism for Energy Communities under Operating Envelopes

Here, we propose an operating envelopes (OEs) aware energy community market mechanism that dynamically charges/rewards its members based on two-part pricing. The OEs are imposed exogenously by a regulated distribution system operator (DSO) on the energy community's revenue meter and is subject to a generalized net energy metering (NEM) tariff design. By formulating the interaction of the community operator and its members as a Stackelberg game, we show that the proposed two-part pricing achieves a Nash equilibrium and maximizes the community's social welfare in a decentralized fashion while ensuring that the community's operation abides by the OEs. The market mechanism conforms with the cost-causation principle and guarantees community members a surplus level no less than their maximum surplus when they autonomously face the DSO. The dynamic and uniform community price is a monotonically decreasing function of the community's aggregate renewable generation. We also analyze the impact of exogenous parameters such as NEM rates and OEs on the value of joining the community. Lastly, through numerical studies, we showcase the community's welfare, and pricing, and compare its members' surplus to customers under the DSO's regime.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Game-Theoretic Strategies for Cyber-Physical Infrastructures Under Component Disruptions

In this work, networked infrastructures of recursively defined systems composed of discrete cyber and physical components are considered. The components of basic systems at the finest levels can be disrupted by cyber or physical means, and can be reinforced to survive at certain costs. A problem of ensuring the infrastructure performance is formulated as a game between a provider and an attacker, who probabilistically choose components to reinforce and attack, respectively. The disruptions of this infrastructure are characterized using the aggregate failure correlation function that specifies the conditional failure probability of the infrastructure given the failure of an individual system at that level. The survival probabilities of basic systems satisfy simple product-form, first-order differential equations expressed in terms of the multiplier functions. The utility functions of the provider and attacker are composed of the reward and cost terms, both expressed in terms of the component reinforcement and attack probabilities. The Nash equilibrium of this game is characterized, along with the sensitivity functions of the survival probabilities of basic systems that highlight their dependence individually on the cost-benefit terms, the correlation functions, and the multiplier functions. These results are illustrated using simplified models of a distributed cloud servers infrastructure, a 5G data network infrastructure, a high performance computing federation, and a smart energy grid infrastructure.

42 ENGINEERING↗
DOE OSTI2022

A Non-Cooperative Game-Based Distributed Beam Scheduling Framework for 5G Millimeter-Wave Cellular Networks

Here, this paper studies the problem of distributed beam scheduling for 5G millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging to different operators share the same spectrum without centralized coordination among them. Our goal is to design efficient distributed scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to the average and instantaneous power consumption constraints of the BSs. We propose a Media Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lyapunov stochastic optimization framework and non-cooperative games. In particular, we first decompose the original utility maximization problem into two sub-optimization problems for each time frame, which are a convex optimization problem and a non-convex optimization problem, respectively. By formulating the distributed scheduling problem as a non-cooperative game where each BS is a player attempting to optimize its own utility, we provide a distributed solution to the non-convex sub-optimization problem via finding the Nash Equilibrium (NE) of the game whose weights are determined optimally by the Lyapunov optimization framework. Finally, we conduct simulation under various network settings to show the effectiveness of the proposed game-based beam scheduling algorithm in comparison to that of several reference schemes.

42 ENGINEERING↗
DOE OSTI2023

Automated Adversary-in-the-Loop Cyber-Physical Defense Planning

Security of cyber-physical systems (CPS) continues to pose new challenges due to the tight integration and operational complexity of the cyber and physical components. To address these challenges, this article presents a domain-aware, optimization-based approach to determine an effective defense strategy for CPS in an automated fashion—by emulating a strategic adversary in the loop that exploits system vulnerabilities, interconnection of the CPS, and the dynamics of the physical components. Our approach builds on an adversarial decision-making model based on a Markov Decision Process (MDP) that determines the optimal cyber (discrete) and physical (continuous) attack actions over a CPS attack graph. The defense planning problem is modeled as a non-zero-sum game between the adversary and defender. We use a model-free reinforcement learning method to solve the adversary’s problem as a function of the defense strategy. We then employ Bayesian optimization (BO) to find an approximate best-response for the defender to harden the network against the resulting adversary policy. This process is iterated multiple times to improve the strategy for both players. We demonstrate the effectiveness of our approach on a ransomware-inspired graph with a smart building system as the physical process. Numerical studies show that our method converges to a Nash equilibrium for various defender-specific costs of network hardening.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Costs of symmetric strategic games with defenses

A companion note discusses the crisis stability of symmetric offensive missile forces. This note extends the analysis to include symmetric defensive forces. It derives Nash equilibrium optimal missile defenses, which are used to study the impact of varying defenses on strike costs and stability. It treats the option to strike first as a random decision by nature, which is consistent with previous experience and provides a rational basis for interaction and deterrence without which the study of stability is vacuous.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2021

Game-Theoretic Approach for Grace-Period Policy in Supercomputers

Job scheduling at supercomputing facilities is important for achieving high utilization of these valuable resources while ensuring effective execution of jobs submitted by users. The jobs are scheduled according to their specified resource demands such as expected job completion times, and the available resources based on allocations. Jobs that overrun their allocated times are terminated, for example, after a grace-period. It is non-trivial and often very complex for users to accurately estimate the completion times of their jobs, and consequently they face a dilemma: underestimate the job time to have a higher priority and risk job termination due to overrun, or overestimate it to ensure its completion and risk its delayed execution. In this paper, we investigate whether providing grace-period can benefit facility performance by developing a game- theoretic model between a facility provider and multiple users for a simplified scheduling scenario based on job execution times. We present closed-form expressions for the provider’s and user’s best-response strategies to maximize their respective utility functions. We describe conditions under which offering a grace-period is advantageous to both facility provider and users by deriving the Nash equilibrium of the game.

He, Fei↗
DOE OSTI2023

Game-Theoretic Strategies for Quantum-Conventional Network Infrastructures

Fundamentally and practically, quantum networks and conventional networks are inextricably tied, since the basic quantum protocols such as teleportation require both networks and the conventional network fiber is also used for the quantum network. A Recursive System of Systems (RSOS) model is developed for quantum-conventional (QC) networks by modeling the correlations at various levels based on the failure and attack modes of quantum, conventional and hybrid components and the propagative effects across QC boundaries. A game-theoretic formulation is developed to capture the cost-benefit trade-offs of the provider in defending against component attacks, using sum-form utility functions. By applying the Nash Equilibrium results, the conditions and sensitivity functions of the survivalprobabilities of a QC network at different levels are derived using the strong dependencies between quantum and conventional infrastructures. The results provide insights into the dependenciesbetween conventional and quantum networks, including cross QC boundary effects in terms of disruption impact of conventional networks on quantum networks, and vice versa.

Rao, Nageswara↗
NASA NTRS1969

Nonzero-sum differential games.

Differential games theory with nonzero sum for application to economic analysis, discussing Nash equilibrium, minimax and noninferior strategies set

Ho, Y. C.↗