Study of optimal and adaptive control theory Final report, May 1964 - Jun. 1966
Optimal and adaptive control theory with application to large launch vehicles
OPTIMAL CONTROL↗
SEARCH · Search NASA
Results for “optimization theory”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras
It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.
Byrnes, C. I.↗
A linearized theory method of constrained optimization for supersonic cruise wing design
A linearized theory wing design and optimization procedure which allows physical realism and practical considerations to be imposed as constraints on the optimum (least drag due to lift) solution is discussed and examples of application are presented. In addition to the usual constraints on lift and pitching moment, constraints are imposed on wing surface ordinates and wing upper surface pressure levels and gradients. The design procedure also provides the capability of including directly in the optimization process the effects of other aircraft components such as a fuselage, canards, and nacelles.
Miller, D. S.↗
Observable optimization for precision theory: machine learning energy correlators
The practice of collider physics typically involves the marginalization of multi-dimensional collider data to uni-dimensional observables relevant for some physics task. In many cases, such as classification or anomaly detection, the observable can be arbitrarily complicated, such as the output of a neural network. However, for precision measurements, the observable must correspond to something computable systematically beyond the level of current simulation tools. In this work, we demonstrate that precision-theory-compatible observable space exploration can be systematized by using neural simulation-based inference techniques from machine learning. We illustrate this approach by exploring the space of marginalizations of the energy 3-point correlator to optimize sensitivity to the top quark mass. We first learn the energy-weighted probability density from simulation, then search in the space of marginalizations for an optimal triangle shape. Although simulations and machine learning are used in the process of observable optimization, the output is an observable definition which can be then computed to high precision and compared directly to data without any memory of the computations which produced it. We find that the optimal marginalization is isosceles triangles on the sphere with a side ratio approximately $1 : 1 : \sqrt{2}$ (i.e. right triangles) within the set of marginalizations we consider.
Jets and Jet Substructure↗
Primer Vector Optimization: Survey of Theory, New Analysis and Applications
In this paper, a summary of primer vector theory is presented. The applicability of primer vector theory is examined in an effort to understand when and why the theory can fail. For example, since the Calculus of Variations is based on "small" variations, singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyse that employ small variations. Two examples, the initialization of an orbit and a line of apsides rotation, are presented. Recommendations, future work, and the possible addition of other optimization techniques are also discussed.
Guzman, J. J.↗
Application of linear optimal control and filtering theory to the Saturn V launch vehicle.
Linear optimal control and least square filtering theory application to control system design of Saturn 5 launch vehicle
Blackburn, T. R.↗
Investigation, development, and application of optimal output feedback theory. Volume 3: The relationship between dynamic compensators and observers and Kalman filters
Relationships between observers, Kalman Filters and dynamic compensators using feedforward control theory are investigated. In particular, the relationship, if any, between the dynamic compensator state and linear functions of a discrete plane state are investigated. It is shown that, in steady state, a dynamic compensator driven by the plant output can be expressed as the sum of two terms. The first term is a linear combination of the plant state. The second term depends on plant and measurement noise, and the plant control. Thus, the state of the dynamic compensator can be expressed as an estimator of the first term with additive error given by the second term. Conditions under which a dynamic compensator is a Kalman filter are presented, and reduced-order optimal estimaters are investigated.
Broussard, John R.↗
Atikokan Digital Twin, Part B: Bayesian decision theory for process optimization in a biomass energy system
Not Available
Spinti, Jennifer P. (ORCID:0000000299570710)↗
The Entropy Economy and the Kolmogorov Learning Cycle: Leveraging the intersection of Machine Learning and Algorithmic Information Theory to jointly optimize energy and learning
Not Available
Evans, Scott C. (ORCID:0009000475513641)↗
A Low Temperature Cyclopentane Oxidation Kinetics Model: Optimization of A Theory Based Sub Mechanism Against Experiment.
Abstract not provided.
Demireva, Maria↗
Extended Hartree-Fock wavefunctions - General theory of optimized-valence configurations and its application to diatomic molecules.
Optimized valence configurations method from generalization of extended Hartree-Fock wavefunctions for intrashell correlations of atomic or molecular systems
Das, G.↗
An optimal control model of human response. I - Theory and validation
Optimal manual control model of human compensatory tracking response
Baron, S.↗
Investigation, development and application of optimal output feedback theory. Vol. 4: Measures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics
Some measures of eigenvalue and eigenvector sensitivity applicable to both continuous and discrete linear systems are developed and investigated. An infinite series representation is developed for the eigenvalues and eigenvectors of a system. The coefficients of the series are coupled, but can be obtained recursively using a nonlinear coupled vector difference equation. A new sensitivity measure is developed by considering the effects of unmodeled dynamics. It is shown that the sensitivity is high when any unmodeled eigenvalue is near a modeled eigenvalue. Using a simple example where the sensor dynamics have been neglected, it is shown that high feedback gains produce high eigenvalue/eigenvector sensitivity. The smallest singular value of the return difference is shown not to reflect eigenvalue sensitivity since it increases with the feedback gains. Using an upper bound obtained from the infinite series, a procedure to evaluate whether the sensitivity to parameter variations is within given acceptable bounds is developed and demonstrated by an example.
Halyo, Nesim↗
Digital robust control law synthesis using constrained optimization
Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.
Mukhopadhyay, Vivekananda↗
Theory of the optimally coupled Q-switched laser
The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.
Degnan, John J.↗
Control law synthesis and optimization software for large order aeroservoelastic systems
A flexible aircraft or space structure with active control is typically modeled by a large-order state space system of equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics and gust spectra. The control law of this multi-input/multi-output (MIMO) system is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented on an onboard digital microprocessor. A software package for performing an analog or digital control law synthesis for such a system, using optimal control theory and constrained optimization techniques is described.
Mukhopadhyay, V.↗
Transient Growth Theory Prediction of Optimal Placing of Passive and Active Flow Control Devices for Separation Delay in LPT Airfoils
An analysis of the non-modal growth of perturbations in a boundary layer in the presence of a streamwise pressure gradient is presented. The analysis is based on PSE equations for an incompressible fluid. Examples with Falkner-Skan profiles indicate that a favorable pressure gradient decreases the non-modal growth while an unfavorable pressure gradient leads to an increase of the amplification. It is suggested that the transient growth mechanism be utilized to choose optimal parameters of tripping elements on a low-pressure turbine (LPT) airfoil. As an example, a boundary layer flow with a streamwise pressure gradient corresponding to the pressure distribution over a LPT airfoil is considered. It is shown that there is an optimal spacing of the tripping elements and that the transient growth effect depends on the starting point. At very low Reynolds numbers, there is a possibility to enhance the transient energy growth by means of wall cooling.
Tumin, Anatoli↗
A Julia Framework for Graph-Structured Nonlinear Optimization
Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective functions, and data) within nodes and edges of a graph, and this representation can be used to visualize, manipulate, and solve the problem. In this work, we present a Julia framework for modeling and solving graph-structured nonlinear optimization problems. Our framework integrates the modeling package Plasmo.jl (which facilitates the construction and manipulation of graph models) and the nonlinear optimization solver MadNLP.jl (which provides capabilities for exploiting graph structures to accelerate solution). We illustrate with a simple example how model construction and manipulation can be performed in an intuitive manner using Plasmo.jl and how the model structure can be exploited by MadNLP.jl. We also demonstrate the scalability of the framework by targeting a large-scale, stochastic gas network problem that contains over 1.7 million variables.
Cole, David↗