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A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
The Mission Data System framework defines closed-loop control system abstractions from State Analysis including interfaces for state variables, goals, estimators, and controllers that can be adapted to implement a goal-oriented control system. The framework further provides an execution environment that includes a goal scheduler, execution engine, and fault monitor that support the expression of goal network activity plans. Using these frameworks, adapters can build a goal-oriented control system where activity coordination is verified before execution begins (plan time), and continually during execution. Plan failures including violations of safety constraints expressed in the plan can be handled through automatic re-planning. This version optimizes a number of key interfaces and features to minimize dependencies, performance overhead, and improve reliability. Fault diagnosis and real-time projection capabilities are incorporated. This version enhances earlier versions primarily through optimizations and quality improvements that raise the technology readiness level. Goals explicitly constrain system states over explicit time intervals to eliminate ambiguity about intent, as compared to command-oriented control that only implies persistent intent until another command is sent. A goal network scheduling and verification process ensures that all goals in the plan are achievable before starting execution. Goal failures at runtime can be detected (including predicted failures) and handled by adapted response logic. Responses can include plan repairs (try an alternate tactic to achieve the same goal), goal shedding, ignoring the fault, cancelling the plan, or safing the system.
GaussFit is a new computer program for solving least-squares and robust estimation problems. It has a number of unique features, including a complete programming language designed especially to formulate estimation problems, a built-in compiler and interpreter to support the programming language, and a built-in algebraic manipulator for calculating the required partial derivatives analytically. These features make GaussFit very easy to use, so that even complex problems can be set up and solved with minimal effort. GaussFit can correctly handle many cases of practical interest: nonlinear models, exact constraints, correlated observations, and models where the equations of condition contain more than one observed quantity. An experimental robust estimation capability is built into GaussFit so that data sets contaminated by outliers can be handled simply and efficiently.
An important element of Artemis and NASA’s campaign to explore the Moon is the autonomous onboard two-level targeter (TLT) used during all cislunar flight phases. The function of the TLT is to autonomously recompute the burn targets for the upcoming burn (or multiple burns) in response to navigation and vehicle dispersion providing a solution that meets all of the trajectory constraints. Although the TLT has been utilized previously as a ground-based planning tool, and flown onboard during the Artemis I mission, it’s complexity and iterative nature make is difficult to incorporate into and support rapid analyses such as robust optimal trajectory design applications where speed is essential. In this paper, a set of generalized linear targeting algorithms that mimics many of the properties of the TLT is derived. The generalized algorithms can handle single or multiple impulsive maneuvers, with multiple constraints at multiple fixed or variable times. A linear targeting algorithm for finite burn maneuvers is also derived. The generalized linear targeting algorithms are exceptionally fast and easy to implement in Monte Carlo analysis, linear covariance (LinCov) analysis, and robust optimal trajectory design. Several cislunar flight examples are provided.
The design of aerodynamic components of aircraft, such as wings or engines, involves a process of obtaining the most optimal component shape that can deliver the desired level of component performance, subject to various constraints, e.g., total weight or cost, that the component must satisfy. Aerodynamic design can thus be formulated as an optimization problem that involves the minimization of an objective function subject to constraints. A new aerodynamic design optimization procedure based on neural networks and response surface methodology (RSM) incorporates the advantages of both traditional RSM and neural networks. The procedure uses a strategy, denoted parameter-based partitioning of the design space, to construct a sequence of response surfaces based on both neural networks and polynomial fits to traverse the design space in search of the optimal solution. Some desirable characteristics of the new design optimization procedure include the ability to handle a variety of design objectives, easily impose constraints, and incorporate design guidelines and rules of thumb. It provides an infrastructure for variable fidelity analysis and reduces the cost of computation by using less-expensive, lower fidelity simulations in the early stages of the design evolution. The initial or starting design can be far from optimal. The procedure is easy and economical to use in large-dimensional design space and can be used to perform design tradeoff studies rapidly. Designs involving multiple disciplines can also be optimized. Some practical applications of the design procedure that have demonstrated some of its capabilities include the inverse design of an optimal turbine airfoil starting from a generic shape and the redesign of transonic turbines to improve their unsteady aerodynamic characteristics.
Sample preparation and sample handling are among the most critical operations associated with X-ray diffraction (XRD) analysis. These operations require attention in a laboratory environment, but they become a major constraint in the deployment of XRD instruments for robotic planetary exploration. We are developing a novel sample handling system that dramatically relaxes the constraints on sample preparation by allowing characterization of coarse-grained material that would normally be impossible to analyze with conventional powder-XRD techniques.
A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.
We present a decentralized failure-tolerant algorithm for optimizing electric vehicle (EV) charging, using charging stations as computing agents. The algorithm is based on the alternating direction method of multipliers (ADMM) and it has the following features: (i) It handles capacity, peak demand, and ancillary services coupling constraints. (ii) It does not require a central agent collecting information and performing coordination (e.g. an aggregator), instead all agents exchange information and computations are carried out in a fully decentralized fashion. (iii) It can withstand the failure of any number of computing agents, as long as the remaining computing agents are in a connected communications network. We construct this algorithm by reformulating the optimal EV charging problem in a decomposable form, amenable to ADMM, and then developing efficient decentralized solution methods for the subproblems dealing with coupling constraints. We conduct numerical experiments on industry-scale synthetic EV charging datasets, with up to 1,152 charging stations, using a high performance computing cluster. The experiments demonstrate that the proposed algorithm can solve the optimal EV charging problem fast enough to permit the integration of EV charging with real-time electricity markets, even in the presence of failures.
To meet PIP-II upgrade requirements, Fermilab Booster losses need to be reduced by 50% compared to present levels. So far, simulations are not good enough to predict loss patterns. Thus, an extensive Booster tune up will be necessary to achieve required performance. In this paper we present an effort to build a data-driven loss model using Bayesian techniques, and subsequently to rebalance losses for higher trip margins. We first created several sets of spatially and temporally isolated orbit and optics knobs, and trained Gaussian process models for each beam loss monitor as well as beam current. Novel techniques of uncertainty constraints and approximate GP fitting were introduced to handle safety and timing requirements. We then performed single and multi-objective tuning using scalarized objectives comprised of critical beam loss locations. We achieved significant rebalancing of losses, increasing margins by 25%, as well as an overall improvement in transmission efficiency of 0.4%. Automated data collection is being developed so that more accurate surrogate models can be trained over time.
Nine million measurements a day are transmitted from each functional ALSEP on the moon and continuously collected on earth for use in long-term scientific analysis. Periodically, this massive flow of intricate data is examined on a real-time basis to evaluate ALSEP performance and to study the need for new commands to any of the ALSEP systems. A worldwide complex of facilities and personnel has the challenging task of efficient and timely data processing and dissemination. This paper describes facility characteristics and support activities and details certain constraints imposed on ALSEP hardware design by data handling requirements. The highlights of the first two years of lunar data management are reviewed.
The Software Implemented Fault Tolerance SIFT system, is written in PASCAL except for about a page of machine code. The SIFT system implements a small time sharing system in which PASCAL programs for separate application tasks are executed according to a schedule with real time constraints. The PASCAL language has no provision for handling the notion of an interrupt such as the B930 clock interrupt. The PASCAL language also lacks the notion of running a PASCAL subroutine for a given amount of time, suspending it, saving away the suspension, and later activating the suspension. Machine code was used to overcome these inadequacies of PASCAL. Code which handles clock interrupts and suspends processes is called a dispatcher. The time sharing/virtual machine idea is completely destroyed by the reconfiguration task. After termination of the reconfiguration task, the tasks run by the dispatcher have no relation to those run before reconfiguration. It is impossible to view the dispatcher as a time-sharing system implementing virtual BDX930s running concurrently when one process can wipe out the others.
This work is concerned with the control problem of a multi-robot system handling a payload with unknown mass properties. Force constraints at the grasp points are considered. Robust control schemes are proposed that cope with the model uncertainty and achieve asymptotic path tracking. To deal with the force constraints, a strategy for optimally sharing the task is suggested. This strategy basically consists of two steps. The first detects the robots that need help and the second arranges that help. It is shown that the overall system is not only robust to uncertain payload parameters, but also satisfies the force constraints.
Mars Global Surveyor (MGS) avionics system architecture comprises much of the electronics on board the spacecraft: electrical power, attitude and articulation control, command and data handling, telecommunications, and flight software. Schedule and cost constraints dictated a mix of new and inherited designs, especially hardware upgrades based on findings of the Mars Observer failure review boards.
Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learn- ing to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.
Software verification is recognized as an important and difficult problem. We present a norel framework, based on symbolic execution, for the automated verification of software. The framework uses annotations in the form of method specifications an3 loop invariants. We present a novel iterative technique that uses invariant strengthening and approximation for discovering these loop invariants automatically. The technique handles different types of data (e.g. boolean and numeric constraints, dynamically allocated structures and arrays) and it allows for checking universally quantified formulas. Our framework is built on top of the Java PathFinder model checking toolset and it was used for the verification of several non-trivial Java programs.
This document describes Management by Trajectory (MBT), a concept for future air traffic management (ATM) in which every flight operates in accordance with a four-dimensional trajectory (4DT) that is negotiated between the airspace user and the Federal Aviation Administration (FAA) to respect the airspace user's goals while complying with National Airspace System (NAS) constraints. In the present-day NAS, the ATM system attempts to predict the trajectory for each flight based on the approved flight plan and scheduled or controlled departure time. However, once the aircraft starts to move, controllers tactically manage the aircraft to implement traffic management restrictions, separate otherwise conflicting aircraft, and address arising NAS constraints. Tactical controller actions are not directly communicated to the automation systems or other stakeholders. Furthermore, the initial trajectory prediction does not anticipate these disruptions or how they will impact the flight. Consequently, and compounded by gaps in required data and models, trajectory predictions are less accurate than possible, which affects Traffic Flow Management (TFM) performance. A cornerstone of the MBT concept is that all air vehicles have, at all times, an assigned 4DT from their current state to their destination. These assigned trajectories consist of trajectory constraints and descriptions. Pilots and air traffic controllers, with the aid of automation, operate the aircraft to comply with the assigned trajectory, unless first negotiating a revision. Equipped aircraft have substantial responsibility for complying with the assigned trajectory without controller intervention. To maximize the operational flexibility available to the airspace user, the assigned trajectory only imposes trajectory constraints as required to achieve the ATM goals of NAS constraint compliance and aircraft separation. Trajectory descriptions are added to the assigned trajectory to ensure sufficient predictability. To further improve trajectory prediction accuracy, airspace users supplement the assigned trajectory by broadcasting intent information and updating it as necessary. Air vehicle intent is a more detailed description of the airspace user's plan for how the flight will fly the assigned trajectory. Air vehicle intent can change freely, without negotiation, as long as it remains in compliance with the assigned trajectory. Aircraft assigned trajectories, air vehicle intent, and predicted trajectories are shared, creating a common view among stakeholders. A NAS Constraint Service gathers and publishes information about all known NAS constraints, enabling airspace users to be informed participants in trajectory negotiation. Trajectory constraints in the assigned trajectory are mapped to NAS constraints to facilitate identifying which aircraft are affected when NAS constraints change. To support efficient trajectory negotiation, all aircraft provide current information about air vehicle capabilities. Assigned trajectories are constructed to satisfy all known NAS constraints, improving trajectory stability and predictability. Uncertainty and disruptions are handled by modifying the assigned trajectory as far in advance as possible. By proactively negotiating changes to the assigned trajectory, rather than relying on controller-selected tactical actions such as vectors to resolve traffic conflicts or implement miles-in-trail restrictions, MBT keeps aircraft on closed trajectories that are fully known to all stakeholders. Since reactive air traffic control actions cannot be predicted in advance, the downstream trajectory cannot be accurately predicted until they happen. Reliable trajectory predictions allow the system to identify needed modifications to trajectories further in advance, where they can be negotiated and communicated as amendments (i.e., additional or altered trajectory constraints) to the assigned trajectory. Decision Support Tools (DSTs) aid controllers in rapidly defining and communicating closed trajectories to the aircraft and support all stakeholders in trajectory negotiation. Anticipated MBT benefit mechanisms include more accurate trajectory predictions, improved ATM performance and robustness to off-nominal conditions, increased flexibility and operational efficiency, reduced impediments to emerging classes of airspace users accessing NAS resources, reduced environmental impacts, and enhanced safety.
Experience gained through the Shuttle Orbital Flight Test program has matured the engineering understanding of the Shuttle on-orbit control system. The geneology of the control systems (called digital autopilots, or DAPs, and used by the Shuttle for on-orbit operations) is reviewed, the flight experience gained during the flight test program is examined within the context of preflight analysis and test results, and issues for the operational phase of the Shuttle, including constraints upon both operations and analysis still required to increase confidence in the Shuttle's ability to handle capabilities not experienced during the flight test program are addressed. Two orbital autopilots have resulted from computer memory and time constraints on a flight control system, with many different, flight phase unique requirements. The transition DAP, used for insertion and deorbit, has more active sensors and redundancy but a less complex data processing scheme excluding state estimation with fewer choices of operational mode.