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High-precision control of tracked field robots in the presence of unknown traction coefficients
Accurate steering through crop rows that avoids crop damage is one of the most important tasks for agricultural robots utilized in various field operations, such as monitoring, mechanical weeding, or spraying. In practice, varying soil conditions can result in off-track navigation due to unknown traction coefficients so that it can cause crop damage. To address this problem, this work presents the development, application, and experimental results of a real-time receding horizon estimation and control (RHEC) framework applied to a fully autonomous mobile robotic platform to increase its steering accuracy. Recent advances in cheap and fast microprocessors, as well as advances in solution methods for nonlinear optimization problems, have made nonlinear receding horizon control (RHC) and receding horizon estimation (RHE) methods suitable for field robots that require high-frequency (milliseconds) updates. A real-time RHEC framework is developed and applied to a fully autonomous mobile robotic platform designed by the authors for in-field phenotyping applications in sorghum fields. Nonlinear RHE is used to estimate constrained states and parameters, and nonlinear RHC is designed based on an adaptive system model that contains time-varying parameters. The capabilities of the real-time RHEC framework are verified experimentally, and the results show an accurate tracking performance on a bumpy and wet soil field. Finally, the mean values of the Euclidean error and required computation time of the RHEC framework are equal to 0.0423 m and 0.88 ms, respectively.
Iterative methods in GPU-resident linear solvers for nonlinear constrained optimization
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra methods are often inefficient. For example, methods for solving ill-conditioned linear systems have relied on conditional branching, which degrades performance on hardware accelerators such as graphical processing units (GPUs). To improve the efficiency of solving ill-conditioned systems, our computational strategy separates computations that are efficient on GPUs from those that need to run on traditional central processing units (CPUs). Our strategy maximizes the reuse of expensive CPU computations. Iterative methods, which thus far have not been broadly used for ill-conditioned linear systems, play an important role in our approach. In particular, we extend ideas from Arioli et al., (2007) to implement iterative refinement using inexact LU factors and flexible generalized minimal residual (FGMRES), with the aim of efficient performance on GPUs. In conclusion, we focus on solutions that are effective within broader application contexts, and discuss how early performance tests could be improved to be more predictive of the performance in a realistic environment.
Designing stellarator coils by a modified Newton method using FOCUS
To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.
Coordination of Behind-the-Meter Energy Storage and Building Loads: Optimization with Deep Learning Models*
With the increasing penetration of renewable energy systems and energy storage systems in buildings, it is critical to optimize system operation. In this paper, we develop an optimization strategy to minimize the operation cost as well as maintain indoor thermal comfort, for a building integrated with battery and PV. A Recurrent Neural Network (RNN) is used to predict building thermal load and zone temperatures. A black-box optimization algorithm known as nonlinear optimization by mesh adaptive direct search (NOMADS) is employed in simulation to provide look-ahead optimal battery dispatch and zone temperature set-point schedules so that the operation cost is minimized. Field data collected from a medium sized office building at Pacific Northwest National Laboratory (PNNL) integrated with Photovoltaic (PV) system model and battery storage system model is used to demonstrate the proposed methodology. Compared with rule based methods, the optimization strategy obtained a lower cost of operation while satisfying comfort constraints.
TAO 3.10 Users Manual
The Toolkit for Advanced Optimization (TAO) focuses on the development of algorithms and software for the solution of large-scale optimization problems on high-performance architectures. Areas of interest include unconstrained and bound-constrained optimization, nonlinear least squares problems, optimization problems with partial differential equation constraints, and variational inequalities and complementarity constraints.
TAO Users Manual (Rev. 3.15)
The Toolkit for Advanced Optimization (TAO) focuses on the development of algorithms and software for the solution of large-scale optimization problems on high-performance architectures. Areas of interest include unconstrained and bound-constrained optimization, nonlinear least squares problems, optimization problems with partial differential equation constraints, and variational inequalities and complementarity constraints. The development of TAO was motivated by the scattered support for parallel computations and the lack of reuse of external toolkits in current optimization software. Our aim is to produce high-quality optimization software for computing environments ranging from workstations and laptops to massively parallel high-performance architectures. Our design decisions are strongly motivated by the challenges inherent in the use of large-scale distributed memory architectures and the reality of working with large, often poorly structured legacy codes for specific applications.
Realizing the Materials-Designed-To-Environments Promise of Additive Manufacturing Through a Fundamentally Different Approach to Optimization of Nonlinear Solid Mechanics Structures
Additive Manufacturing (AM) is expected to play a large role in the labs-wide goals of accelerating innovation and leading in modern engineering. More specifically, AM is seen as a key enabling technology for increasing the agility of nuclear deterrence and other national security applications involving complex coupled environments. However, the impact of AM on these initiatives has not been as wide-ranging as hoped because – despite its unique qualities – the focus has mostly been on detailed qualification to force AM components into pre-existing performance envelopes. This paradigm fundamentally precludes the novel possibilities afforded by the geometric and material flexibility of AM. In particular, the engineering of small-scale features to undergo buckling and contact can cause large geometric and symmetry changes which provide responsiveness to different environments. Despite almost a decade of observing such behavior, there exists no way to systematically design for AM to exploit it. Our goal for this project was to connect material design to multi-environment component performance by reconceptualizing how to design for AM to exploit the buckling and contact of small-scale features.
Diffusion With Attention For Nonlinear Inverse Optimization
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Nonlinear studies, optimal control
Attitude control for earth satellite in elliptic orbit, linearization in attitude control, and computation of optimal controls by method based on second variations
Gradient optimization and nonlinear control
The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.
Aircraft design for mission performance using nonlinear multiobjective optimization methods
A new technique which converts a constrained optimization problem to an unconstrained one where conflicting figures of merit may be simultaneously considered was combined with a complex mission analysis system. The method is compared with existing single and multiobjective optimization methods. A primary benefit from this new method for multiobjective optimization is the elimination of separate optimizations for each objective, which is required by some optimization methods. A typical wide body transport aircraft is used for the comparative studies.
Aircraft design for mission performance using nonlinear multiobjective optimization methods
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Comparison of Traditional Design Nonlinear Programming Optimization and Stochastic Methods for Structural Design
Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.
Preconditioning of Matrix-Free Full-Space Trust-Region SQP Algorithms for Nonlinear PDE Optimization.
Abstract Not Provided
Discete optimality in nonlinear model reduction: analysis and application to CFD.
Abstract not provided.
Distributed Detector Systems as a Problem in Optimization with Nonlinear Constraints
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