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Results for “Nonlinear robust 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.

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NASA NTRS1988

The expanded Lagrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

NASA NTRS1989

Two-time scale stabilization of a flexible arm with output feedback

An approach is presented to designing a control system with output feedback for a lightweight flexible arm. A two-time-scale dynamic model is obtained which allows the adoption of a composite control strategy. First a slow control can be designed for the slow (rigid) subsystem, and then a fast stabilizing control for the fast (flexible) subsystem. The problem of the lack of full state measurements connected with the fast control design is solved. An output-feedback, low-order dynamic compensator whose optimal gains are computed by a convergent numerical algorithm is designed. A more robust design can be achieved if a loop transfer recovery procedure is introduced. The design procedure is tested by means of nonlinear simulation, and the results are discussed.

Siciliano, Bruno↗

DOE OSTI2026

Deep Learning enabled spectral energy conversion for in situ exposure measurements

A detector-specific deep learning (DL) approach is presented for spectra-to-exposure conversion using large-format sodium iodide (NaI(Tl)) detectors deployed for in situ environmental radiation measurements in emergency response scenarios. Accurate determination of exposure from NaI spectra is challenging due to poor energy resolution, partial energy absorption, and the strong sensitivity of traditionally deployed analytical conversion methods to calibrated source geometry and pre-deployment assumptions. Here, to address these limitations, a multi-layer perceptron model was trained on a hybrid in situ /Monte Carlo dataset constructed to span a broad range of photon energies, spatial extents, and realistic deployment variability, representative of general in situ emergency response conditions. The DL model was evaluated against commonly fielded analytical approaches under matched simulation conditions, including a single-factor method, a G-function method, and a modeled pressurized ion chamber (PIC) baseline. This study was intentionally computational in scope to enable controlled, like-for-like comparisons between conversion techniques while minimizing confounding real-world variability. Comparison to the modeled PIC provides contextual benchmarking and is not intended as a field inter-comparison with deployed instruments. Across the evaluated 20 keV to 3 MeV energy range, the DL approach consistently exhibited higher accuracy and reduced variance relative to the analytical methods against a deterministically calculated exposure. This may indicate improved robustness to spectral complexity without reliance on source-, geometric-, or spectral region-specific optimization. While results do not represent real-world validation, the presented work demonstrates that deep learning may effectively learn the nonlinear detector response-to-exposure relationship for asymmetric NaI(Tl) detectors and offers a promising pathway for improving in situ exposure estimation using spectroscopic systems already integrated into initial real-time emergency response operations.

61 RADIATION PROTECTION AND DOSIMETRY↗

NASA NTRS1994

Nonlinear control of magnetic bearings

In this paper we present a variety of nonlinear controllers for the magnetic bearing that ensure both stability and robustness. We utilize techniques of discontinuous control to design novel control laws for the magnetic bearing. We present in particular sliding mode controllers, time optimal controllers, winding algorithm based controllers, nested switching controllers, fractional controllers, and synchronous switching controllers for the magnetic bearing. We show existence of solutions to systems governed by discontinuous control laws, and prove stability and robustness of the chosen control laws in a rigorous setting. We design sliding mode observers for the magnetic bearing and prove the convergence of the state estimates to their true values. We present simulation results of the performance of the magnetic bearing subject to the aforementioned control laws, and conclude with comments on design.

Pradeep, A. K.↗

DOE OSTI2025

Robust multiresonant nonlocal metasurfaces by rational design

Abstract Dielectric metasurfaces supporting optical resonances have become a promising platform for quantum and nonlinear optics. However, resonant metasurfaces remain limited in their capacity to independently control the behavior of many distinct resonances despite efforts in computational optimization and inverse design. In this work, we overcome longstanding limitations by introducing a generalized rational design paradigm based on symmetry. Specifically, we use symmetry-broken metasurfaces with periodic “quadromer” lattices comprised of four nanostructures per unit cell to enable extensive control of multiple optical resonances. The rationally designed metasurfaces are readily fabricable, and we experimentally demonstrate metasurfaces that support up to four high Q-factor resonances with deliberately chosen free-space polarizations, spectral separations, and mode profiles. Our design paradigm may unlock new applications for multiresonant metasurfaces in quantum and nonlinear optics, optical sensing, and augmented reality displays.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

NASA NTRS1992

Robust intelligent flight control for hypersonic vehicles

Intelligent optimization methods are applied to the problem of real-time flight control for a class of airbreathing hypersonic vehicles (AHSV). The extreme flight conditions that will be encountered by single-stage-to-orbit vehicles, such as the National Aerospace Plane, present a tremendous challenge to the entire spectrum of aerospace technologies. Flight control for these vehicles is particularly difficult due to the combination of nonlinear dynamics, complex constraints, and parametric uncertainty. An approach that utilizes all available a priori and in-flight information to perform robust, real time, short-term trajectory planning is presented.

Chamitoff, Gregory Errol↗

NASA NTRS1987

Nonlinear feedback control of multiple robot arms

Multiple coordinated robot arms are modeled by considering the arms: (1) as closed kinematic chains, and (2) as a force constrained mechanical system working on the same object simultaneously. In both formulations a new dynamic control method is discussed. It is based on a feedback linearization and simultaneous output decoupling technique. Applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, by choosing a general output equation, researchers can superimpose the position and velocity error feedback with the force-torque error feedback in the task space simultaneously.

Tarn, T. J.↗

NASA NTRS1988

New nonlinear control algorithms for multiple robot arms

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Tarn, T. J.↗

NASA NTRS2024

Spacecraft Modeling, Attitude Determination, and Control: Quaternion-Based Approach

Spacecraft attitude determination and control is an important part of a spacecraft to achieve its designed mission. As of today, many spacecrafts have been successfully launched, and most of them have performed well as they were designed. Many research papers have been published to address the attitude determination and control design problems. Several text books are available for students to learn the technology and for engineers to use as references. The most popular spacecraft models for attitude determination algorithms and control design methods are the Euler angle models and the quaternion models . The Euler angle models have been proved very efficient as the linearized models are controllable, and all standard linear control system design methods are directly applicable. The drawbacks related to the Euler angle methods are (a) the designs based on linearized models may not globally stabilize the original nonlinear spacecraft, i.e., the design may not work when the attitude of the spacecraft is far away from the point where the linearization is performed; (b) the models depend on the rotational sequences, this can be error prone if several teams work on the same project and they use different rotational sequences; (c) for any rotational sequence, there is a singular point where the model is not applicable; and (d) since most attitude determination methods use quaternion to represent the spacecraft attitude, there is a need to transform quaternion into Euler angles. On the other hand, for quaternion models, people have found controllers that can globally stabilize nonlinear spacecraft systems; the models do not depend on rotational sequences and they have no singular point; and the quaternion is provided by attitude determination system and ready to use. The main problem with the quaternion model based control system design is that the linearized quaternion model is not controllable. Therefore, most published design methods heavily rely on Lyapunov functions for the nonlinear spacecraft system. But there is no systematic way to obtain a desired Lyapunov functions. Moreover, the Lyapunov function based designs focus on the closed-loop system stability but pay little attention to the closed-loop system performance. In a series of papers, the author proposed some reduced quaternion models which lead to some controllable linearized spacecraft models. Therefore, all standard linear system theory can be directly applied to analyze and design the spacecraft control systems. We showed that, in some cases, the designed control system is not only optimal for the linearized system, but also globally stabilize the original nonlinear system . Clearly, the reduced quaternion models do not depend on rotational sequences. Due to the special structure of the linearized spacecraft model, some most important design methods, such as LQR design and robust pole assignment design are very simple, enjoy the analytical solutions for some problems, have direct connection to the performance measures, such as settling time, rising time , and percentage of overshoot . All these features are attractive for high quality control system designs. The idea mentioned above is then extended to more spacecraft control problems using specific actuators such as magnetic torque bars and control momentum gyroscopes. These types of actuators may not provide exactly desired torques. Most existing methods use different conversions to get approximate solutions, meaning that these actuators may generate a torque close to but not equal to the desired one. Using the reduced quaternion models that incorporate the actuators into the system model, the control inputs are not torques but the operational parameters. The main benefit of this idea is that the control actions are not approximate but accurate. As all actuators have their operational limit, design with input constraints are also considered in this book by using recently developed interior-point optimization techniques. This book grows up from my research on the spacecraft attitude determination and control design methods in more than a decade which is focused on using reduced quaternion models because of their merits stated above. The book provides all necessary background materials on orbital dynamics, rotations and quaternion, frequently used reference frames, transformations between reference frames, space environment and disturbance torques, ephemeris astronomical vector calculations and measurement instruments, spacecraft control actuators and their models, so that the readers will get a global picture and can apply all these information into the spacecraft system modeling, attitude determination, and spacecraft control system designs, which is the main purpose of this book. This book is different from existing books in that we focus on quaternion based spacecraft control system designs and we consider only attitude control system design related problems, from spacecraft modeling, to attitude determination and estimation, to control system design method selection, to control algorithm development, and to the simulation of the control system designs. Moreover, this book addresses different attitude control tasks in the spacecraft life cycle, including spacecraft maneuver, orbit raising, attitude control, and rendezvous. Finally, this book emphasizes the state space design methods rather than the classical frequency design methods.

Attitude determination and control↗

DOE OSTI2024

Leveraging design of experiments to build chemometric models for the quantification of uranium (VI) and HNO3 by Raman spectroscopy

Partial least squares regression (PLSR) and support vector regression (SVR) models were optimized for the quantification of U(VI) (10–320 g L −1 ) and HNO 3 (0.6–6 M) by Raman spectroscopy with optimized calibration sets chosen by optimal design of experiments. The designed approach effectively minimized the number of samples in the calibration set for PLSR and SVR by selecting sample concentrations with a quadratic process model, despite complex confounding and covarying spectral features in the spectra. The top PLS2 model resulted in percent root mean square errors of prediction for U(VI), HNO 3 , and NO 3 − of 3.7%, 3.6%, and 2.9%, respectively. PLS1 models performed similarly despite modeling an analyte with a majority linear response (i.e., uranyl symmetric stretch) and another with more covarying vibrational modes (i.e., HNO 3 ). Partial least squares (PLS) model loadings and regression coefficients were evaluated to better understand the relationship between weaker Raman bands and covarying spectral features. Support vector machine models outperformed PLS1 models, resulting in percent root mean square error of prediction values for U(VI) and HNO 3 of 1.5% and 3.1%, respectively. The optimal nonlinear SVR model was trained using a similar number of samples (11) compared with the PLSR model, even though PLS is a linear modeling approach. The generic D-optimal design presented in this work provides a robust statistical framework for selecting training set samples in disparate two-factor systems. This approach reinforces Raman spectroscopy for the quantification of species relevant to the nuclear fuel cycle and provides a robust chemometric modeling approach to bolster online monitoring in challenging process environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Real-time control of connected vehicles in signalized corridors using pseudospectral convex optimization

Recent advances in Connected and Automated Vehicle (CAV) technologies have opened up new opportunities to enable safe, efficient, and sustainable transportation systems. However, developing reliable and rapid speed control algorithms in highly dynamic environments with complex inter-vehicle interactions and nonlinear vehicle dynamics is still a daunting task. In this paper, we develop a novel speed control method for CAVs to produce optimal speed profiles that minimize the fuel consumption and avoid idling at signalized intersections. To this end, an optimal control problem is formulated using the information of the upcoming traffic signal to adapt vehicles' speeds to avoid frequent stop-and-go driving patterns. Here, by applying the pseudospectral discretization method and the sequential convex programming method, the computational efficiency is greatly improved, enabling potential real-time on-vehicle applications. In addition, the algorithm is implemented under a model predictive control framework to ensure online control with instant response for collision avoidance and robust vehicle coordination. The proposed algorithm is verified through numerical simulations of three different traffic scenarios. The convergence and accuracy of the proposed approach are demonstrated by comparing with a popular nonlinear solver. Furthermore, the benefit of the proposed method in both traffic mobility and fuel efficiency is validated using the speed profile determined from a traffic following model in a simulation software as the baseline.

42 ENGINEERING↗

NASA NTRS2010

Absolute Stability Analysis of a Phase Plane Controlled Spacecraft

Many aerospace attitude control systems utilize phase plane control schemes that include nonlinear elements such as dead zone and ideal relay. To evaluate phase plane control robustness, stability margin prediction methods must be developed. Absolute stability is extended to predict stability margins and to define an abort condition. A constrained optimization approach is also used to design flex filters for roll control. The design goal is to optimize vehicle tracking performance while maintaining adequate stability margins. Absolute stability is shown to provide satisfactory stability constraints for the optimization.

Jang, Jiann-Woei↗

DOE OSTI2026

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗

DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1975

Control optimization, stabilization and computer algorithms for aircraft applications

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Source record↗

NASA NTRS1984

Application of augmented-Lagrangian methods in meteorology: Comparison of different conjugate-gradient codes for large-scale minimization

A Lagrange multiplier method using techniques developed by Bertsekas (1982) was applied to solving the problem of enforcing simultaneous conservation of the nonlinear integral invariants of the shallow water equations on a limited area domain. This application of nonlinear constrained optimization is of the large dimensional type and the conjugate gradient method was found to be the only computationally viable method for the unconstrained minimization. Several conjugate-gradient codes were tested and compared for increasing accuracy requirements. Robustness and computational efficiency were the principal criteria.

Navon, I. M.↗

NASA NTRS1996

Parallelization of a Parabolized Navier-Stokes Solver with a Design Optimizer

The design of future supersonic aircraft, such as the High Speed Civil Transport (HSCT), will rely heavily on computational methods for aircraft design and the prediction of the complex aerodynamics encountered in flight. Parabolized Navier-Stokes (PNS) equation flow solvers are recognized as efficient and accurate computational tools for the solution of supersonic and hypersonic flow-fields, while design optimizers have the potential to be valuable tools within the overall design process. Presently, however, the execution of the flow solver in conjunction with a design optimizer presents a computationally intensive and formidable problem. To meet the challenges and increasing demand for multidisciplinary numerical tools which are faster, more robust and provide greater functionality, alternative strategies are explored to increase computational throughput by coupling a design optimizer and flow solver in a parallel processing environment. To address this problem the parallel processing of a PNS flow solver with a nonlinear constraint design optimizer is investigated as an alternative computational method.

Pallis, J. M.↗

NASA NTRS1997

Sliding Mode Control of a Slewing Flexible Beam

An output feedback sliding mode controller (SMC) is proposed to minimize the effects of vibrations of slewing flexible manipulators. A spline trajectory is used to generate ideal position and velocity commands. Constrained nonlinear optimization techniques are used to both calibrate nonlinear models and determine optimized gains to produce a rest-to-rest, residual vibration-free maneuver. Vibration-free maneuvers are important for current and future NASA space missions. This study required the development of the nonlinear dynamic system equations of motion; robust control law design; numerical implementation; system identification; and verification using the Sandia National Laboratories flexible robot testbed. Results are shown for a slewing flexible beam.

Wilson, David G.↗