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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Analogy Between the Collatz Conjecture and Sliding Mode Control

The Collatz Conjecture is a famous mathematics problem that is simple to state and understand but remains unsolved. In this paper, the problem is recast as a discrete-time nonlinear system. and viewed in a new light from the perspective of nonlinear systems and feedback control theory. In particular, connections are made between the Collatz sequence of numbers and the behavior of closed-loop dynamical systems designed using a feedback control method called sliding mode control. Trajectories of such systems are characterized by a reaching phase and a sliding phase, the latter of which exhibits exponential convergence. As sliding mode control design is rooted in Lyapunov stability theory, the analogy suggests a new direction for proving or disproving the Collatz Conjecture. Although several possible approaches are discussed, no formal proof is given in this paper.

Collatz conjecture↗
DOE OSTI2021

A Neural Lyapunov Approach to Transient Stability Assessment in Interconnected Microgrids

We propose a neural Lyapunov approach to assessing transient stability in power electronic-interfaced microgrid interconnections. The problem of transient stability assessment is cast as one of learning a neural network-structured Lyapunov function in the state space. Based on the function learned, a security region is estimated for monitoring the security of interconnected microgrids in real-time operation. The efficacy of the approach is tested and validated in a grid-connected microgrid and a three-microgrid interconnection. A comparison study suggests that the proposed method can achieve a less conservative characterization of the security region, as compared with a conventional approach.

Huang, Tong↗
NASA NTRS2004

An Approach to V&V of Embedded Adaptive Systems

Rigorous Verification and Validation (V&V) techniques are essential for high assurance systems. Lately, the performance of some of these systems is enhanced by embedded adaptive components in order to cope with environmental changes. Although the ability of adapting is appealing, it actually poses a problem in terms of V&V. Since uncertainties induced by environmental changes have a significant impact on system behavior, the applicability of conventional V&V techniques is limited. In safety-critical applications such as flight control system, the mechanisms of change must be observed, diagnosed, accommodated and well understood prior to deployment. In this paper, we propose a non-conventional V&V approach suitable for online adaptive systems. We apply our approach to an intelligent flight control system that employs a particular type of Neural Networks (NN) as the adaptive learning paradigm. Presented methodology consists of a novelty detection technique and online stability monitoring tools. The novelty detection technique is based on Support Vector Data Description that detects novel (abnormal) data patterns. The Online Stability Monitoring tools based on Lyapunov's Stability Theory detect unstable learning behavior in neural networks. Cases studies based on a high fidelity simulator of NASA's Intelligent Flight Control System demonstrate a successful application of the presented V&V methodology. ,

Liu, Yan↗
NASA NTRS1990

Stability of stationary barotropic modons by Lyapunov's direct method

A new Liapunov stability condition is formulated for the shallow-water equations, using a gage-variable formalism. This sufficient condition is derived for the class of perturbations that conserve the total mass. It is weaker than existing stability criteria, i.e., it applies to a wider class of flows. Formal stability to infinitesimally small perturbations of arbitrary shape is obtained for two classes of large-scale geophysical flows: pseudo-eastward flow with constant shear, and localized coherent structures of modon type.

Sakuma, H.↗
DOE OSTI2023

Large-Signal Stability of Phase-Balanced Equilibria in Single-Phase Grid-Forming Inverter Systems

This article explores the setup where large numbers of single-phase grid-forming inverters with droop control across distribution networks self-organize into a stable and balanced system with 120° phase offsets across aggregates in the absence of balanced three-phase generating resources or external communication. A suite of circuit- and system-theoretic notions are leveraged to derive a dynamical model for phase-angle differences across aggregates of inverters connected in the three phases. Focusing on this model, large-signal stability is established and the region of attraction of the phase-balanced equilibria is determined with the aid of a Lyapunov function. Experimental validation for a bench-top prototype network is included to support the analytical developments. Altogether, the effort supports the vision of facilitating balanced operation of distribution networks with grid-forming inverters during service disruptions at the bulk transmission network.

Droop control↗
NASA NTRS2017

Evaluating the Stability of NASA's Space Launch System with Adaptive Augmenting Control

NASA's baseline Space Launch System (SLS) flight control system (FCS) design includes an adaptive augmenting control (AAC) component that modifies the attitude control system response to provide the classical gain-scheduled control architecture with additional performance and robustness. The NASA Engineering and Safety Center (NESC) teamed with the Space Launch System (SLS) Program to perform a comprehensive assessment of the stability and robustness of the FCS with AAC. This paper provides an overview of the approach, specific analysis techniques, and outcomes that were particularly relevant for the SLS Program. Multiple analysis techniques that specifically target the nonlinear AAC were commissioned as part of this assessment, which was completed outside of the Program's standard design analysis cycle. The following analyses were included, with each technique adding its own valuable insights: Lyapunov-based stability analysis, classical stability analysis with static AAC gain variations, circle criterion-based analysis of the FCS with a time-varying element, time-domain stability margin assessment, Monte Carlo simulations with expanded dispersions, and an extensive set of stressing cases. Several of the completed analyses focused on determining whether the inclusion of AAC introduced risk to the FCS, while others quantified the benefits of the adaptive augmentation.

Tannen S Vanzwieten↗
NASA NTRS1982

The applicability of Lyapunov characteristic numbers in the study of the stability of satellite orbits

It is pointed out that the Lyapunov Characteristic Numbers constitute a new tool for determining stability of trajectories of dynamical systems, or, even more generally, of solutions of systems of ordinary differential equations. In contrast with the characteristic exponents, which apply only to periodic solutions, the Lyapunov Characteristic Numbers apply to arbitrary nonperiodic solutions as well. A description is presented of the numerical experiments which have been made in order to investigate the practical value of the Lyapunov Characteristic Number and the Kolmogorov Entropy for the purpose of estimating the stability of trajectories and/or numerical integration methods in celestial mechanics. It is found that the Lyapunov Characteristic Numbers are extremely useful for the classification of the solutions of nonintegrable dynamical systems, especially in order to distinguish between quasi-periodic and chaotic solutions. However, the Lyapunov Characteristics Numbers do not appear to be useful for the purpose of evaluating numerical integration methods.

Broucke, R.↗
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↗
NASA NTRS2010

A Spectral Lyapunov Function for Exponentially Stable LTV Systems

This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.

Zhu, J. Jim↗
DOE OSTI2021

Neural Lyapunov Control for Power System Transient Stability: A Deep Learning-Based Approach

We report that power system control and transient stability analysis play essential roles in secure system operation. Control of power systems typically involves highly nonlinear and complex dynamics. Most of the existing works address such problems with additional assumptions in system dynamics, leading to a requirement for a complete and general solution. This paper, therefore, proposes a novel control framework for various power system control and stability problems leveraging a learning-based approach. The proposed framework includes a two-module structure that iteratively and jointly learns the candidate Lyapunov function and control law via deep neural networks in a learning module. Meanwhile, it guides the learning procedure towards valid results satisfying Lyapunov conditions in a falsification module. The introduced termination criteria ensure provable system stability. This control framework is verified through several studies handling different types of power system control problems. The results show that the proposed framework is generalizable and can simplify the control design for complex power systems with the stability guarantee and enlarged region of attraction.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Blockchain-Enabled Cyber-Secure Microgrid Control Using Consensus Algorithm

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 neighbouring 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.

blockchains↗
NASA NTRSDate not supplied

Controls Algorithms, Models, and Stability Assessments of the RCS and TVC systems on Mars Ascent Vehicle

This paper presents a control systems overview of the Mars Ascent Vehicle (MAV) control design and stability analysis with two separate control methods: Thrust Vector Control (TVC) based control using main engine thrust and Reaction Control System (RCS) via thrusters. A pole-placement TVC controller is proposed to address quickly peaking thrust produced by the MAV solid propulsion engine. The controllerutilizes real-time parameter estimation to calculate control gains using an online pole-placement method. The pole-placement technique allows the controller to maintain constant stability margins throughout the flight under changing parameters and rapidly peaking thrust. A mathematical stability proof via Lyapunov inequality and Nichols method is demonstrated to support the stability of the method. In addition to the TVC control, a phase-plane based RCS control logic is applied to the vehicle for roll control during ascent and all axes during coast phases of flight. The logic implemented is an on-off type logic that applies pre-determined thrusters firings in reference to boundary parameters of pointing and rate error chosen to balance desired pointing with stability. A describing function methodology is applied to the non-linear phase plane loop response to determine linear stability across all flight phases. The controller additionally applies command alteration logic to output signals to account for RCS hardware limitations. The following paper will provide the methodology for controller implementation of the TVC and RCS, and provide a summary of results of the MAV performance applying the aforementioned control design.

Han Woong Bae↗
DOE OSTI2023

Out-of-time-order correlators and Lyapunov exponents in sparse SYK

We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order of N, the standard result for the q-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter, k. We present an algorithm to sum the diagrams at any given order of 1/(kq) n . We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finite N becomes more significant for larger values of N.

2D gravity↗