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A Variation on a Random Coordinate Minimization Method for Constrained Polynomial Optimization

IEEE CONTROL SYSTEMS LETTERS 2018年第3期2卷 531-536页

作者： Calafiore, Giuseppe C. Possieri, Corrado Politecn Torino Dipartimento Elettron & Telecomunicaz I-10129 Turin Italy CNR IEIIT I-10129 Turin Italy

In this letter we propose an algorithm for solving constrained polynomial minimization problems. The algorithm is a variation on the random coordinate descent, in which transverse steps are sometimes taken. Differently from other methods, the proposed technique is guaranteed to converge in probability to the global solution of the minimization problem, even when the objective polynomial is nonconvex. The technique appears to be promising for tackling nonlinear control problems in which the standard sum-of-squares methods may fail due to the problem size. The theoretical results are corroborated by numerical tests that validate the efficiency of the method.

关键词： Optimization algorithms numerical algorithms optimization stochastic systems

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Cooperative Multiple Agent-Based Algorithm for Evacuation Planning for Victims with Different Urgencies

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JOURNAL OF AEROSPACE INFORMATION SYSTEMS 2018年第6期15卷 382-395页

作者： Oh, Byung Hoon Kim, Kwangyeon Choi, Han-Lim Hwang, Inseok Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA Korea Adv Inst Sci & Technol Dept Aerosp Engn Daejeon 305701 South Korea

A well-organized evacuation plan is crucial to save more lives in the aftermath of natural disasters. In this paper, a mathematical model and an efficient solution approach are proposed for optimal planning of a fleet of aerial vehicles to save victims with different levels of urgency. Evacuation planning is a task assignment problem combined with scheduling of aerial vehicles with different capabilities while considering complex conditions such as multiple bases for the vehicles, victims with different urgency levels at multiple locations, and multiple safe locations (for example, hospitals and refuges). In our previous work, the problem was formulated as integer linear programming to provide optimal solution. Because the integer linear programming, however, is intractable for a large-scale disaster problem, a heuristic method called the cooperative multiagent-based algorithm is proposed to solve the large-scale problem in practical time. The proposed algorithm defines simple rules for vehicle agents and demand agents (victims), and it applies cooperative interaction between agents to efficiently find a suboptimal solution. The computational efficiency and the performance of the algorithm are demonstrated using illustrative numerical examples based on realistic data.

关键词： numerical algorithms Mathematical Models Helicopters Particle Swarm Optimization Federal Emergency Management Agency Unmanned Aerial Vehicle Aircraft Operations Genetic Algorithm Flight Vehicle Sorting algorithms

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Model predictive control for linear differential-algebraic equations⁎

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IFAC-PapersOnLine 2018年第20期51卷 98-103页

作者： Ilchmann, Achim Witschel, Jonas Worthmann, Karl Technische Universität Ilmenau Germany

We are concerned with Model Predictive Control (MPC) of constrained linear systems governed by regular differential-algebraic equations. The contribution is twofold: First, we provide a characterization of the set of admissible control functions to clarify what the actual input is. This is essential for the design of numerical algorithms. Secondly, we present a blueprint for the construction of suitable terminal costs and terminal constraints such that asymptotic stability of the origin w.r.t. the MPC closed-loop is guaranteed provided initial feasibility. To this end, we exploit recent results on the unconstrained linear quadratic regulator problem using recently introduced concepts of input index and an augmented system. © 2018

关键词： Model predictive control Algebra Asymptotic stability Differential equations Linear systems Predictive control systems Constrained linear systems Differential algebraic equations Linear quadratic regulator Linear quadratic regulator problems Model based controls numerical algorithms Predictive control Terminal constraint

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Adjoint-Based Optimization for Thrust Performance of Three-Dimensional Pitching-Rolling Plate

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AIAA JOURNAL 2019年第9期57卷 3716-3727页

作者： Xu, Min Wei, Mingjun Li, Chengyu Dong, Haibo New Mexico State Univ Dept Mech & Aerosp Engn Las Cruces NM 88001 USA Kansas State Univ Dept Mech & Nucl Engn Manhattan KS 66506 USA Villanova Univ Dept Mech Engn Villanova PA 19085 USA Univ Virginia Dept Mech & Aerosp Engn Charlottesville VA 22904 USA

An adjoint-based optimization is applied to study the thrust performance of a pitching-rolling ellipsoidal plate in a uniform stream at Reynolds number 100. To achieve the highest thrust, the optimal kinematics of pitching-rolling motion is sought in a control space including the pitching amplitude, the rolling amplitude, and the phase delay between the pitching and rolling motions. A continuous adjoint approach with boundary motion being handled by noncylindrical calculus is developed as a computationally efficient optimization algorithm to deal with large control space with a morphing domain. The comparison between the optimal motion and other reference motions shows a significant improvement of thrust from the increase of the rolling amplitude and an optimal phase delay of 122.6 deg between the pitching and rolling motions. The combination of these two factors impacts the overall thrust performance through their strong effects on the angle of attack, the leading-edge vortex circulation, and the pressure distribution on the plate. Further wake structure analysis suggests that the optimal motion improves its propulsive performance by generating a stronger leading-edge vortex and straightening the wake deflection.

关键词： Reynolds Number Vortex Structure Angle of Attack Flapping Frequency numerical algorithms Optimal Kinematics Shape Optimization Flow Velocity Navier Stokes Equations Immersed Boundary Method

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A parallel algorithm to produce long polymer chains in molecular dynamics

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JOURNAL OF CHEMICAL PHYSICS 2019年第22期150卷 224902-224902页

作者： Lemarchand, C. A. Bousquet, D. Schnell, B. Pineau, N. CEA DAM DIF F-91297 Arpajon France MICHELIN 23 Pl Carmes Dechaux F-63040 Clermont Ferrand France

Generating initial configurations of polymer melts above the entanglement molecular weight is a challenge in molecular dynamics and Monte Carlo simulations. In this work, we adapt an algorithm mimicking a chemical polymerization to all-atom force fields. The principle of this algorithm is to start from a bath of monomers between which bonds are created and relaxed sequentially. Our implementation is parallel and efficient. The parallelization is that of a classical molecular dynamics code and enables the user to generate large systems, up to 7 x 10(6) atoms. The efficiency of the algorithm comes from the linear scaling between the simulation time and the chain length in the limit of very long chains. The implementation is able to produce long polymer chains, up to approximate to 2000 carbon atoms, with thermodynamic and local structural properties in good agreement with their experimental and numerical counterparts. Moreover, the chain conformations are close to being equilibrated right after the end of the polymerization process, corresponding to only a few hundred of picoseconds of simulation, despite a systematical drift from Gaussian-like behavior when the density of reactively available monomers decreases. Finally, the algorithm proposed in this work is versatile in nature because the bond creation can be easily modified to create copolymers, block copolymers, and mixtures of polymer melts with other material.

关键词： Composite materials Polymers Equilibrium thermodynamics Molecular dynamics Probability theory numerical algorithms

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Efficient solver for a special class of convection-diffusion problems

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PHYSICS OF FLUIDS 2019年第2期31卷 023606-023606页

作者： Karedla, Narain Thiele, Jan Christoph Gregor, Ingo Enderlein, Joerg Georg August Univ Inst Phys 3 D-37077 Gottingen Germany

We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard to treat due to the presence of a convection term, represented by a first order derivative in the spatial co-ordinate. Our algorithm reduces the convection-diffusion equation to a pure diffusion problem within a complex-valued potential which can be solved efficiently and accurately using conventional parabolic partial differential equation solvers. Published under license by AIP Publishing.

关键词： Stochastic processes Operator theory Capillary flows Partial differential equations numerical integration Finite difference methods numerical algorithms

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Model reduction of constrained mechanical systems in M-M.E.S.S.

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IFAC-PapersOnLine 2018年第2期51卷 661-666页

作者： Saak, Jens Voigt, Matthias Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstraße 1 MadgeburgD-39104 Germany Technische Universität Berlin Institut für Mathematik Straße des 17. Juni 136 BerlinD-10623 Germany

We discuss balanced truncation model reduction of constrained mechanical systems. The incorporation of the algebraic constraints leads to linear differential-algebraic control systems of index 2 or 3. Then for the square-root method in balanced truncation, the solution of projected Lyapunov equations is required. In this paper we discuss how to avoid the explicit construction of the projectors and the formulation of a projection-avoiding balanced truncation method which is suitable for efficient numerical computations. We have implemented this method in the Matlab package M-M.E.S.S. and present some numerical results for illustration. © 2018

关键词： Continuous time systems Algebra Control theory Lyapunov functions Mechanics numerical methods Constraints Lyapunov equation Mathematical systems theories Mechanical systems Model reduction numerical algorithms Singular system

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Nonlinear optical properties and applications of 2D materials: theoretical and experimental aspects

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NANOPHOTONICS 2019年第1期8卷 63-97页

作者： You, J. W. Bongu, S. R. Bao, Q. Panoiu, N. C. UCL Dept Elect & Elect Engn Torrington Pl London WC1E 7JE England Shenzhen Univ Key Lab Optoelect Devices & Syst Minist Educ & Guangdong Prov Coll Elect Sci & Technol Shenzhen 518060 Peoples R China Monash Univ Dept Mat Sci & Engn Clayton Vic 3800 Australia Monash Univ ARC Ctr Excellence Future Low Energy Elect Techno Clayton Vic 3800 Australia

In this review, we survey the recent advances in nonlinear optics and the applications of two-dimensional (2D) materials. We briefly cover the key developments pertaining to research in the nonlinear optics of graphene, the quintessential 2D material. Subsequently, we discuss the linear and nonlinear optical properties of several other 2D layered materials, including transition metal chalcogenides, black phosphorus, hexagonal boron nitride, perovskites, and topological insulators, as well as the recent progress in hybrid nanostructures containing 2D materials, such as composites with dyes, plasmonic particles, 2D crystals, and silicon integrated structures. Finally, we highlight a few representative current applications of 2D materials to photonic and optoelectronic devices.

关键词： nonlinear optics 2D materials numerical algorithms experimental techniques

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Modeling realistic multiphase flows using a non-orthogonal multiple-relaxation-time lattice Boltzmann method

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PHYSICS OF FLUIDS 2019年第4期31卷 042105-042105页

作者： Fei, Linlin Du, Jingyu Luo, Kai H. Succi, Sauro Lauricella, Macro Montessori, Andrea Wang, Qian Tsinghua Univ Dept Energy & Power Engn Ctr Combust Energy Key Lab Thermal Sci & Power EngnMinist Educ Beijing 100084 Peoples R China CNR Ist Applicaz Calcolo Via Taurini 19 I-00185 Rome Italy Tsinghua Univ Inst Nucl & New Energy Technol Key Lab Adv Reactor Engn & Safety Minist Educ Beijing 100084 Peoples R China UCL Dept Mech Engn Torrington Pl London WC1E 7JE England Ist Italiano Tecnol Ctr Life Nano Sci La Sapienza 295 Viale Regina Elena I-00161 Rome Italy Harvard Inst Appl Computat Sci Cambridge MA 02138 USA Shanghai Jiao Tong Univ Sch Mech Engn Shanghai 200240 Peoples R China

In this paper, we develop a three-dimensional multiple-relaxation-time lattice Boltzmann method (MRT-LBM) based on a set of non-orthogonal basis vectors. Compared with the classical MRT-LBM based on a set of orthogonal basis vectors, the present non-orthogonal MRT-LBM simplifies the transformation between the discrete velocity space and the moment space and exhibits better portability across different lattices. The proposed method is then extended to multiphase flows at large density ratio with tunable surface tension, and its numerical stability and accuracy are well demonstrated by some benchmark cases. Using the proposed method, a practical case of a fuel droplet impacting on a dry surface at high Reynolds and Weber numbers is simulated and the evolution of the spreading film diameter agrees well with the experimental data. Furthermore, another realistic case of a droplet impacting on a super-hydrophobic wall with a cylindrical obstacle is reproduced, which confirms the experimental finding of Liu et al. ["Symmetry breaking in drop bouncing on curved surfaces," Nat. Commun. 6, 10034 (2015)] that the contact time is minimized when the cylinder radius is comparable with the droplet radius. Published under license by AIP Publishing.

关键词： Multiphase flows Capillarity numerical algorithms Lattice Boltzmann methods Navier Stokes equations Interfacial flows

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Toward computational algorithm for time-fractional Fokker-Planck models

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ADVANCES IN MECHANICAL ENGINEERING 2019年第10期11卷

作者： Freihet, Asad Hasan, Shatha Alaroud, Mohammad Al-Smadi, Mohammed Ahmad, Rokiah Rozita Din, Ummul Khair Salma Al Balqa Appl Univ Ajloun Coll Dept Appl Sci Ajloun Jordan Univ Kebangsaan Malaysia Fac Sci & Technol Sch Math Sci Bangi 43600 Selangor Malaysia

This article describes an efficient algorithm based on residual power series to approximate the solution of a class of partial differential equations of time-fractional Fokker-Planck model. The fractional derivative is assumed in the Caputo sense. The proposed algorithm gives the solution in a form of rapidly convergent fractional power series with easily computable coefficients. It does not require linearization, discretization, or small perturbation. To test simplicity, potentiality, and practical usefulness of the proposed algorithm, illustrative examples are provided. The approximate solutions of time-fractional Fokker-Planck equations are obtained by the residual power series method are compared with those obtained by other existing methods. The present results and graphics reveal the ability of residual power series method to deal with a wide range of partial fractional differential equations emerging in the modeling of physical phenomena of science and engineering.

关键词： Caputo fractional derivatives Fokker-Planck equation residual power series numerical algorithms

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