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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.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Solving the optimal attention allocation problem in manual control

Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.

Kleinman, D. L.↗
NASA NTRS1988

Nearly-grazing optimal trajectories for noncoplanar, aeroassisted orbital transfer

This paper discusses aeroassisted orbital transfer maneuvers under the assumption that the terminal orbital inclinations are different. Both GEO-to-LEO and LEO-to-LEO transfers are considered in connection with a spacecraft which is controlled during the atmospheric pass via the angle of attack and the angle of bank. Within the framework of classical optimal control, the following problems are studied: the minimization of the total characteristic velocity (P1); the minimization of the time integral of the square of the path inclination (P5); and the minimization of the peak heating rate (Q1). Numerical solutions are obtained by means of the sequential gradient-restoration logarithm for optimal control problems under the conditions that, for the problem (P1), the plane change components are optimized, while for the problems (P5) and (Q1), the plane change components are kept at the levels determined for problem (P1). The engineering implications of the solutions are discussed, in order to determine the most useful solutions in the light of energy requirements and heat transfer requirements.

Miele, A.↗
NASA NTRS2002

Quadratic Optimization in the Problems of Active Control of Sound

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

Loncaric, J.↗
NASA NTRS1972

Adaptive control of stochastic linear systems with unknown parameters

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Ku, R. T.↗
DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Robust Control of Wave Energy Converters Using Unstructured Uncertainty

In the design of ocean wave energy converters, proper control design is essential to the maximization of the power generation performance for the device. However, in realistic applications, this control design must be undertaken in the presence of model uncertainty. This paper considers the use of robust control theory to optimize the nominal performance for a wave energy converter in stochastic waves, subject to the constraint that the controller be stability-robust to unstructured uncertainties. We formulate the problem as a multi-objective optimal control problem, in which the primary objective is the maximization of power generation for the nominal system, and the competing objective is the norm of the uncertainty input/output channel. This optimal control problem is nonconvex, and we therefore propose an iterative algorithm that can be used to arrive at a local optimal solution. This iterative approach employs the concept of Iterative Convex Overbounding, in the context of the classical Method of Centers. Here, the methodology is demonstrated on a model of a single, buoy- type wave energy converter.

16 TIDAL AND WAVE POWER↗
NASA NTRS1989

Minimum-variance reduced-order estimation algorithms from Pontrygin's minimum principle

A uniform derivation of minimum-variance reduced-order (MVRO) filter-smoother algorithms from Pontrygin's Minimum Principle is presented. An appropriate performance index for a general class of reduced order estimation problem is formulated herein to yield optimal results over the entire time interval of estimation. These results provide quantitative criteria for measuring the performance of certain classes of heuristically designed, suboptimal reduced-order estimators as well as explicit guidance to the suboptimal filter design process with both continuous and discrete filter-smoother algorithms being considered. By the duality principle, the algorithms of reduced-order estimation can be easily extended to the deterministic problems of optimal control (i.e., the regulator and linear tracking problem).

Ebrahimi, Yaghoob S.↗
NASA NTRS1975

Continuous performance measurement in flight systems

The desired response of many man machine control systems can be formulated as a solution to an optimal control synthesis problem where the cost index is given and the resulting optimal trajectories correspond to the desired trajectories of the man machine system. Optimal control synthesis provides the reference criteria and the significance of error information required for performance measurement. The synthesis procedure described provides a continuous performance measure (CPM) which is independent of the mechanism generating the control action. Therefore, the technique provides a meaningful method for online evaluation of man's control capability in terms of total man machine performance.

Connelly, E. M.↗
DOE OSTI2023

Load Shedding for Voltage Regulation With Probabilistic Agent Compliance

With the increased observability and controllability of distribution systems, the share of behind-the-meter systems is trending upwards rapidly. As a consequence, the impact of human behaviors on system performance can no longer be ignored and should be reflected in the energy management system models. In this paper, we discuss the problem of distribution system voltage control by active power curtailment where the agent compliance of the load curtailment signal is probabilistic. We discuss the modeling of the optimal voltage control problem with probabilistic agent compliance as a chance-constrained optimization problem, its tractable safe approximation using convex restriction, and a scenario-based mixed-integer reformulation as well as the associated solution method based on augmented Lagrangian method. The numerical simulation on IEEE test system validates the effectiveness of the proposed approach in obtaining high-quality feasible load curtailment signal with low computational cost, which makes it a viable tool for real time decision making.

augmented Lagrangian method↗
DOE OSTI2024

Analysis of Control Behavior in Eco-Driving Speed Optimization Using Pontryagin’s Minimum Principle

The energy efficiency of autonomous vehicles can be improved by selecting an optimized speed profile. Energy savings can be maximized by performing control optimization with knowledge of the powertrain characteristics and future driving conditions. Previous studies have shown that Pontryagin’s minimum principle (PMP) performs well in vehicle speed optimization problems. Building on the methods proposed in previous studies, the contribution of this study is to derive meaningful observations from the concepts and results of PMP to enhance the understanding of the control problem. In particular, the switching behavior of the control mode is analyzed with supportive variables, such as ξ and mv, which dictates the changes in the control modes. Additionally, the existence of the singular control is analyzed, which helps in understanding the cruise driving in the control problem. Finally, we obtain several solutions that satisfy various boundary conditions along with a map of the reachable states, and discuss the impact of cruise driving. This is helpful for designing practical control concepts for real-world applications based on this map. Previous studies have contributed significantly to this control problem; however, this study provides a better understanding of the issue and offers guidance and inspiration for future real-world applications based on these meaningful observations.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1999

Proper Orthogonal Decomposition in Optimal Control of Fluids

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Ravindran, S. S.↗
NASA NTRS1989

Recursive multibody dynamics and discrete-time optimal control

A recursive algorithm is developed for the solution of the simulation dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is shown to be identical to that encountered in a discrete-time optimal control problem. For each relevant quantity in the multibody dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs' function for the chain of bodies.

Deleuterio, G. M. T.↗
NASA NTRS1975

Solution of an optimal control lifting body entry problem by an improved method of perturbation functions

This paper presents a solution to a complex lifting reentry three-degree-of-freedom problem by using the calculus of variations to minimize the integral of the sum of the aerodynamics loads and heat rate input to the vehicle. The entry problem considered does not have state and/or control constraints along the trajectory. The calculus of variations method applied to this problem gives rise to a set of necessary conditions which are used to formulate a two point boundary value (TPBV) problem. This TPBV problem is then numerically solved by an improved method of perturbation functions (IMPF) using several starting co-state vectors. These vectors were chosen so that each one had a larger norm with respect to show how the envelope of convergence is significantly increased using this method and cases are presented to point this out.

Garcia, F., Jr.↗
NASA NTRS1987

Optimization and guidance of abort landing trajectories in a windshear

The abort landing problem for flight trajectories in the presence of windshear is considered with reference to flight in a vertical plane. The optimal trajectory (OT) problem is a minimax problem or Chebyshev problem of optimal control which can be converted into a Bolza problem through suitable transformations. Numerical results for several combinations of windshear intensities and initial altitudes are presented. A guidance trajectory (GT) law is implemented in feedback control form, subject to prescribed bounds on the angle of attack and its time derivative. Simplified guidance trajectories (SGT) are then considered, leading to a safe target altitude guidance. Conclusions derived for strong-to-severe windshear conditions include GT and SGT preserving the basic properties of OT, and the peak altitude drop of GT and SGT being less than that of the constant pitch trajectory and the maximum angle-of-attack trajectory.

Miele, A.↗