Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control...
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Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems. (C) 2018 Elsevier Ltd. All rights reserved.
The 'equation-free toolbox' empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable scientists and engineers to immediately use microscopic simulators to perform macro-scal...
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The 'equation-free toolbox' empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable scientists and engineers to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because micro-scale simulations are often the best available description of a system. The methodology bypasses the derivation of macroscopic evolution equations by computing the micro-scale simulator only over short bursts in time on small patches in space, with bursts and patches well-separated in time and space respectively. We introduce the suite of coded equation-free functions in an accessible way, link to more detailed descriptions, discuss their mathematical support, and introduce a novel and efficient algorithm for Projective Integration. Some facets of toolbox development of equation-free functions are then detailed. Download the toolbox functions and use to empower efficient and accurate simulation in a wide range of science and engineering problems.
The potential for numerical instabilities of Dynamic Mode Decomposition (DMD), which assumes the completeness of the eigenspace is discussed for cases where the underlying system is defective or nearly defective. A nu...
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The potential for numerical instabilities of Dynamic Mode Decomposition (DMD), which assumes the completeness of the eigenspace is discussed for cases where the underlying system is defective or nearly defective. A numerically stable approach based on Schur decomposition is presented. The proposed method complements the DMD for cases where eigendecomposition is ill-conditioned. Both mathematical analysis and the results of numerical experiments are presented.
Polynomial Chaos Expansions (PCEs) offer an efficient alternative to assess the statistical properties of a model output taking into account the statistical properties of several uncertain model inputs, particularly, ...
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Polynomial Chaos Expansions (PCEs) offer an efficient alternative to assess the statistical properties of a model output taking into account the statistical properties of several uncertain model inputs, particularly, under the restriction of probing the forward model as little as possible. The use of PCE knows a steady increase in recent literature with applications spanning from mere system analysis to robust control design and optimization. The principle idea is to model the output as a series expansion, with the expansion basis depending only on the stochastic variables. The basis is then chosen so that it is better suited to support the uncertainty propagation. Once the expansion coefficients have been identified, accessing the statistical moments benefits the linearity of the expansion and the properties of the moment operator. As a result, the first two statistical moments of the model output can be computed easily using well known analytical expressions. For high-order moments, analytical expressions also exist but are inefficient to evaluate. In this letter we present three strategies to efficiently calculate high-order moments from the expansion model and provide an empirical study of the associated computation time supporting any potential users in making an informed choice.
This letter discusses the eco-driving problem, considering both electric and conventional powertrains, and presents a pathway to solving it numerically using an indirect collocation method. Despite the low-order syste...
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This letter discusses the eco-driving problem, considering both electric and conventional powertrains, and presents a pathway to solving it numerically using an indirect collocation method. Despite the low-order system dynamics, the piecewise fuel/efficiency map, gear shifting, and real-world traffic/road situations bring system discontinuities/switchings and pure state constraints into the problem formulation, which make the problem highly nonlinear and nontrivial to solve. This letter introduces smooth approximations to convert the original problem to an unconstrained (and penalized) smooth boundary-value problem. This approach eliminates the discussion of the switching structure and leads to a lightweight Newton-method-based solution procedure.
During the atmospheric entry phase at hypersonic speed, the radio communication from/to a space vehicle can be disrupted due to the formation of a plasma sheath within the surrounding flow field. In order to character...
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During the atmospheric entry phase at hypersonic speed, the radio communication from/to a space vehicle can be disrupted due to the formation of a plasma sheath within the surrounding flow field. In order to characterize such communication blackout phases, this work presents a numerical methodology combining Computational Fluid Dynamic (CFD) simulations of ionized chemically reacting entry flows by means of Computational Object-Oriented Libraries for Fluid Dynamics (COOLFluiD) and a ray tracing analysis by means of the newly developed BlackOut RAy Tracer (BORAT). The latter is based on the numerical solution of the 3D Eikonal system of equations, offering a fast, efficient and accurate method to analyse the interaction between electromagnetic signals and weakly ionised plasmas. The proposed methodology, and BORAT in particular, is first verified on popular benchmark cases and then used to analyse the European Space Agency (ESA) 2016 ExoMars Schiaparelli entry flight into Martian environment. The corresponding results demonstrate the validity of the proposed ray tracing approach for predicting communication blackout, where signals emitted from the on-board antenna undergo reflection and refraction from the plasma surrounding the entry vehicle, and the advantage of a 3D approach for analysing real flight configuration.(c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS)...
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The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flow solver. The spatial derivative terms of the system of equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried out using an implicit dual time-stepping method, and the robustness and performance of the numerical algorithm are enhanced by applying the preconditioning technique and calculating the automated AC parameter based on the local flow conditions. At first, the steady viscous incompressible flow for a two-dimensional plane jet is computed to assess the accuracy and performance of the solution method by applying the UPCBCs in comparison with the simplified BCs. Then, the simulation of the unsteady incompressible viscous flow around a two-dimensional NACA0012 airfoil at the Reynolds number 800 and the angle of attack 20 degrees is performed, and it is indicated that the computational cost of the solution is considerably decreased by implementing the UPCBCs at the artificial far-field boundary compared with the simplified BCs, which is remarkably valuable for the DNSs. Finally, the computation of the transition to unsteady for the incompressible flow around a three-dimensional NACA0012 wing at the same conditions of the two-dimensional case is successfully performed, and the results obtained are compared with those of previous studies that exhibit good agreement. Indications are that the present solution method by applying the UPCBCs at the artificial far-field boundary can be effect
Robustness is a key challenge in the integration of learning and control. In machine learning and robotics, two common approaches to promote robustness are adversarial training and domain randomization. Both of these ...
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Robustness is a key challenge in the integration of learning and control. In machine learning and robotics, two common approaches to promote robustness are adversarial training and domain randomization. Both of these approaches have analogs in control theory: adversarial training relates to H-infinity control and dynamic game theory, while domain randomization relates to theory for systems with stochastic model parameters. We propose a stochastic dynamic game framework that integrates both of these complementary approaches to modeling uncertainty and promoting robustness. We describe policy iteration algorithms in both model-based and model-free settings to compute equilibrium strategies and value functions. We present numerical experiments that illustrate their effectiveness and the value of combining uncertainty representations in our integrated framework. We also provide an open-source implementation of the algorithms to facilitate their wider use.
The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing (cooperative) and decreasing (competitive) components, and this decomposition allows for, e.g., efficient comput...
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The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing (cooperative) and decreasing (competitive) components, and this decomposition allows for, e.g., efficient computation of reachable sets and forward invariant sets. A main challenge in this approach, however, is identifying an appropriate decomposition function. In this letter, we show that any continuous-time dynamical system with a Lipschitz continuous vector field is mixed-monotone, and we provide a construction for the decomposition function that yields the tightest approximation of reachable sets when used with the standard tools for mixed-monotone systems. Our construction is similar to that recently proposed by Yang and Ozay for computing decomposition functions of discrete-time systems where we make appropriate modifications for the continuous-time setting and also extend to the case with unknown disturbance inputs. As in Yang's and Ozay's work, our decomposition function construction requires solving an optimization problem for each point in the state-space;however, we demonstrate through example how tight decomposition functions can sometimes be calculated in closed form. As a second contribution, we show how under-approximations of reachable sets can be efficiently computed via the mixed-monotonicity property by considering the backward-time dynamics.
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