Bang-bang control is ubiquitous for Optimal Control Problems (OCPs) where the constrained control variable appears linearly in the dynamics and cost function. Based on the Pontryagin's Minimum Principle, the indir...
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ISBN:
(数字)9781624107115
ISBN:
(纸本)9781624107115
Bang-bang control is ubiquitous for Optimal Control Problems (OCPs) where the constrained control variable appears linearly in the dynamics and cost function. Based on the Pontryagin's Minimum Principle, the indirect method is widely used to numerically solve OCPs because it enables one to derive the theoretical structure of the optimal control. However, discontinuities in the bang-bang control structure may result in numerical difficulties for the gradient-based indirect method. In this case, smoothing or regularization procedures are usually applied to eliminating the discontinuities of bang-bang controls. Traditional smoothing or regularization procedures generally modify the cost function by adding a term depending on a small parameter, or introducing a small error into the state equation. Those procedures may complexify the numerical algorithms or degenerate the convergence performance. To overcome these issues, we propose a bounded smooth function, called normalized.. 2-norm function, to approximate the sign function in terms of the switching function. The resulting optimal control is smooth and can be readily embedded into the indirect method. Then, the simplicity and improved performance of the proposed method over some existing methods are numerically demonstrated by a minimal-time oscillator problem and a minimal-fuel low-thrust trajectory optimization problem that involves many revolutions.
Abstract: This paper studies the development of a multiscale approach to calculate the gas flows near solid surfaces taking into account microscopic effects. In this line of research, the problem of setting boundary c...
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Energy retrofit of existing buildings demands an accurate assessment of the thermal performance of the building envelope. In response, the THERMOG research project is developing a comprehensive tool to meet this requi...
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Energy retrofit of existing buildings demands an accurate assessment of the thermal performance of the building envelope. In response, the THERMOG research project is developing a comprehensive tool to meet this requirement by delivering precise and practical insight into building envelope thermal efficiency. The paper presents the development and application of innovative algorithms for the pre- and post-processing of thermal images, specifically tailored to address challenges in analyzing 20 buildings subjected to comprehensive photogrammetric and thermographic investigations. A significant obstacle in this study was the lack of georeferencing in the thermal images, an issue that poses considerable challenges in aligning and correlating these images with their photogrammetric counterparts. To address these challenges, a novel methodology that primarily focuses on the processing of thermal images was developed, combining image processing techniques with algorithms tailored to reconstruct building facades and other areas of interest. The pre-processing phase centers on refining thermal image quality through noise reduction, image sharpening, and contrast enhancement, followed by detailed facades and reconstruction of critical building elements. Although the complete testing of this algorithm is planned for the 20 buildings, preliminary assessments have shown promising results in improving the fidelity and utility of thermal data. Also, it provides a framework for more nuanced and detailed analysis of building envelopes, which is crucial for energy efficiency diagnostics and architectural conservation.
Mead-Marcus type model describing the vibrations on a multilayer smart beam with arbitrary number of layers is considered with hinged boundary conditions. The model is known to be exactly observable in an appropriate ...
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Mead-Marcus type model describing the vibrations on a multilayer smart beam with arbitrary number of layers is considered with hinged boundary conditions. The model is known to be exactly observable in an appropriate Hilbert space with a single boundary sensor measurement. As a standard Finite Differences-based model reduction is considered, it is proved that the model reduction lacks exact observability uniformly as the mesh parameter goes to zero, h? 0. This is a known phenomenon caused by spurious (artificial) high-frequency eigenvalues. First, it is proved that the exact observability can be retained by the implementation of the direct Fourier filtering technique. However, the optimality of the applied filtering demands further investigation. For this reason, an alternate model reduction is investigated by cleverly reducing the order of the model together with the consideration of equidistant grid points and averaging operators, as in Liu and Guo (2019, 2020, and 2021). This new model reduction successfully retains the exact observability uniformly as h?0. Moreover, it does not need a further numerical filtering. Our results are based on carefully analyzing the spectrum of the system matrix, and they are applicable to the standard Euler-Bernoulli and Rayleigh beam equations. The numerical simulations are provided to compare reduced models and to show the strength of introduced results.
This letter presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The proposed scheme combines forward-backward...
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This letter presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The proposed scheme combines forward-backward iterations with solutions to trust-region subproblems: the former ensures global convergence, whereas the latter enables fast update directions. We discuss how the algorithm is able to exploit exact Hessian information of the smooth objective term through a linear Newton approximation, while benefiting from the structure of box-constraints or $\ell _{1}$ -regularization. An open-source C++ implementation of PANTR is made available as part of the NLP solver library ALPAQA. Finally, the effectiveness of the proposed method is demonstrated in nonlinear model predictive control applications.
Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. numerical discretization of the continuous system is an integral part of subsequ...
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Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback linearizability of such sampled systems is dependent upon the choice of discretization map or technique. In this letter, for feedback linearizable continuous-time systems, we utilize the idea of retraction maps to construct discretizations that are feedback linearizable as well. We also propose a method to functionally compose discretizations to obtain higher-order integrators that are feedback linearizable.
Structures in the Circular Restricted Three-Body Problem (CR3BP) are vital to enable multiple space mission concepts, yet delivering their counterparts in a Higher-Fidelity Ephemeris Model (HFEM) poses a non-trivial t...
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ISBN:
(数字)9781624107115
ISBN:
(纸本)9781624107115
Structures in the Circular Restricted Three-Body Problem (CR3BP) are vital to enable multiple space mission concepts, yet delivering their counterparts in a Higher-Fidelity Ephemeris Model (HFEM) poses a non-trivial task. Achieving a seamless transition between the CR3BP and HFEM necessitates a thorough comprehension of the underlying dynamical factors that impede the process. This investigation leverages the Elliptic Restricted Three-Body Problem (ER3BP) as an intermediate model between the CR3BP and HFEM, employing numerical continuation and bifurcation analysis to characterize the challenges associated with the transition process. Specifically, the focus is on the Earth-Moon L-2 halo orbit family. A subset of the family exhibits a proliferation of fold bifurcations with respect to the eccentricity of the model, serving as an indicator for transition-challenging behavior as analyzed within the ER3BP.
algorithms for the computation of the (weighted) geometric mean G of two positive definite matrices are described and discussed. For large and sparse matrices the problem of computing the product y=Gb\documentclass[12...
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algorithms for the computation of the (weighted) geometric mean G of two positive definite matrices are described and discussed. For large and sparse matrices the problem of computing the product y=Gb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y=Gb$$\end{document}, and of solving the linear system Gx=b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Gx=b$$\end{document}, without forming G, is addressed. An analysis of the conditioning is provided. Substantial numerical experimentation is carried out to test and compare the performances of these algorithms in terms of CPU time, numerical stability, and number of iterative steps.
Deep learning (DL) has become an integral part of solutions to various important problems, which is why ensuring the quality of DL systems is essential. One of the challenges of achieving reliability and robustness of...
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ISBN:
(纸本)9781450392211
Deep learning (DL) has become an integral part of solutions to various important problems, which is why ensuring the quality of DL systems is essential. One of the challenges of achieving reliability and robustness of DL software is to ensure that algorithm implementations are numerically stable. DL algorithms require a large amount and a wide variety of numerical computations. A naive implementation of numerical computation can lead to errors that may result in incorrect or inaccurate learning and results. A numerical algorithm or a mathematical formula can have several implementations that are mathematically equivalent, but have different numerical stability properties. Designing numerically stable algorithm implementations is challenging, because it requires an interdisciplinary knowledge of software engineering, DL, and numerical analysis. In this paper, we study two mature DL libraries PyTorch and Tensorflow with the goal of identifying unstable numerical methods and their solutions. Specifically, we investigate which DL algorithms are numerically unstable and conduct an in-depth analysis of the root cause, manifestation, and patches to numerical instabilities. Based on these findings, we launch DeepStability, the first database of numerical stability issues and solutions in DL. Our findings and DeepStability provide future references to developers and tool builders to prevent, detect, localize and fix numerically unstable algorithm implementations. To demonstrate that, using DeepStability we have located numerical stability issues in Tensorflow, and submitted a fix which has been accepted and merged in.
The present paper shows the main characteristic of a numerical simulation tool, developed in the framework of the European H2020 project MAHEPA, to estimate optimal flight performance of a generic aircraft featuring a...
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ISBN:
(数字)9781624107047
ISBN:
(纸本)9781624107047
The present paper shows the main characteristic of a numerical simulation tool, developed in the framework of the European H2020 project MAHEPA, to estimate optimal flight performance of a generic aircraft featuring a Hybrid powertrain. The purpose of the study is to determine optimal flight trajectories together with optimal power controls when a powertrain with multi-energy or multi-power sources (as the case of a generic hybrid one) is considered. For this purpose a complete new software has been developed, which is composed by three main parts: a mission performance "analyser" where the system dynamics of the problem is determined and it solves the aircraft Equation of Motion;a powertrain simulator that determines the operating conditions of the powertrain components and it ultimately computes the consumption of each energy source;a numerical algorithm that optimizes the aircraft control variables to determine both the optimum flight trajectory and the power management according to a certain objective functions and a variety of constraints. Different study cases are discussed when two existing flying hybrid aircraft are considered: a Hybrid-Electric (HE) Pipistrel Panthera aircraft and a Fuel-Cell hybrid (FCH) Pipistrel HY4. Results are presented also depending on the capability to simulate the entire mission as a whole (Single-Phase approach) as well as through the distinction of different flight segments as in the case of the Multi-Phase approach. In addition, two different resolution algorithms are tested in order to evaluate what are the aspects that might dictate the selection of the most suitable one.
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