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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Optimizing airport runway improvement program - A dynamic programming approach

In order to reduce the air traffic delay in the terminal area, an immediate remedy is to increase airport capacity by an expansion of the existing runway system. The runway expansion program is often limited by budgetary constraints; the expensive facilities for a long-term improvement cannot be built at once. When a runway improvement strategy is being considered for a longer planning horizon, the investiment decision depends upon the interrelations of its composite periods. The problem, therefore, is to determine how time factor and investment decisions interact to yield an optimal improvement scheme that meets demand at a minimum cost. With this objective in mind, a dynamic programming methodology is employed to determine the optimal planning scheme. Also, an example runway improvement problem is tested to illustrate how a dynamic programming model is practical in actual application.

Yu, J. C.↗
NASA NTRS1994

Data compression of discrete sequence: A tree based approach using dynamic programming

A dynamic programming based approach for data compression of a ID sequence is presented. The compression of an input sequence of size N to that of a smaller size k is achieved by dividing the input sequence into k subsequences and replacing the subsequences by their respective average values. The partitioning of the input sequence is carried with the intention of reducing the mean squared error in the reconstructed sequence. The complexity involved in finding the partitions which would result in such an optimal compressed sequence is reduced by using the dynamic programming approach, which is presented.

Shivaram, Gurusrasad↗
NASA NTRS1974

The Earth and Ocean Physics Applications Program (EOPAP). Ocean dynamics program

SEASAT-A is a research oriented program consisting of a spacecraft, precision ground tracking systems, and data processing and modelling capabilities that address both scientific and application programs problems in ocean surface dynamics for the EOPAP program. An array of active radar and passive microwave and infrared instruments allows for quantitative measurements of oceanic, atmospheric, and geodetic parameters under stormy wind and wave conditions, as well as over regions lying under a cloud cover.

Apel, J. R.↗
NASA NTRS2011

Runway Scheduling Using Generalized Dynamic Programming

A generalized dynamic programming method for finding a set of pareto optimal solutions for a runway scheduling problem is introduced. The algorithm generates a set of runway fight sequences that are optimal for both runway throughput and delay. Realistic time-based operational constraints are considered, including miles-in-trail separation, runway crossings, and wake vortex separation. The authors also model divergent runway takeoff operations to allow for reduced wake vortex separation. A modeled Dallas/Fort Worth International airport and three baseline heuristics are used to illustrate preliminary benefits of using the generalized dynamic programming method. Simulated traffic levels ranged from 10 aircraft to 30 aircraft with each test case spanning 15 minutes. The optimal solution shows a 40-70 percent decrease in the expected delay per aircraft over the baseline schedulers. Computational results suggest that the algorithm is promising for real-time application with an average computation time of 4.5 seconds. For even faster computation times, two heuristics are developed. As compared to the optimal, the heuristics are within 5% of the expected delay per aircraft and 1% of the expected number of runway operations per hour ad can be 100x faster.

optmization↗
NASA NTRS2020

Squash-Box Feasibility Driven Differential Dynamic Programming

Recently, Differential Dynamic Programming (DDP) and other similar algorithms have become the solvers of choice when performing non-linear Model Predictive Control (nMPC) with modern robotic devices. The reason is that they have a lower computational cost per iteration when compared with off-the-shelf Non-Linear Programming (NLP) solvers, which enables its online operation. However, they cannot handle constraints, and are known to have poor convergence capabilities. In this paper, we propose a method to solve the optimal control problem with control bounds through a squashing function (i.e., a sigmoid, which is bounded by construction). It has been shown that a naive use of squashing functions damage the convergence rate. To tackle this, we first propose to add a quadratic barrier that avoids the difficulty of the plateau produced by the sigmoid. Second, we add an outer loop that adapts both the sigmoid and the barrier; it makes the optimal control problem with the squashing function converge to the original control-bounded problem. To validate our method, we present simulation results for different types of platforms including a multi-rotor, a biped, a quadruped and a humanoid robot.

Navarro, Angel Santamaria↗
NASA NTRS2012

Joint Chance-Constrained Dynamic Programming

This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.

Ono, Masahiro↗
NASA NTRS2016

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗
NASA NTRS2016

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗
NASA NTRS2010

Configuring Airspace Sectors with Approximate Dynamic Programming

In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.

Bloem, Michael↗
NASA NTRS1989

Two stage gear tooth dynamics program

The epicyclic gear dynamics program was expanded to add the option of evaluating the tooth pair dynamics for two epicyclic gear stages with peripheral components. This was a practical extension to the program as multiple gear stages are often used for speed reduction, space, weight, and/or auxiliary units. The option was developed for either stage to be a basic planetary, star, single external-external mesh, or single external-internal mesh. The two stage system allows for modeling of the peripherals with an input mass and shaft, an output mass and shaft, and a connecting shaft. Execution of the initial test case indicated an instability in the solution with the tooth paid loads growing to excessive magnitudes. A procedure to trace the instability is recommended as well as a method of reducing the program's computation time by reducing the number of boundary condition iterations.

Boyd, Linda S.↗
DOE OSTI2020

The Heuristic Dynamic Programming Approach in Boost Converters

In this study, a heuristic dynamic programming controller is proposed to control a boost converter. Conventional controllers such as proportional-integral-derivative (PID) or proportional-integral (PI) are designed based on the linearized small-signal model near the operating point. Therefore, the performance of the controller during the start-up, the load change, or the input voltage variation is not optimal since the system model changes by varying the operating point. The heuristic dynamic programming controller optimally controls the boost converter by following the approximate dynamic programming. The advantage of the HDP is that the neural network-based characteristic of the proposed controller enables boost converters to easily cope with large disturbances. An HDP with a well-trained critic and action networks can perform as an optimal controller for the boost converter. To compare the effectiveness of the traditional PI-based and the HDP boost converter, the simulation results are provided.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming

In this report, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform controllability and boundedness assumptions for the problem data, we prove that the directional derivative of the optimal state and control at time $k$, $x^*_k$, and $u^*_k$, with respect to the reference signal at time $i$, $d_i$, will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length. The key technical step is to prove that a version of the convexification approach proposed by Verschueren et al. can be applied to the KKT conditions and results in a convex quadratic program with uniformly bounded data. In turn, Riccati techniques can be further employed to obtain the sensitivity result, borne from the observation that the directional derivatives are solutions of quadratic programs with structure similar to the KKT conditions themselves. We validate our findings with numerical experiments on a small nonlinear, nonconvex, dynamic program.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Adaption of a corrector module to the IMP dynamics program

The corrector module of the RAEIOS program and the IMP dynamics computer program were combined to achieve a date-fitting capability with the more general spacecraft dynamics models of the IMP program. The IMP dynamics program presents models of spacecraft dynamics for satellites with long, flexible booms. The properties of the corrector are discussed and a description is presented of the performance criteria and search logic for parameter estimation. A description is also given of the modifications made to add the corrector to the IMP program. This includes subroutine descriptions, common definitions, definition of input, and a description of output.

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