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All sources NASA NTRS DOE OSTI

DOE OSTI2015

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.

Ma, Xiao↗

NASA NTRS2017

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Parrish, Nathan L.↗

DOE OSTI2014

Dual-energy cone-beam CT with a flat-panel detector: Effect of reconstruction algorithm on material classification

Purpose: Cone-beam CT (CBCT) with a flat-panel detector (FPD) is finding application in areas such as breast and musculoskeletal imaging, where dual-energy (DE) capabilities offer potential benefit. The authors investigate the accuracy of material classification in DE CBCT using filtered backprojection (FBP) and penalized likelihood (PL) reconstruction and optimize contrast-enhanced DE CBCT of the joints as a function of dose, material concentration, and detail size. Methods: Phantoms consisting of a 15 cm diameter water cylinder with solid calcium inserts (50–200 mg/ml, 3–28.4 mm diameter) and solid iodine inserts (2–10 mg/ml, 3–28.4 mm diameter), as well as a cadaveric knee with intra-articular injection of iodine were imaged on a CBCT bench with a Varian 4343 FPD. The low energy (LE) beam was 70 kVp (+0.2 mm Cu), and the high energy (HE) beam was 120 kVp (+0.2 mm Cu, +0.5 mm Ag). Total dose (LE+HE) was varied from 3.1 to 15.6 mGy with equal dose allocation. Image-based DE classification involved a nearest distance classifier in the space of LE versus HE attenuation values. Recognizing the differences in noise between LE and HE beams, the LE and HE data were differentially filtered (in FBP) or regularized (in PL). Both a quadratic (PLQ) and a total-variation penalty (PLTV) were investigated for PL. The performance of DE CBCT material discrimination was quantified in terms of voxelwise specificity, sensitivity, and accuracy. Results: Noise in the HE image was primarily responsible for classification errors within the contrast inserts, whereas noise in the LE image mainly influenced classification in the surrounding water. For inserts of diameter 28.4 mm, DE CBCT reconstructions were optimized to maximize the total combined accuracy across the range of calcium and iodine concentrations, yielding values of ∼88% for FBP and PLQ, and ∼95% for PLTV at 3.1 mGy total dose, increasing to ∼95% for FBP and PLQ, and ∼98% for PLTV at 15.6 mGy total dose. For a fixed iodine concentration of 5 mg/ml and reconstructions maximizing overall accuracy across the range of insert diameters, the minimum diameter classified with accuracy >80% was ∼15 mm for FBP and PLQ and ∼10 mm for PLTV, improving to ∼7 mm for FBP and PLQ and ∼3 mm for PLTV at 15.6 mGy. The results indicate similar performance for FBP and PLQ and showed improved classification accuracy with edge-preserving PLTV. A slight preference for increased smoothing of the HE data was found. DE CBCT discrimination of iodine and bone in the knee was demonstrated with FBP and PLTV at 6.2 mGy total dose. Conclusions: For iodine concentrations >5 mg/ml and detail size ∼20 mm, material classification accuracy of >90% was achieved in DE CBCT with both FBP and PL at total doses <10 mGy. Optimal performance was attained by selection of reconstruction parameters based on the differences in noise between HE and LE data, typically favoring stronger smoothing of the HE data, and by using penalties matched to the imaging task (e.g., edge-preserving PLTV in areas of uniform enhancement)

62 RADIOLOGY AND NUCLEAR MEDICINE↗

NASA NTRS1973

Evaluation of glide paths for landing a VTOL airplane using linear regulator theory.

A method of evaluating certain characteristics of approach paths for VTOL airplanes is presented which is based on the solution of the matrix Riccati equation to obtain an optimal state variable feedback controller. The longitudinal equations of motion of the airplane are linearized about a preselected path and the resulting system of equations is treated as a linear, time-varying regulator. The controller which minimizes a quadratic cost function is applied to the linearized system to determine the airplane's ability to return to the prescribed path given a specified initial error in altitude. The procedure is applied to the XC-142A, tilt-wing, V/STOL airplane, under decelerating approach conditions with a glide path consisting of two segments, the first having a smaller angle of descent than the second.

Reid, G. F.↗

NASA NTRS1979

Ambiguity resolution for satellite Doppler positioning systems

The implementation of satellite-based Doppler positioning systems frequently requires the recovery of transmitter position from a single pass of Doppler data. The least-squares approach to the problem yields conjugate solutions on either side of the satellite subtrack. It is important to develop a procedure for choosing the proper solution which is correct in a high percentage of cases. A test for ambiguity resolution which is the most powerful in the sense that it maximizes the probability of a correct decision is derived. When systematic error sources are properly included in the least-squares reduction process to yield an optimal solution the test reduces to choosing the solution which provides the smaller valuation of the least-squares loss function. When systematic error sources are ignored in the least-squares reduction, the most powerful test is a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudoinverse of a reduced-rank square matrix. A formula for computing the power of the most powerful test is provided. Numerical examples are included in which the power of the test is computed for situations that are relevant to the design of a satellite-aided search and rescue system.

Argentiero, P.↗

NASA NTRS2003

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

In this paper we present, a comparison of trajectory optimization approaches for the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP). Quasi- Newton and Nelder-Meade Simplex. Several cost function parameterizations are considered for the direct approach. We choose one direct approach that appears to be the most flexible. Both the direct and indirect methods are applied to a variety of test cases which are chosen to demonstrate the performance of each method in different flight regimes. The first test case is a simple circular-to-circular coplanar rendezvous. The second test case is an elliptic-to-elliptic line of apsides rotation. The final test case is an orbit phasing maneuver sequence in a highly elliptic orbit. For each test case we present a comparison of the performance of all methods we consider in this paper.

Hughes, Steven P.↗

DOE OSTI2025

Superconductivity and normal-state transport in compressively strained La 2 PrNi 2 O 7 thin films

The discovery of superconductivity under high pressure in Ruddlesden-Popper phases of bulk nickelates has sparked great interest in stabilizing ambient pressure superconductivity in thin-film form using epitaxial strain. Recently, signs of superconductivity have been observed in compressively strained bilayer nickelate thin films with an onset temperature exceeding 40 K, albeit with broad and two-step-like transitions. Here, in this study, we report intrinsic superconductivity and normal-state transport properties in compressively strained La 2 PrNi 2 O 7 thin films, achieved through a combination of isovalent Pr substitution, growth optimization, and precision ozone annealing. The superconducting onset occurs above 48 K, with zero resistance reached above 30 K, and the critical current density at 1.4 K is 100-fold larger than previous reports. The normal-state resistivity exhibits quadratic temperature dependence indicative of Fermi liquid behaviour, and other phenomenological similarities to transport in overdoped cuprates suggest parallels in their emergent properties.

Liu, Yidi [SLAC National Accelerator Laboratory (S↗

DOE OSTI2020

LOGAN: High-Performance GPU-Based X-Drop Long-Read Alignment

Pairwise sequence alignment is one of the most computationally intensive kernels in genomic data analysis, accounting for more than 90% of the runtime for key bioinformatics applications. This method is particularly expensive for third-generation sequences due to the high computational cost of analyzing sequences of length between 1Kb and 1Mb. Given the quadratic overhead of exact pairwise algorithms for long alignments, the community primarily relies on approximate algorithms that search only for high-quality alignments and stop early when one is not found. In this work, we present the first GPU optimization of the popular X-drop alignment algorithm, that we named LOGAN. Results show that our high-performance multi-GPU implementation achieves up to 181.6 GCUPS and speed-ups up to 6.6× and 30.7× using 1 and 6 NVIDIA Tesla V100, respectively, over the state-of-the-art software running on two IBM Power9 processors using 168 CPU threads, with equivalent accuracy. We also demonstrate a 2.3× LOGAN speed-up versus ksw2, a state-of-art vectorized algorithm for sequence alignment implemented in minimap2, a long-read mapping software. Furthermore, to highlight the impact of our work on a real-world application, we couple LOGAN with a many-to-many long-read alignment software called BELLA, and demonstrate that our implementation improves the overall BELLA runtime by up to 10.6×. Finally, we adapt the Roofline model for LOGAN and demonstrate that our implementation is near optimal on the NVIDIA Tesla V100s.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Optimal output feedback control of linear systems in presence of forcing and measurement noise

The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration.

Joshi, S. M.↗

NASA NTRS1975

Design of optimal partial state feedback controllers for linear systems in stochastic environments

The problem of obtaining an optimal control law, which is constrained to be a feedback of the available measurements, is considered for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise. Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite duration cases. The feedback gain matrices are constrained to be constant for the infinite duration cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. Computational aspects are discussed via application to two continuous time processes, including a helicopter/slung load system subjected to measurement noise and random wind gust input.

Joshi, S. M.↗

NASA NTRS1987

Precise computer controlled positioning of robot end effectors using force sensors

A major problem in space applications of robotics and docking of spacecraft is the development of technology for automated precise positioning of mating components with smooth motion and soft contact. To achieve the above objective, a design method was developed for optimally placing the closed-loop poles of a discretized robotic control system at exact prescribed locations inside the unit circle of the complex z-plane. The design method combines the merits of the pole placement and the linear quadratic design approaches. The proposed design procedure is based on the assignment of one real eigenvalue or two complex conjugate (or real) eigenvalues at each design step. The method involves solutions of simple algebraic equations and this is considered to be efficient for on-line or off-line computations. Also, two methods for the linearization of the nonlinear model of a robotic manipulator were presented. Since automatic control of multi-degree freedom robotic manipulators involves high nonlinear equations of systems, a pilot project was proposed involving the control of a one-dimensional system. This simple system can be readily implemented for testing the concepts and algorithms.

Shieh, Leang S.↗

DOE OSTI2016

WE-H-BRA-03: Development of a Model to Include the Evolution of Resistant Tumor Subpopulations Into the Treatment Optimization Process for Schedules Involving Targeted Agents in Chemoradiation Therapy

Purpose: To develop a model that includes the process of resistance development into the treatment optimization process for schedules that include targeted therapies. Further, to validate the approach using clinical data and to apply the model to assess the optimal induction period with targeted agents before curative treatment with chemo-radiation in stage III lung cancer. Methods: Growth of the tumor and its subpopulations is modeled by Gompertzian growth dynamics, resistance induction as a stochastic process. Chemotherapy induced cell kill is modeled by log-cell kill dynamics, targeted agents similarly but restricted to the sensitive population. Radiation induced cell kill is assumed to follow the linear-quadratic model. The validation patient data consist of a cohort of lung cancer patients treated with tyrosine kinase inhibitors that had longitudinal imaging data available. Results: The resistance induction model was successfully validated using clinical trial data from 49 patients treated with targeted agents. The observed recurrence kinetics, with tumors progressing from 1.4–63 months, result in tumor growth equaling a median volume doubling time of 92 days [34–248] and a median fraction of pre-existing resistance of 0.035 [0–0.22], in agreement with previous clinical studies. The model revealed widely varying optimal time points for the use of curative therapy, reaching from ∼1m to >6m depending on the patient’s growth rate and amount of pre-existing resistance. This demonstrates the importance of patient-specific treatment schedules when targeted agents are incorporated into the treatment. Conclusion: We developed a model including evolutionary dynamics of resistant sub-populations with traditional chemotherapy and radiation cell kill models. Fitting to clinical data yielded patient specific growth rates and resistant fraction in agreement with previous studies. Further application of the model demonstrated how proper timing of chemo-radiation could minimize the probability of resistance, increasing tumor control significantly.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Optimal inputs for system identification

Identification criteria are presented for linear dynamic systems with and without process noise. With process noise, the state equations are replaced by the Kalman filter equations. If the identification performance index is expanded in a Taylor's series with respect to the parameters to be identified, then maximizing the weighting factor of the quadratic term with respect to the inputs will insure that an identification algorithm will converge more rapidly and to a more accurate result than with nonoptimal inputs. The expectation of this weighting factor is the Fisher information matrix, and its inverse is a lower bound for the covariance of the parameters. Direct and indirect methods of calculating the information matrix are presented for systems with and without process noise.

Reid, D. B.↗

DOE OSTI2018

Numerical study of a smoothing algorithm for the complementarity system over the second-order cone

This paper deals with the complementarity system over the second-order cone (denoted by CSSOC) which contains a wide class of problems. We extend a class of regularized Chen–Harker–Kanzow–Smale smoothing functions studied by Huang and Sun (Appl Math Optim 52:237–262, 2005) for the linear complementarity problem to the CSSOC. Based on this class of functions, we propose a smoothing algorithm for solving the CSSOC. Under weak assumptions, we prove that the proposed algorithm has global and local quadratic convergence. The proposed algorithm is different from existing smoothing algorithms for solving the CSSOC because it adopts a new nonmonotone line search rule. In addition, our algorithm solves a new equation reformulation of the CSSOC. Numerical experiments indicate that the proposed algorithm is quite effective.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Surface Anchoring and Director Distribution in a Grandjean–Cano Wedge

Theoretical calculations of the director distribution in a Grandjean–Cano wedge in relation to the anchoring strength and mutual orientation of the easy axes at the wedge surfaces are performed for various model surface anchoring potentials. Comparison of the theory and experiment allows one to propose the socalled model D-potential, quadratic in angle of director deviation from the easy axes, as the best one in fitting the experiment in the angular range of performed measurements. To satisfy general requirements on the wedge surface, a modified D-potential is proposed. The optimal conditions of the experiment aimed at restoring the potential in the whole range of its definition (in particular, nonparallel orientation of the easy axes at the wedge surfaces) are formulated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1989

Convergence of infinite dimensional sampled LQR problems - Theory and numerical results

A theory is developed for the convergence of the closed-loop solution to infinite-dimensional discrete-time linear-quadratic regulator (LQR) problems on the infinite time interval to the solution of a corresponding continuous-time LQR problem as the length of the sampling interval tends toward zero. Convergence of solutions to the operator algebraic Riccati equation and corresponding optimal feedback control gains is guaranteed under appropriate uniform stabilizability and detectability conditions and consistent sampling. Also presented are numerical results involving the optimal LQ control of a heat or diffusion equation, a hereditary or delay differential equation, and a hybrid system of ordinary and partial differential equations describing the transverse vibration of a cantilevered Voigt-Kelvin viscoelastic beam with tip mass.

Rosen, I. G.↗

NASA NTRS1990

A computational algorithm for spacecraft control and momentum management

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Dzielski, John↗