Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Quadratic Optimization”

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.

At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

An optimization program based on the method of feasible directions: Theory and users guide

The theory and user instructions for an optimization code based on the method of feasible directions are presented. The code was written for wide distribution and ease of attachment to other simulation software. Although the theory of the method of feasible direction was developed in the 1960's, many considerations are involved in its actual implementation as a computer code. Included in the code are a number of features to improve robustness in optimization. The search direction is obtained by solving a quadratic program using an interior method based on Karmarkar's algorithm. The theory is discussed, focusing on the important and often overlooked role played by the various parameters guiding the iterations within the program. Also discussed is a robust approach for handling infeasible starting points. The code was validated by solving a variety of structural optimization test problems that have known solutions obtained by other optimization codes. It has been observed that this code is accurate and robust: it has solved a variety of problems from different starting points. However, the code is inefficient in that it takes considerable CPU time as compared with certain other available codes. Further work is required to improve its efficiency while retaining its robustness.

Ashok D. Belegundu↗
DOE OSTI2025

Dynamic Modeling, Trajectory Optimization, and Linear Control of Cable-Driven Parallel Robots for Automated Panelized Building Retrofits

The construction industry faces a growing need for automation to reduce costs, improve accuracy and productivity, and address labor shortages. One area that stands to benefit significantly from automation is panelized prefabricated building envelope retrofits, which can improve a building’s energy efficiency in heating and cooling interior spaces. In this paper, we propose using cable-driven parallel robots (CDPRs), which can effectively lift and handle large objects, to install these panels. However, implementing CDPRs presents significant challenges because of their nonlinear dynamics, complex trajectory planning, and precise control requirements. To tackle these challenges, this work focuses on a new application of established control and trajectory optimization theories in a CDPR simulation of a building envelope retrofit under real-world conditions. We first model the dynamics of CDPRs, highlighting the critical role of damping in system behavior. Building on this dynamic model, we formulate a trajectory optimization problem to generate feasible and efficient motion plans for the robot under operational and environmental constraints. Given the high precision required in the construction industry, accurately tracking the optimized trajectory is essential. However, challenges such as partial observability and external vibrations complicate this task. To address these issues, a Linear Quadratic Gaussian control framework is applied, enabling the robot to track the optimized trajectories with precision. Simulation results show that the proposed controller enables precise end effector positioning with errors under 4 mm, even in the presence of external wind disturbances. Through comprehensive simulations, our approach allows for an in-depth exploration of the system’s nonlinear dynamics, trajectory optimization, and control strategies under controlled yet highly realistic conditions. The results demonstrate the feasibility of CDPRs for automating panel installation and provide insights into their practical deployment.

CDPR↗
NASA NTRS1978

ORACLS: A system for linear-quadratic-Gaussian control law design

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.↗
NASA NTRS1991

Optimal digital redesign of cascaded analogue controllers

This paper presents a new, optimal digital redesign technique for finding an optimal cascaded digital controller from the given continuous-time counterpart by minimizing a quadratic performance index. The control gains can be obtained by solving a set of Liapunov equations. The developed optimal cascaded digital controller enables the state and/or outputs of the digitally controlled closed-loop sampled-data system to optimally match those of the original continuous-time closed-loop system at any instant between sampling periods. The developed control law can be implemented using inexpensive and reliable digital electronics with a relatively long sampling period.

Shieh, L. S.↗
DOE OSTI2015

Robust Utility Maximization Under Convex Portfolio Constraints

We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Development of a nearshore oscillating surge wave energy converter with variable geometry

This paper presents an analysis of a novel wave energy converter concept that combines an oscillating surge wave energy converter (OSWEC) with control surfaces. The control surfaces allow for a variable device geometry that enables the hydrodynamic properties to be adapted with respect to structural loading, absorption range and power-take-off capability. The device geometry is adjusted on a sea state-to-sea state time scale and combined with wave-to-wave manipulation of the power take-off (PTO) to provide greater control over the capture efficiency, capacity factor, and design loads. This work begins with a sensitivity study of the hydrodynamic coefficients with respect to device width, support structure thickness, and geometry. A linear frequency domain analysis is used to evaluate device performance in terms of absorbed power, foundation loads, and PTO torque. Previous OSWEC studies included nonlinear hydrodynamics, in response a nonlinear model that includes a quadratic viscous damping torque that was linearized via the Lorentz linearization. Inclusion of the quadratic viscous torque led to construction of an optimization problem that incorporated motion and PTO constraints. Results from this study found that, when transitioning from moderate-to-large sea states the novel OSWEC was capable of reducing structural loads while providing a near constant power output.

16 TIDAL AND WAVE POWER↗
DOE OSTI2026

Extreme-scale EV charging infrastructure planning for last-mile delivery using high-performance parallel computing

Here, this paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Capacity allocation↗
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 NTRS1970

Minimax control of a system with process uncertainty in substate space

The control of a single input-single output plant with parameter uncertainty was approached using a minimax technique. A linear time invariant controller results which requires only partial state feedback and is optimal in the sense that it minimizes a quadratic criterion involving tracking error, control, and parameter uncertainty. Bounded input-bounded output stability is guaranteed provided the transfer function has only left half plane zeros. If uncertainties are bounded, it is always possible to stabilize the system when sufficient control amplitude is available. The number of states required to generate the control is equal to the system order less the number of zeros.

Basuthakur, S.↗
NASA NTRS1971

Satellite tracking by combined optimal estimation and control techniques.

Combined optimal estimation and control techniques are applied for the first time to satellite tracking systems. Both radio antenna and optical tracking systems of NASA are considered. The optimal estimation is accomplished using an extended Kalman filter resulting in an estimated state of the satellite and of the tracking system. This estimated state constitutes an input to the optimal controller. The optimal controller treats a linearized system with a quadratic performance index. The maximum principle is applied and a steady-state approximation to the resulting Riccati equation is obtained. A computer program, RATS, implementing this algorithm is described. A feasibility study of real-time implementation, tracking simulations, and parameter sensitivity studies are also reported.

Dressler, R. M.↗
NASA NTRS1974

Modern control techniques in active flutter suppression using a control moment gyro

Development of organized synthesis techniques, using concepts of modern control theory was studied for the design of active flutter suppression systems for two and three-dimensional lifting surfaces, utilizing a control moment gyro (CMG) to generate the required control torques. Incompressible flow theory is assumed, with the unsteady aerodynamic forces and moments for arbitrary airfoil motion obtained by using the convolution integral based on Wagner's indicial lift function. Linear optimal control theory is applied to find particular optimal sets of gain values which minimize a quadratic performance function. The closed loop system's response to impulsive gust disturbances and the resulting control power requirements are investigated, and the system eigenvalues necessary to minimize the maximum value of control power are determined.

Buchek, P. M.↗
NASA NTRS1979

A connection between block and convolutional codes

Convolutional codes of any rate and any constraint length give rise to a sequence of quasi-cyclic codes. Conversely, any quasi-cyclic code may be convolutionally encoded. Among the quasi-cyclic codes are the quadratic residue codes, Reed-Solomon codes and optimal BCH codes. The constraint length K for the convolutional encoding of many of these codes (Golay, (48, 24) QR, etc.) turns out to be surprisingly small. Thus using the soft decoding techniques for convolutional decoding, a new maximum likelihood decoding algorithm for many block codes is established. Conversely an optimal quasi-cyclic code will yield a convolutional encoding with optimal local properties and therefore with good infinite convolutional coding properties.

Solomon, G.↗
NASA NTRS1981

Considerations of open-loop, closed-loop, and adaptive multicyclic control systems

Four different types of self-tuning regulators were studied for multicyclic control of helicopter vibration. A numerical simulation of the helicopter is made, using a multivariable frequency-domain model, in terms of transfer function with six input control harmonics and six output harmonics. The model characteristics vary with flight speed. An off-line identification of model characteristics is made, using the least-squared-error method and using a succession of input and output measurements. The on-line identification of model characteristics is made using the Kalman filter solution. The optimal controls are calculated from the minimization of quadratic performance function based on response and multicyclic inputs. The performance of various regulators or controllers is judged from the stability, transient response, convergence time, and amplitude of the steady state.

Chopra, I.↗
NASA NTRS1991

On convexity of H-infinity Riccati solutions

The authors revealed several important eigen properties of the stabilizing solutions of the two H-infinity Riccati equations and their product. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H-infinity norm. Two examples are used to illustrate the algorithms.

Li, X. P.↗
NASA NTRS1991

Nonlinear time-series-based adaptive control applications

A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.

Mohler, R. R.↗
NASA NTRS1990

Integrated Aerodynamic and Control System Design of Oblique Wing Aircraft

An efficient high speed aircraft design must achieve a high lift to drag ratio at transonic and supersonic speeds. In 1952 Dr. R. T. Jones proved that for any flight Mach number minimum drag at a fixed lift is achieved by an elliptic wing planform with an appropriate oblique sweep angle. Since then, wind tunnel tests and numerical flow models have confirmed that the compressibility drag of oblique wing aircraft is lower than similar symmetrical sweep designs. At oblique sweep angles above thirty degrees the highly asymmetric planform gives rise to aerodynamic and inertia couplings which affect stability and degrade the aircraft's handling qualities. In the case of the NASA-Rockwell Oblique Wing Research Aircraft, attempts to improve the handling qualities by implementing a stability augmentation system have produced unsatisfactory results because of an inherent lack of controllability in the proposed design. The present work focuses on improving the handling qualities of oblique wing aircraft by including aerodynamic configuration parameters as variables in the control system synthesis to provide additional degrees of freedom with which to further decouple the aircraft's response. Handling qualities are measured using a quadratic cost function identical to that considered in optimal control problems, but the controller architecture is not restricted to full state feedback. An optimization procedure is used to simultaneously solve for the aircraft configuration and control gains which maximize a handling qualities measure, while meeting imposed constraints on trim. In some designs wing flexibility is also modeled and reduced order controllers are implemented. Oblique wing aircraft synthesized by this integrated design method show significant improvement in handling qualities when compared to the originally proposed closed loop aircraft. The integrated design synthesis method is then extended to show how handling qualities may be traded for other types of mission performance (drag, weight, etc.). Examples are presented which show how performance can be maximized while maintaining a desired level of handling quality.

Morris, Stephen James↗