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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Chebyshev Polynomial↗
DOE OSTI2022

Data-Driven Simulation-Based Planning for Electric Airport Shuttle Systems: A Real-World Case Study

Many airports are adopting battery electric buses in their shuttle fleets due to concerns over air quality and regulations. This study proposes a simulation-based optimization modeling framework to help airport shuttle operators effectively deploy electric buses. We evaluated a planned airport electric shuttle system with an event-driven simulator. Empirical data collected from existing systems were used to drive the simulations. We then proposed a simulation-based optimization model to determine the battery capacity, charging power, and number of chargers so that predefined objective(s) (e.g., minimizing total capital cost, minimizing emissions) are optimized. Compared to existing studies, the primary contribution of the proposed method is that it can model the real-world stochastic nature of operations in an electric bus system with much higher fidelity. To demonstrate the proposed modeling framework, we study a real-world shuttle system at the Dallas-Fort Worth International Airport, and present extensive numerical studies. When considering partial fleet electrification, the model can provide a set of Pareto optimal solutions. When considering full fleet electrification, the optimal solution requires a 50-kWh battery capacity and four 210-kW chargers, resulting in a total capital cost of $26,744,000. The results demonstrate that the proposed modeling framework can effectively optimize the planning of electric airport shuttle systems with partial or full fleet electrification.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗
DOE OSTI2020

Efficient proactive vehicle relocation for on-demand mobility service with recurrent neural networks

One major challenge for on-demand mobility service (OMS) providers is to seamlessly match empty vehicles with trip requests so that the total vacant mileage is minimized. In this work, we develop an innovative data-driven approach for devising efficient vehicle relocation policy for OMS that (1) proactively relocates vehicles before the demand is observed and (2) reduces the inequality among drivers' income so that the proactive relocation policy is fair and is likely to be followed by drivers. Our approach represents the fusion of optimization and machine learning methods, which comprises three steps: First, we formulate the optimal proactive relocation as an optimal/stable matching problems and solve for global optimal solutions based on historical data. Second, the optimal solutions are then grouped and fed to train the deep learning models which consist of fully connected layers and long short-term memory networks. Low rank approximation is introduced to reduce the model complexity and improve the training performances. Finally, we use the trained model to predict the relocation policy which can be implemented in real time. We conduct comprehensive numerical experiments and sensitivity analyses to demonstrate the performances of the proposed method using New York City taxi data. Here, the results suggest that our method will reduce empty mileage per trip by 54-70% under optimal matching strategy, and a 25-32% reduction can also be achieved by following stable matching strategy. We also validate that the predicted relocation policies are robust in the presence of uncertain passenger demand level and passenger trip-requesting behavior.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Posiform planting: generating QUBO instances for benchmarking

We are interested in benchmarking both quantum annealing and classical algorithms for minimizing quadratic unconstrained binary optimization (QUBO) problems. Such problems are NP-hard in general, implying that the exact minima of randomly generated instances are hard to find and thus typically unknown. While brute forcing smaller instances is possible, such instances are typically not interesting due to being too easy for both quantum and classical algorithms. In this contribution, we propose a novel method, called posiform planting , for generating random QUBO instances of arbitrary size with known optimal solutions, and use those instances to benchmark the sampling quality of four D-Wave quantum annealers utilizing different interconnection structures (Chimera, Pegasus, and Zephyr hardware graphs) and the simulated annealing algorithm. Posiform planting differs from many existing methods in two key ways. It ensures the uniqueness of the planted optimal solution, thus avoiding groundstate degeneracy, and it enables the generation of QUBOs that are tailored to a given hardware connectivity structure, provided that the connectivity is not too sparse. Posiform planted QUBOs are a type of 2-SAT boolean satisfiability combinatorial optimization problems. Our experiments demonstrate the capability of the D-Wave quantum annealers to sample the optimal planted solution of combinatorial optimization problems with up to 5, 627 qubits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Fast Iterative Multi-site Hosting Capacity Analysis for Distribution Systems With Search Space Pruning

Interconnection studies for distributed energy resources (DERs) is a time-intensive process, primarily due to the necessity of solving large number of power flow scenarios. Hosting capacity analysis (HCA) is a time-consuming aspect of interconnection studies that is divided into single-site HCA (SHCA) and multi-site HCA (MHCA). From a computational and understandable standpoint, the industry seeks iteration-based solutions for SHCA, although it doesn't maximize the total DER hosting capacity (DERHC) of the grid, as MHCA does. While non-iterative solutions are available for MHCA, they involve a trade-off between the modeling accuracy of the distribution system, solution quality, and ease of understanding. In this work, we present a fast iterative solution for MHCA, reducing computational complexity by eliminating the need to solve power flows for a large amount of search space, thus making iterative solutions feasible. This iterative approach guarantees both a global optimal solution with sufficient time and a fast, close-to-optimal solution through efficient search space pruning. It also easily integrates with existing utility HCA tools. The results are demonstrated on select locations in the IEEE-123 bus system for community-scale interconnection studies. We highlight the benefits of skipping the need to solve millions of power flows, all while maximizing the grid's total DERHC.

Guddanti, Kishan Prudhvi↗
NASA NTRS1976

Lagrange duality theory for convex control problems

The Lagrange dual to a control problem is studied. The principal result based on the Hahn-Banach theorem proves that the dual problem has an optimal solution if there exists an interior point for the constraint set. A complementary slackness condition holds, if the primal problem has an optimal solution. A necessary and sufficient condition for the optimality of solutions to the primal and the dual problem is also presented.

Hager, W. W.↗
NASA NTRS1989

An algorithm for the systematic disturbance of optimal rotational solutions

An algorithm for introducing a systematic rotational disturbance into an optimal (i.e., single axis) rotational trajectory is described. This disturbance introduces a motion vector orthogonal to the quaternion-defined optimal rotation axis. By altering the magnitude of this vector, the degree of non-optimality can be controlled. The metric properties of the distortion parameter are described, with analogies to two-dimensional translational motion. This algorithm was implemented in a motion-control program on a three-dimensional graphic workstation. It supports a series of human performance studies on the detectability of rotational trajectory optimality by naive observers.

Grunwald, Arthur J.↗
DOE OSTI2021

Tuning successive linear programming to solve AC optimal power flow problem for large networks

Successive linear programming (SLP) is a practical approach for solving large-scale nonlinear optimization problems. Alternating current optimal power flow (ACOPF) is no exception, particularly the large size of real-world networks. However, in order to achieve tractability, it is essential to tune the SLP algorithm presented in the literature. This paper presents a modified SLP algorithm to solve the ACOPF problem, specified by the U.S. Department of Energy’s (DOE) Grid Optimization (GO) Competition Challenge 1, within strict time limits. The algorithm first finds a near-optimal solution for the relaxed problem (i.e., Stage 1). Then, it finds a feasible solution in the proximity of the near-optimal solution (i.e., Stage 2 and Stage 3). The numerical experiments on test cases ranging from 500-bus to 30,000-bus systems show that the algorithm is tractable. Here the results show that our proposed algorithm is tractable and can solve more than 80% of test cases faster than the well-known Interior Point Method while significantly reduce the number of iterations required to solve ACOPF. The number of iterations is considered an important factor in the examination of tractability which can drastically reduce the computational time required within each iteration.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2012

Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems

In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.

planetary soft landing↗
DOE OSTI2022

Integrating tactical planning, operational planning and scheduling using data-driven feasibility analysis

Supply chain operations and scheduling are well-studied problems in the literature. Although these problems are related, they are often solved sequentially. This uncoordinated approach usually leads to sub-optimal solutions. Here this paper proposes a methodology for integrating scheduling operations into the supply chain network, motivated by the available enterprise data, and feasibility analysis. Existing literature on integrated models for addressing the supply chain is reviewed and classified. Then the mathematical model formulation for each level is discussed, after which the proposed data-driven integrated framework is described. The methodology is tested on two different case studies of varying dimensions. For each case study, the solution solves a multi-objective problem with the overall aim of an optimal solution that is robust towards achieving optimal cost while keeping customer satisfaction in mind.

42 ENGINEERING↗
NASA NTRS2016

Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission.

Design↗
NASA NTRS2012

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

In this paper, we propose to solve the constrained optimization problem in two phases. The first phase uses heuristic methods such as the ant colony method, particle swarming optimization, and genetic algorithm to seek a near optimal solution among a list of feasible initial populations. The final optimal solution can be found by using the solution of the first phase as the initial condition to the SQP algorithm. We demonstrate the above problem formulation and optimization schemes with a large-scale network that includes the DSN ground stations and a number of spacecraft of deep space missions.

Communication Network Scheduling↗
DOE OSTI2020

A General Framework for Bounding Approximate Dynamic Programming Schemes

For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity in computing optimal solutions characterized by Bellman’s principle of optimality. A wide range of approximate dynamic programming (ADP) methods now exists. It is of great interest to guarantee that the performance of an ADP scheme be at least some known fraction, say ß , of optimal. This letter introduces a general approach to bounding the performance of ADP methods, in this sense, in the stochastic setting. The approach is based on new results for bounding greedy solutions in string optimization problems, where one has to choose a string (ordered set) of actions to maximize an objective function. This bounding technique is inspired by submodularity theory, but submodularity is not required for establishing bounds. Instead, the bounding is based on quantifying certain notions of curvature of string functions; the smaller the curvatures the better the bound. The key insight is that any ADP scheme is a greedy scheme for some surrogate string objective function that coincides in its optimal solution and value with those of the original optimal control problem. The ADP scheme then yields to the bounding technique mentioned above, and the curvatures of the surrogate objective determine the value ß of the bound. The surrogate objective and its curvatures depend on the specific ADP.

discrete event systems↗
NASA NTRS1989

A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Bless, Robert R.↗
NASA NTRS1991

User's guide for NETS/PROSSS

Expensive analysis programs are often combined with optimization procedures to solve engineering problems. To obtain an optimal solution requires numerous iterations between the analysis program and the optimizer. This often becomes prohibitive due to the cost and amount of computer time needed to converge to an optimal solution. NETS/PROSSS was developed to address this problem. The purpose of this paper is to serve as a user's guide for NETS/PROSSS. The key features include the neural network, determining the training pairs for the neural network, and the approximated analysis/optimization process. A small problem is given to serve as an example of how to apply the system.

Rogers, James L.↗
NASA NTRS2017

Fast and Reliable Approximations for Interplanetary Low-Thrust Transfers

A three-step process bridges the gap between lower-fidelity solutions that ignore optimal dynamics and fully optimized solutions that are computationally expensive to generate. First, analytic solutions for transfers with free time and angle characterize the evolution of the shape and orientation of the orbit. Next, optimal control theory supplies the thrust vector with variable specific impulse while satisfying flight time and transfer angle constraints. Transfers with the additional constraint of constant specific impulse then provide a more realistic thruster model for preliminary trade studies. These approximations deliver a hundredfold improvement in run time at the expense of a few percent error in mass.

Landau, Damon↗
DOE OSTI2024

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

distributionally robust optimization↗
NASA NTRS1996

Multi Objective Controller Design for Linear System via Optimal Interpolation

We propose a methodology for the design of a controller which satisfies a set of closed-loop objectives simultaneously. The set of objectives consists of: (1) pole placement, (2) decoupled command tracking of step inputs at steady-state, and (3) minimization of step response transients with respect to envelope specifications. We first obtain a characterization of all controllers placing the closed-loop poles in a prescribed region of the complex plane. In this characterization, the free parameter matrix Q(s) is to be determined to attain objectives (2) and (3). Objective (2) is expressed as determining a Pareto optimal solution to a vector valued optimization problem. The solution of this problem is obtained by transforming it to a scalar convex optimization problem. This solution determines Q(O) and the remaining freedom in choosing Q(s) is used to satisfy objective (3). We write Q(s) = (l/v(s))bar-Q(s) for a prescribed polynomial v(s). Bar-Q(s) is a polynomial matrix which is arbitrary except that Q(O) and the order of bar-Q(s) are fixed. Obeying these constraints bar-Q(s) is now to be 'shaped' to minimize the step response characteristics of specific input/output pairs according to the maximum envelope violations. This problem is expressed as a vector valued optimization problem using the concept of Pareto optimality. We then investigate a scalar optimization problem associated with this vector valued problem and show that it is convex. The organization of the report is as follows. The next section includes some definitions and preliminary lemmas. We then give the problem statement which is followed by a section including a detailed development of the design procedure. We then consider an aircraft control example. The last section gives some concluding remarks. The Appendix includes the proofs of technical lemmas, printouts of computer programs, and figures.

Ozbay, Hitay↗