Mathematical programming and the control of Markov chains
Linear and dynamic programming and Markov chain optimal control
Kleinman, A. J.↗
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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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Nineteen sixty-seven behavioral model of man - His chains revealed
Dynamic characteristics of physical-chemical systems in human behavior, and structural nature of brain
DYNAMIC PROPERTY↗
Constraint Embedding Technique for Multibody System Dynamics
Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with closure-constraints into an equivalent tree-topology system, and thus allows one to take advantage of the host of techniques available to the latter class of systems. This technology is highly suitable for the class of multibody systems where the closure-constraints are local, i.e., where they are confined to small groupings of bodies within the system. Important examples of such local closure-constraints are constraints associated with four-bar linkages, geared motors, differential suspensions, etc. One can eliminate these closure-constraints and convert the system into a tree-topology system by embedding the constraints directly into the system dynamics and effectively replacing the body groupings with virtual aggregate bodies. Once eliminated, one can apply the well-known results and algorithms for tree-topology systems to solve the dynamics of such closed-chain system.
Woo, Simon S.↗
Charge and Spin Dynamics of the Hubbard Chains
We calculate the local correlation functions of charge and spin for the one-chain and two-chain Hubbard model using density matrix renormalization group method and the recursion technique. Keeping only finite number of states we get good accuracy for the low energy excitations. We study the charge and spin gaps, bandwidths and weights of the spectra for various values of the on-site Coulomb interaction U and the electron filling. In the low energy part, the local correlation functions are different for the charge and spin. The bandwidths are proportional to t for the charge and J for the spin respectively.
Park, Youngho↗
Consequence and Resilience Modeling for Chemical Supply Chains
The U.S. chemical sector produces more than 70,000 chemicals that are essential material inputs to critical infrastructure systems, such as the energy, public health, and food and agriculture sectors. Disruptions to the chemical sector can potentially cascade to other dependent sectors, resulting in serious national consequences. To address this concern, the U.S. Department of Homeland Security (DHS) tasked Sandia National Laboratories to develop a predictive consequence modeling and simulation capability for global chemical supply chains. This paper describes that capability , which includes a dynamic supply chain simulation platform called N_ABLE(tm). The paper also presents results from a case study that simulates the consequences of a Gulf Coast hurricane on selected segments of the U.S. chemical sector. The case study identified consequences that include impacted chemical facilities, cascading impacts to other parts of the chemical sector. and estimates of the lengths of chemical shortages and recovery . Overall. these simulation results can DHS prepare for and respond to actual disruptions.
Stamber, Kevin L.↗
New Factorization Techniques and Parallel (log N) Algorithms for Forward Dynamics Solution of Single Closed-Chain Robot Manipulators
In this paper parallel 0(log N) algorithms for dynamic simulation of single closed-chain rigid multibody system as specialized to the case of a robot manipulatoar in contact with the environment are developed.
Factorization Techniques↗
An approach to simultaneous control of trajectory and interaction forces in dual-arm configurations
An approach to the control of constrained dynamic systems such as multiple arm systems, multifingered grippers, and walking vehicles is described. The basic philosophy is to utilize a minimal set of inputs to control the trajectory and the surplus input to control the constraint or interaction forces and moments in the closed chain. A dynamic control model for the closed chain is derived that is suitable for designing a controller in which the trajectory and the interaction forces and moments are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. These ideas are illustrated through a planar example in which two arms are used for cooperative manipulation. Results from a simulation are used to illustrate the efficacy of the method.
Yun, Xiaoping↗
Dynamical Mechanisms Underlying the 2022/23 California Flooding: Analysis With A Stationary Wave Model
In late December 2022 and the first half of January 2023, much of California experienced an unprecedented series of atmospheric rivers that produced heavy rains and near-record flooding. Previous work shows that a chain of dynamical events contributed to the extreme precipitation, including the development of a Rossby wave (as a result of forcing linked to the MJO) that emerged from the Indian Ocean in mid-December, and the subsequent development of a persistent positive Pacific North American (PNA) pattern that ultimately directed moisture onto the US West Coast starting in late December. Here, we use a stationary wave model (SWM) to further elucidate the dynamical and thermodynamical processes that drove the aforementioned chain of events. The results reveal the following: 1) The mid-December Rossby wave was likely induced by vorticity stretching and advection in the middle East linked indirectly to the MJO, 2) The initial development of the PNA in late December was triggered by transient and stretching sources of vorticity in the Pacific that were themselves induced by the aforementioned Rossby wave, and 3) The PNA was maintained through mid-January in part by diabatic heating west of Hawaii that was associated with anomalous precipitation influenced by the PNA circulation anomalies, thus representing a feedback on the PNA. One key finding from the SWM analysis is the limited direct role of tropical heating for inducing any of the dynamical mechanisms related to the California extreme event.
Anthony M. DeAngelis↗
Dynamical Mechanisms Underlying the 2022/23 California Flooding: Analysis With A Stationary Wave Model
In late December 2022 and the first half of January 2023, much of California experienced an unprecedented series of atmospheric rivers that produced heavy rains and near-record flooding. Previous work shows that a chain of dynamical events contributed to the extreme precipitation, including the development of a Rossby wave (as a result of forcing linked to the MJO) that emerged from the Indian Ocean in mid-December, and the subsequent development of a persistent positive Pacific North American (PNA) pattern that ultimately directed moisture onto the US West Coast starting in late December. Here, we use a stationary wave model (SWM) to further elucidate the dynamical and thermodynamical processes that drove the aforementioned chain of events. The results reveal the following: 1) The mid-December Rossby wave was likely induced by vorticity stretching and advection in the middle East linked indirectly to the MJO, 2) The initial development of the PNA in late December was triggered by transient and stretching sources of vorticity in the Pacific that were themselves induced by the aforementioned Rossby wave, and 3) The PNA was maintained through mid-January in part by diabatic heating west of Hawaii that was associated with anomalous precipitation influenced by the PNA circulation anomalies, thus representing a feedback on the PNA. One key finding from the SWM analysis is the limited direct role of tropical heating for inducing any of the dynamical mechanisms related to the California extreme event.
Anthony M. DeAngelis↗
Unified formulation of dynamics for serial rigid multibody systems
There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, and a variety of algorithms to solve the serial chain forward dynamics problem have been proposed. In this paper, the economy of representation and analysis tools provided by the spatial operator algebra are used to clarify the inherent structure of these algorithms, to identify those that are similar, and to study the relationships among the ones that are distinct. For the purposes of this study, the algorithms are categorized into three classes: algorithms that require the explicit computation of the mass matrix, algorithms that are completely recursive in nature, and algorithms of intermediate complexity. In addition, alternative factorizations for the mass matrix and closed form expressions for its inverse are derived. These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix.
Jain, Abhinandan↗
Translocation of a Polymer Chain across a Nanopore: A Brownian Dynamics Simulation Study
We carried out Brownian dynamics simulation studies of the translocation of single polymer chains across a nanosized pore under the driving of an applied field (chemical potential gradient). The translocation process can be either dominated by the entropic barrier resulted from restricted motion of flexible polymer chains or by applied forces (or chemical gradient across the wall), we focused on the latter case in our studies. Calculation of radius of gyrations at the two opposite sides of the wall shows that the polymer chains are not in equilibrium during the translocation process. Despite this fact, our results show that the one-dimensional diffusion and the nucleation model provide an excellent description of the dependence of average translocation time on the chemical potential gradients, the polymer chain length and the solvent viscosity. In good agreement with experimental results and theoretical predictions, the translocation time distribution of our simple model shows strong non-Gaussian characteristics. It is observed that even for this simple tubelike pore geometry, more than one peak of translocation time distribution can be generated for proper pore diameter and applied field strengths. Both repulsive Weeks-Chandler-Anderson and attractive Lennard-Jones polymer-nanopore interaction were studied, attraction facilitates the translocation process by shortening the total translocation time and dramatically improve the capturing of polymer chain. The width of the translocation time distribution was found to decrease with increasing temperature, increasing field strength, and decreasing pore diameter.
Tian, Pu↗
Nonlinear strain-displacement relations and flexible multibody dynamics
Dynamics of chains of flexible bodies undergoing large rigid body motions, but small elastic deflections are considered. The role of nonlinear strain-displacement relations in the development of the motion equations correct to first order in elastic deflections is investigated. The general form of these equations linearized only in the small elastic deflections is presented, and the relative significance of various nonlinear terms is studied both analytically and through the use of the numerical simulations. Numerical simulations are performed for a two link chain constrained to move in the plane, subject to hinge torques. Each link is modeled as a thin beam. Slew maneuver simulation results are compared for models with and without properly modeled kinematics of deformation. The goal of this case study is to quantify the importance of the terms in the equations of motion which arise from the inclusion of nonlinear strain-displacement relations. It is concluded that unless the consistently linearized equations in elastic deflections and speeds are available and necessary, the inconsistently (prematurely) linearized equations should be replaced in all cases by ruthlessly linearized equations: equations in which all nonlinear terms involving the elastic deflections and speeds are ignored.
Padilla, Carlos E.↗
Sustaining NASA-Invented Thermal Protection System Materials for Future Missions
TPS is needed for NASA and many emerging commercial space missions and is dependent on an industrial base for future availability. Supply chains are dynamic and global. Change to constituent availability, after the fact, can impact missions. In addition to external vendor capability, NASA needs to maintain the in-house expertise and use SMEs to engage industry to assess the risk of atrophy on a constant basis and propose risk mitigation options to the Leadership as needed.
Matt Gasch↗
Contracting Quality Early in the Lifecycle Using AS9145 Data Deliverables
Development schedules and a highly dynamic supply chain are a challenge to developers of complex systems produced at low volume. Flaws in designs, parts and materials availability problems, poor manufacturability, and a lack of knowledge about critical items and key process attributes can be realized well before traditional second-party quality assurance activities begin. Supplier audits and product inspections may have little mitigating effect once these foundational problems have been realized. Their impacts can be significant lifecycle disruption, cost overruns, inability to deliver to plan, and even project cancellation. AS9145, Requirements for Advanced Product Quality Planning and Production Part Approval Process, can be used to drive quality engineering practices into early development lifecycles to significantly reduce this late-cycle risk and to reduce the cost of quality overall. Since its initial publication in 2016, it has had very limited adoption by the DoD, no adoption by NASA, and sparse adoption in the aerospace and defense supply chain. A task group within the Aerospace Industries Association's (AIA) Joint Strategic Quality Council (JSQC) identified that both acquirers and suppliers see as AS9145 as a cost-adder and are hesitant to use it as an alternative to late-stage-heavy quality assurance approaches. A lack of prior use creates large capability gaps in request-for-proposal (RFP) teams, proposal teams, suppliers’ quality management systems (QMS), and in experienced personnel executing the early lifecycle approach. To create a more realizable on-ramp for using AS9145 in the space and defense sectors, the AIA JSQC task team created five deliverable requirements descriptions (DRDs) that can be used in a contract to begin to engage both parties in early lifecycle quality engineering and quality assurance activities, that reduce exposure to late-stage cost and schedule collapse due to unidentified risks in design, supply chain, and manufacturability. These DRDs drive the parties to engage in planning and analysis discussions early on to understand what production risks can be known and how they will focus resources based on safety criticality and the key elements of design and construction. The suppliers and acquirers who will produce the data and information required by the DRD will be able to incrementally evolve their QMS and the acquirer will incrementally be able to track and understand the benefits of cost shifting from late to early development phases. A white paper describing this approach and the five recommended DRDs will be published by the AIA in late 2024 or early 2025.
Jeannette Plante↗
Space Launch System: CLVTOPS Toolchain for SLS Liftoff Separation Analysis
This presentation showcases the unique technical capabilities of the CLVTOPS multi-body flight dynamics tool chain developed by Marshall Space Flight Center (MSFC) for analyzing NASA’s Space Launch System (SLS) liftoff events. The CLVTOPS tool chain integrates high-fidelity simulations, geometric algorithms, advanced data analytics, and post-flight telemetry to demonstrate positive clearance between separating bodies and inform design decisions that enhance mission reliability. Proper liftoff separation is crucial to the success of the launch vehicle’s mission; vehicle impacts with the launch tower and supporting components incur a heightened risk of mission failure. For liftoff analysis, the CLVTOPS tool chain enables the integration of vehicle, launch pad, and environmental input models for the investigation of key clearance effectors. Furthermore, a novel capability of the CLVTOPS tool chain allows for verification and validation of trajectory reconstruction via photogrammetric imagery analysis. The following sections will walk through the tool chain, SLS liftoff ground rules and assumptions, model integration, pre-flight verification, and post-flight validation of the Artemis I mission liftoff event.
CLVTOPS↗
Recursive Dynamic Equations For Two Robot Arms In A Closed Chain
Paper discusses use of difference equations from Kalman filtering and Bryson-Frazier smoothing to solve equations of forward dynamics of closed chain of robot-arm links. "Forward dynamics" is computation of linear and angular accelerations of joints between links, given set of applied or prescribed joint torques. Paper lays foundation for potential use of filtering and smoothing techniques in dynamics of robots and in design of controls for robots.
Rodriguez, Guillermo↗
Markov chain techniques for predicting the maximum wind in the maximum dynamic pressure region for launching space vehicles
Markov chain techniques for predicting maximum wind in maximum dynamic pressure region for spacecraft launching
Crutcher, H. L.↗
New Factorizations and Fast Parallel Algorithms for Forward Dynamics Solution of Single Closed-Chain Robot Manipulators
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Matrix schur complement factorization↗