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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Space-Split Algorithm for Sensitivity Analysis of Discrete Chaotic Systems With Multidimensional Unstable Manifolds

Accurate approximations of the change of a system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing the linear response of chaotic dynamical systems. In this paper, we propose an algorithm for sensitivity analysis of discrete chaos with an arbitrary number of positive Lyapunov exponents. We combine the concept of perturbation space-splitting, which regularizes Ruelle's original expression, together with measure-based parameterization of the expanding subspace. We use these tools to rigorously derive trajectory-following recursive relations that converge exponentially fast, and construct a memory-efficient Monte Carlo scheme for derivatives of the output statistics. Thanks to the regularization and lack of simplifying assumptions on the system's behavior, our method is immune to the common problems of other popular methods such as the exploding tangent solutions and unphysical shadowing directions. Here, we provide a ready-to-use algorithm, analyze its complexity, and demonstrate several numerical examples of sensitivity computation using physically-inspired low-dimensional systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Chaos, percolation and the coronavirus spread: a two-step model

We discuss a two-step model for the rise and decay of a new coronavirus (Severe Acute Respiratory Syndrome-CoV-2) first reported in December 2019, COVID-19. The first stage is well described by the same equation for turbulent flows, population growth and chaotic maps: a small number of infected, d 0 , grows exponentially to a saturation value, d ∞ . The typical growth time (aggressive spreading of the virus) is given by τ = 1/λ where λ is the Lyapunov exponent. After a time t crit determined by social distancing and/or other measures, the spread decreases exponentially analogous to nuclear decays and non-chaotic maps. Some countries, like China, S. Korea and Italy, are in this second stage while others including the USA are near the end of the growth stage. The model predicted 15,000 (±2250) casualties for the Lombardy region (Italy) at the end of the spreading around May 10, 2020. Without the quarantine, the casualties would have been more than 50,000, one hundred days after the start of the pandemic. Here, the data from the 50 US states are of very poor quality because of an extremely late and confused response to the pandemic, resulting unfortunately in a large number of casualties, more than 70,000 on May 6, 2020, and more than 170,000 on August 21, 2020. S. Korea, notwithstanding the high population density (511/km 2 ) and the closeness to China, responded best to the pandemic with 255 deceased as of May 6, 2020, and 301 on August 21, 2020.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Fast Dynamic Aperture Optimization with Reversal Integration

A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symme- try, a numerical forward integration di ers from its reversal. For chaotic trajectories, cumulative round-o errors are scaled, which results in an exponential growth in the di erence. The exponential e ect, intrinsically associated with the Lyapunov exponent, is a generic indicator of chaos because it represents the sensitivity of chaotic motion to an initial condition. A chaos indicator of the charged particle motion is then obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. \backward integrations." The indicator was con rmed to be ob- servable through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test di raction-limited light source ring, were optimized using this method for the purpose of demonstration.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Model Reference Adaptive Control (MRAC) for Additive Manufacturing (AM)

Model Reference Adaptive Control (MRAC) is based on the fundamental concept that the process under investigation is to be controlled to follow or “track” a reference system (model) characterized by a state/input/output model employing an adaptive optimization algorithm to adjust the controller parameters in real-time. The generic structure of the MRAC is shown in Fig. 1 consisting of the following primary components: Reference model, Process (system) model, controller and the adaption algorithm. The basic structure of the controller is specified by a linear construct with the corresponding real-time adaption algorithms given by a gradient-type (so-called MIT rule) or based on stability theory (Lyapunov, hyperstability). This approach to adaptive control is termed “direct”, since the controller (parameters) are adjusted based on the component models/algorithm in contrast to the “indirect” approach that adjusts the process model parameters applying real-time system identification techniques.

42 ENGINEERING↗
DOE OSTI2023

Protecting and Defending against Autonomous Control Systems and Digital Twin Cyber Attacks: Response Strategy for Hyperparameter attacks of Digital Twin Machine Learning Models in Nuclear Power Plants (Final)

Navigating through the complex tapestry of technological advancements, "Response Strategy for Hyperparameter attacks of Digital Twin Machine Learning Model in Nuclear Power Plants" stands at the intersection of cybersecurity and nuclear power plant operations, embarking on a journey through the intricacies of securing digital twins against malicious cyber activities. As nuclear power plants progressively integrate digital twin technology and machine learning models to optimize operations and ensure system reliability, they inadvertently expose themselves to a new spectrum of vulnerabilities, notably in the realm of hyperparameter attacks. Hyperparameters, integral in machine learning model tuning and optimal performance of digital twins, have emerged as a target for adversaries aiming to destabilize the predictive capabilities and therefore, the operational accuracy of these digital entities within critical infrastructures like nuclear plants. This paper, therefore, meticulously threads the needle through the development of a robust response strategy, poised to shield these digital reflections against calculated hyperparameter manipulations, ensuring that the digital twin can effectively and securely function as a reliable proxy for its physical counterpart. The ensuing sections delve into the orchestrated maelstrom of multi-rate time-changing intelligent coordinated hyperparameter attacks and the implementation of event-triggered predictive control, laying down a structured, predictive, and responsive framework that safeguards the nexus where the digital and physical realms of nuclear power plants coalesce. The operational integrity of digital twins in nuclear power plants depends critically on the security of machine learning hyperparameters. This study makes two different contributions. First, a decision-based idea known as a multi-rate time changing intelligent coordinated hyperparameter attack is put forth. In this attack, many hyperparameters are repeatedly changed using both random and intelligent optimal techniques by the attacker. These assaults introduce varied rates at different attack steps, compromise various amounts of hyperparameters, and improve stealth and flexibility. Second, a technique is developed for event triggered predictive control to rapidly respond to potential hyperparameter attacks. This control integrates a sliding window framework, retaining a history of previous data points and employing linear regression to predict the next data point from the current dataset. The control gain K is determined using the Lyapunov-Krasovskii method, and subsequently, an action is developed. Finally, the outcome of the simulation demonstrates the viability of the proposed method for defending nuclear power plant digital twins from hyperparameter attacks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Limitations for Quantum Algorithms to Solve Turbulent and Chaotic Systems

We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm answering one of their open questions. We provide a further significant limitation for any quantum algorithm that aims to output a quantum state that approximates the normalized solution vector. Given a natural choice of coordinates for a dynamical system with one or more positive Lyapunov exponents and solutions that grow sub-exponentially, we prove that any such algorithm has complexity scaling at least exponentially in the integration time. As such, an efficient quantum algorithm for simulating chaotic systems or regimes is likely not possible.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

State-Constrained Grid-Forming Inverter Control for Robust Operation of AC Microgrids

The control of grid-forming inverters has become an important problem to achieve high efficiency, reliability, and resilience of the future power grid. The distributed control that utilizes a sparse communication network has been proposed for AC microgrids, in which each DG only has access to the information of a small number of its neighboring DGs, reducing the computational complexity and improving the resiliency to faults and unknown parameters. However, these approaches have not provided a clear analysis of the coupling between active/reactive power injections and the voltage magnitude/frequency or a distributed updating law with a solid theoretical foundation. Additionally, in the existing approaches, tracking the references from the secondary control may violate operational constraints.

Xu, Ying↗
DOE OSTI2020

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Secure State Estimation with Asynchronous Measurements for Coordinated Cyber Attack Detection in Active Distribution Systems

Coordinated cyber attacks tamper with measurement data to disrupt the situational awareness of active distribution systems. Various sensors report measurements asynchronously at different rates, which introduces challenges during state estimation. In addition, this forces cyber intruders to exert greater effort to compromise multiple communication channels and launch coordinated attacks. Therefore, multi-channel and asynchronous measurements could be harnessed to develop more secure cyber defense strategies. In this paper, a prediction-correction-based multi-rate observer is designed to exploit the value of asynchronous measurements for the detection of coordinated false data injection (FDI) attacks. First, a time-function-dependent prediction-correction strategy is proposed to adjust the sampling interval for each sensor’s measurement. Then, an observer is designed based on the trade-off between estimation error and the optimal period of the most recent sampling instant, with the convergence of estimation error with the maximum permitted sampling interval. Moreover, the conditions for exponential stability are developed using the Lyapunov–Krasovskii functional technique. Next, a coordinated FDI attack detection strategy is developed based on the dual nonlinear minimization problem. The proposed attack detection and secure state estimation strategies are tested on the IEEE 13-node system. Simulation results show that these schemes are effective in enhancing attack detection based on asynchronous measurements or compromised data.

asynchronous measurements↗
DOE OSTI2023

Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The Stochastic Gause Predator-Prey model: Noise-induced extinctions and invariance

We consider the Gause predator-prey with general bounded or sub‑linear functional responses, – which includes those of Holling types Ⅰ–Ⅳ. – and multiplicative Gaussian noise. In contrast to previous studies, the prey in our model follows logistic dynamics while the predator's population is solely regulated by consumption of the prey. To ensure well-posedeness, we derive explicit Lyapunov‐type criteria ensuring global positivity and moment boundedness of solutions. We find conditions for noise‑induced extinctions, proving that stochasticity can drive either population to collapse even when the deterministic analogue predicts stable coexistence. In the case when the predator becomes extinct, we establish a limiting distribution for the predator's population. Last, for functional responses of Holling type Ⅰ, we provide sufficient conditions on the intensity of the noise for the existence and uniqueness of a stationary distribution.

Gause model↗
DOE OSTI2021

Blockchain-Enabled Cyber-Secure Microgrid Control Using Consensus Algorithm: Preprint

This paper proposes a distributed control method based on a consensus algorithm for distributed energy resources (DERs) using blockchain as a secure communication medium for cyber resilience. Each DER communicates with a local blockchain server that is maintained by the distributed ledger technology to allow for securely sharing local measurements among neighboring assets to achieve the global control objectives, i.e., voltage and frequency regulation as well as accurate power sharing among the DERs, including collective grid-forming capability. To prove that the distributed control can retain system stability under a blockchain-induced variable communication delay, Lyapunov function-based stability analysis is carried out. This paper demonstrates the concept on an 11-bus test case developed in MATLAB Simulink, which has been modified from the IEEE 9-bus test case, to study dynamic operations of the five inverter-based DERs working with a blockchain-induced variable delay. The results validate the superior performance of the proposed control method, compared to heavily compromised operations of the other test cases without the security measure, affected by heavy communication delays and communication interruptions.

blockchain↗
DOE OSTI2023

Modified Virtual Oscillator-Based Operation of Grid-Forming Converters with Single Voltage Sensor: Preprint

This paper proposes a virtual oscillator-based control architecture for a grid-forming converter with an inner current control loop. In general, the virtual oscillator is based on a Lienard type of oscillator equation with a cubic nonlinearity. A virtual oscillator alone cannot accommodate unbalanced or harmonic mitigation while operating converters in grid-forming mode. Therefore, to accomplish better tracking performance, incorporating the provision for nonlinear and/or unbalanced loads, an inner current control loop is utilized that is based on the Lyapunov energy function type control architecture. To reduce the overall cost of implementation and ensure proper phase difference in the generated voltages, the implemented virtual oscillator operates with only one voltage feedback from the point of common coupling. To verify the effectiveness of the proposed approach, the overall system has been modeled in MATTLAB/Simulink and PLECS domain. This paper also presents case studies showing the successful production of low harmonic load voltages under nonideal loading conditions, along with other important results.

dual second order generalized integrator↗
DOE OSTI2023

Finite-Time Analysis of Whittle Index based Q-Learning for Restless Multi-Armed Bandits with Neural Network Function Approximation

Whittle index policy is a heuristic to the intractable restless multi-armed bandits (RMAB) problem. Although it is provably asymptotically optimal, finding Whittle indices remains difficult. In this paper, we present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation, which is an example of nonlinear two-timescale stochastic approximation with Q-function values updated on a faster timescale and Whittle indices on a slower timescale. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle, which couples neural networks with two-timescale Q-learning largely remains unclear. This paper provides a finite-time analysis of Neural-Q-Whittle, where data are generated from a Markov chain, and Q-function is approximated by a ReLU neural network. Our analysis leverages a Lyapunov drift approach to capture the evolution of two coupled parameters, and the nonlinearity in value function approximation further requires us to characterize the approximation error. Combing these provide Neural-Q-Whittle with convergence rate, where is the number of iterations.

reinforcement learning, structured learning, conve↗
DOE OSTI2024

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Safe Physics-Informed Machine Learning for Dynamics and Control

This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques enhance the modeling and control of complex dynamical systems, ensuring safety and stability remains a critical challenge, especially in safety-critical applications like autonomous vehicles, robotics, medical decision-making, and energy systems. We explore various approaches for embedding and ensuring safety constraints, including structural priors, Lyapunov and Control Barrier Functions, predictive control, projections, and robust optimization techniques. Additionally, we delve into methods for uncertainty quantification and safety verification, including reachability analysis and neural network verification tools, which help validate that control policies remain within safe operating bounds even in uncertain environments. The paper includes illustrative examples demonstrating the implementation aspects of safe learning frameworks that combine the strengths of data-driven approaches with the rigor of physical principles, offering a path toward the safe control of complex dynamical systems.

Drgona, Jan↗
DOE OSTI2022

Operation and Control of Soft Switching Solid State Transformer as a Virtual Synchronous Machine for Photovoltaic Application

Possibility for control and operation of a three-phase solid state soft switching transformer based as a virtual synchronous machine or synchronverter has been investigated in this paper. The soft switching solid state transformer is used as an interface between the ac grid and a photovoltaic power generation unit supported by a battery bank. The control architecture investigated in this paper is that of a synchronverter to achieve inertial support to the grid and local loads. The operation of the soft switching solid state transformer has also been investigated as a V S M during unbalanced/distorted grid voltage condition. Control objective to achieve oscillation free power transfer between the ports (photovoltaic, battery and grid) has been achieved. The presented architecture has been verified for several important case studies via numerical simulations based on MATLAB/Simulink domain.

grid current controller↗