SEARCH · Search NASA

Results for “Optimal Control Problem”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,117 records · Page 62

All sources NASA NTRS DOE OSTI

NASA NTRS1992

Robust control of flexible space vehicles with minimum structural excitation: On-off pulse control of flexible space vehicles

Both feedback and feedforward control approaches for uncertain dynamical systems (in particular, with uncertainty in structural mode frequency) are investigated. The control objective is to achieve a fast settling time (high performance) and robustness (insensitivity) to plant uncertainty. Preshaping of an ideal, time optimal control input using a tapped-delay filter is shown to provide a fast settling time with robust performance. A robust, non-minimum-phase feedback controller is synthesized with particular emphasis on its proper implementation for a non-zero set-point control problem. It is shown that a properly designed, feedback controller performs well, as compared with a time optimal open loop controller with special preshaping for performance robustness. Also included are two separate papers by the same authors on this subject.

Wie, Bong↗

NASA NTRS1967

The matrix minimum principle

Extension of Pontryagin maximum principle and application of matrix minimum principle in solving simple optimal linear regulator problem

MATRIX ANALYSIS↗

DOE OSTI2024

Rapid Optimization of Total Variation with Applications in Imaging, Additive Manufacturing, and Qualification

Total Variation optimization penalizes the gradient of a control variable or state. While this work focuses on image processing in particular, it has also found applications in inverse problems and topology optimization. In image processing, the goal is to maintain faithfulness to the original image while denoising and/or deblurring. Additionally, bilevel optimization over the spatially varying regularization weights can illuminate interfaces such as damage regions and other anomalies. We will address two fundamental challenges with TV-optimization: (i) the typical slow convergence of existing TV-optimization methods, and (ii) the selection of spatially varying TV parameters to promote interface detection. Additionally, we will apply such techniques to image data collected in additive manufacturing. In said context, stochasticity in build events induces flaws in the manufactured piece, compromising the integrity of said part. There is a critical need for in-situ monitoring to spot anomalies once they form, and in this setting we apply our total variation and hyperparameter solvers. We will develop a customized algorithm based on for extreme-scale TV-optimization that achieves super-linear or quadratic-convergence, a critical property for real-time, image-by-image analysis. A worst-case outcome is a preprocessing step that enhances image quality in-situ, specifically for out-of-focus and noisy images.

36 MATERIALS SCIENCE↗

NASA NTRS1988

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Bernstein, Dennis S.↗

NASA NTRS2006

Distributed Constrained Optimization with Semicoordinate Transformations

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Macready, William↗

NASA NTRS1992

Control design based on a linear state function observer

An approach to the design of low-order controllers for large scale systems is proposed. The method is derived from the theory of linear state function observers. First, the realization of a state feedback control law is interpreted as the observation of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the given feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. A four-disk system and a lightly damped beam are presented as examples to demonstrate the applicability and efficacy of the proposed method.

Su, Tzu-Jeng↗

NASA NTRS1993

Uncertainty reasoning in expert systems

Intelligent control is a very successful way to transform the expert's knowledge of the type 'if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible' into an actual control. To apply this transformation, one must choose appropriate methods for reasoning with uncertainty, i.e., one must: (1) choose the representation for words like 'small', 'big'; (2) choose operations corresponding to 'and' and 'or'; (3) choose a method that transforms the resulting uncertain control recommendations into a precise control strategy. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From a mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. In this project, a new mathematical formalism (based on group theory) is developed that allows us to solve the problem of optimal choice and thus: (1) explain why the existing choices are really the best (in some situations); (2) explain a rather mysterious fact that fuzzy control (i.e., control based on the experts' knowledge) is often better than the control by these same experts; and (3) give choice recommendations for the cases when traditional choices do not work.

Kreinovich, Vladik↗

NASA NTRS1978

Design of a compensation for an ARMA model of a discrete time system

The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.

Mainemer, C. I.↗

NASA NTRS1979

Singular perturbation techniques for on-line optimal flight path control

This paper presents a partial evaluation on the use of singular perturbation methods for developing computer algorithms for on-line optimal control of aircraft. The evaluation is based on a study of the minimum time intercept problem using F-4 aerodynamic and propulsion data as a base line. The extensions over previous work on this subject are that aircraft turning dynamics (in addition to position and energy dynamics) are included in the analysis, the algorithm is developed for a moving end point and is adaptive to unpredictable target maneuvers, and short range maneuvers that do not have a cruise leg are included. Particular attention is given to identifying those quantities that can be precomputed and stored (as a function of aircraft total energy), thus greatly reducing the onboard computational load. Numerical results are given that illustrate the nature of the optimal intercept flight paths, and an estimate is given for the execution time and storage requirements of the control algorithm.

Calise, A. J.↗

DOE OSTI2019

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

The major goal of the project was to invent, analyze, implement, and apply new algorithms to speed up the computational simulation of complex systems in settings in which multiple simulations are needed. The main efforts we undertook are as follows: 1. Develop novel reduced order methods to reduce the costs of simulations, especially in settings (e.g., UQ, inference, optimization and control) for which numerous simulation are needed and also for nonlocal problems (e.g., fractional derivative, anomalous diffusion, nonlocal mechanics) for which lack of sparsity results in more expensive full-order simulation than encountered in partial differential equations settings; rigorous analyses as well as computational tests were carried out, 2. Develop multifidelity methods based on the usage of a variety of models having different fidelities and different costs to accelerate simulations again in settings where numerous simulations are needed or are especially expensive; rigorous analyses as well as computational tests were carried out, 3. Develop ensemble methods to reduced the costs of simulations again in settings where numerous simulations are needed or are especially expensive; rigorous analyses as well as computational tests were carried out, and 4. Analyze a model for Richardson pair dispersion in turbulent flows and develop discretization methods for the efficient and accurate approximations of the solution of the model; rigorous analyses as well as computational tests were carried out.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1975

Status of input design for aircraft parameter identification

Results are presented on the design of aircraft inputs (i.e. elevator, rudder and aeleron deflection time histories) to identify aircraft stability and control derivatives from flight test data. The problem is first reduced to an optimization problem with differential and integral constraints. The criteria used are either expressed in terms of the Cramer-Rao lower bound on the covariance matrix of the parameter estimates or in terms of the maximum prediction error variance. Both time-domain longitudinal and lateral dynamics of C-8 and Jet Star aircrafts and comparison with doublet type inputs are made.

Mehra, R. K.↗

NASA NTRS1977

Optimal estimation and attitude control of a solar electric propulsion spacecraft

Established procedures of linear, quadratic, Gaussian optimal estimation and control are developed and interpreted for their application to the problem of attitude control of spacecraft with dynamically significant elastic appendages. Results are presented both in general terms and for specific application to a solar electric spacecraft. Comparisons are made between alternative coordinate systems, and a realistic range of design parameters is considered. For single axis control, system evaluation is accomplished by simulation of a fifteenth-order spacecraft plant with alternative second-order, fourth-order, and sixth-order constant gain estimators. Results point out the importance of modeling errors.

Larson, V.↗

NASA NTRS1985

Spline Curves, Wire Frames and Bvalue

The methods that were developed for wire-frame design are described. The principal tools for control of a curve during interactive design are mathematical ducks. The simplest of these devices is an analog of the draftsman's lead weight that he uses to control a mechanical spline also create Ducks for controlling differential and integral properties of curves were created. Other methods presented include: constructing the end of a Bezier polygon to gain quick and reasonably confident control of the end tangent vector, end curvature and end torsion; keeping the magnitude of unwanted curvature oscillations within tolerance; constructing the railroad curves that appear in many engineering design problems; and controlling the frame to minimize errors at mesh points and to optimize the shapes of the curve elements.

Smith, L.↗

NASA NTRS1992

Microgravity vibration isolation: Optimal preview and feedback control

In order to achieve adequate low-frequency vibration isolation for certain space experiments an active control is needed, due to inherent passive-isolator limitations. Proposed here are five possible state-space models for a one-dimensional vibration isolation system with a quadratic performance index. The five models are subsets of a general set of nonhomogeneous state space equations which includes disturbance terms. An optimal control is determined, using a differential equations approach, for this class of problems. This control is expressed in terms of constant, Linear Quadratic Regulator (LQR) feedback gains and constant feedforward (preview) gains. The gains can be easily determined numerically. They result in a robust controller and offers substantial improvements over a control that uses standard LQR feedback alone.

Hampton, R. D.↗

NASA NTRS1991

Implementation of a three degree of freedom, motor/brake hybrid force output device for virtual environment control tasks

The advent of high resolution, physical model based computer graphics has left a gap in the design of input/output technology appropriate for interacting with such complex virtual world models. Since virtual worlds consist of physical models, it is appropriate to output the inherent force information necessary for the simulation to the user. The detailed design, construction, and control of a three degree freedom force output joystick will be presented. A novel kinematic design allows all three axes to be uncoupled, so that the system inertia matrix is diagonal. The two planar axes are actuated through an offset gimbal, and the third through a sleeved cable. To compensate for friction and inertia effects, this transmission is controlled by a force feedforward and a closed force feedback proportional loop. Workspace volume is a cone of 512 cubic inches, and the device bandwidth is maximized at 60 Hz for the two planar and 30 Hz for the third axis. Each axis is controlled by a motor/proportional magnetic particle brake combination fixed to the base. The innovative use of motors and brakes allows objects with high resistive torque requirements to be simulated without the stability and related safety issues involved with high torque, energy storing motors alone. Position, velocity, and applied endpoint force are sensed directly. Different control strategies are discussed and implemented, with an emphasis on how virtual environment force information, generated by the MIT Media Lab Computer Graphics and Animation Group BOLIO system, is transmitted to the device controller. The design constraints for a kinesthetic force feedback device can be summarized as: How can the symbiosis between the sense of presence in the virtual environment be maximized without compromising the interaction task under the constraints of the mechanical device limitations? Research in this field will yield insights to the optimal human sensory feedback mix for a wide spectrum of control and interaction problems. A flexible research tool that is designed as an easily reproducible product prototype has been constructed to explore the variety of possible force interaction.

Russo, Massimo↗

NASA NTRS1994

Hybrid near-optimal aeroassisted orbit transfer plane change trajectories

In this paper, a hybrid methodology is used to determine optimal open loop controls for the atmospheric portion of the aeroassisted plane change problem. The method is hybrid in the sense that it combines the features of numerical collocation with the analytically tractable portions of the problem which result when the two-point boundary value problem is cast in the form of a regular perturbation problem. Various levels of approximation are introduced by eliminating particular collocation parameters and their effect upon problem complexity and required number of nodes is discussed. The results include plane changes of 10, 20, and 30 degrees for a given vehicle.

Calise, Anthony J.↗

DOE OSTI2024

HybridSystemsSimulations.jl - Solving the Merchant Collocated Facilities with JuMP

The development of new clean-generation technologies also leads to new plant-level architectures that combine several generation and storage assets behind the point of connection. These co-located generation resources (Hybrid Systems) primarily operate as merchant assets that employ automated market bidding models and internal Energy Management Systems (EMS) to comply with the operator's signals. Formulating an optimal bidding model requires embedding the EMS control model into the bidding algorithm, resulting in a bi-level optimization problem. In this presentation, we first showcase using JuMP to formulate and solve this problem effectively for multiple merchant systems and the bidding outcomes considering different model formulations. Second, the bidding outcomes are later integrated into a PowerSimulations.jl (also built with JuMP) simulation to study the system-level effects of the various merchant bidding and the interactions between market-clearing models and the embedded EMS model. We will showcase simulations conducted in the RTS system considering different levels of merchant hybrid systems participation. The presentation provides the following specific insights on JuMP usage: 1) the Formulation of specialized bi-level problems with custom cuts to solve the merchant hybrid system bidding problem; 2) the integration of a modular model within a complex simulation workflow supported by JuMP in PowerSimulations.jl; 3) Accelerating the solution of power systems operations simulation that employ agent optimization problems using JuMP.

energy markets↗

DOE OSTI2021

Efficient Automated Driving Strategies Leveraging Anticipation and Optimal Control

Automated vehicles and advanced driver assistance systems bring computation, sensing, and communication technologies that exceed human abilities in some ways. For example, automated vehicles may sense a panorama all at once, do not suffer from human impairments and distractions, and could wirelessly communicate precise data with neighboring vehicles. Prototype and commercial deployments have demonstrated the capability to relieve human operators of some driving tasks up to and including fully autonomous taxi rides in some areas. The ultimate impact of this technology’s large-scale market penetration on energy efficiency remains unclear, with potential negative factors like road use by empty vehicles competing with positive ones like automatic eco-driving. Fundamentally enabled by historic and look-ahead data, this dissertation addresses the use of automated driving and driver assistance to optimize vehicle motion for energy efficiency. Facets of this problem include car following, co-optimized acceleration and lane change planning, and collaborative multi-agent guidance. Optimal control, especially model predictive control, is used extensively to improve energy efficiency while maintaining safe and timely driving via constraints. Techniques including chance constraints and mixed integer programming help overcome uncertainty and non-convexity challenges. Extensions of these techniques to tractor trailers on sloping roads are provided by making use of linear parameter-varying models. To approach the wheel-input energy eco-driving problem over generally shaped sloping roads with the computational potential for closed-loop implementation, a linear programming formulation is constructed. Distributed and collaborative techniques that enable connected and automated vehicles to accommodate their neighbors in traffic are also explored and compared to centralized control. Using simulations and vehicle-in-the-loop car following experiments, the proposed algorithms are benchmarked against others that do not make use of look-ahead information.

Dollar, Robert Austin↗