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MPC-Based Routing and Tracking Architecture for Safe Autonomous Driving in Urban Traffic

SN Computer Science 2024年第4期5卷 375页

作者： Emam, Mostafa Gerdts, Matthias Department of Aerospace Engineering Institute of Applied Mathematics and Scientific Computing University of the Bundeswehr Munich Werner-Heisenberg-Weg 39 Neubiberg Munich 85579 Germany

This paper presents a configurable routing and tracking architecture that uses multi-objective Model Predictive Control (MPC) as its driving algorithm to guarantee safe autonomous driving of different vehicle types. The architecture consists of three main components and primarily relies on labeled map data to generate optimal path and velocity trajectories in accordance with the vehicle type and the desired control objectives. We begin with introducing the overall system architecture and its different inputs, outputs, and components. We also briefly explain the open-source services utilized in this work for trajectory generation, namely OpenStreetMap and GraphHopper. We then focus on formulating the multi-objective MPC problem and its vehicle-specific constraints, which is solved offline to generate the reference path and velocity trajectories. Afterwards, we discuss some adaptions to the system model and the controller operating strategy to incorporate real-time tracking of these trajectories while guaranteeing collision avoidance. Finally, we successfully demonstrate the system’s feasibility by numerically evaluating its performance in a typical urban driving scenario for different vehicles. © The Author(s) 2024.

关键词： Autonomous vehicles GraphHopper Multi-objective MPC OpenStreetMap Route planning Trajectory following

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On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems

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Applied Numerical Mathematics 2025年 216卷 76-97页

作者： Bai, Zhong-Zhi State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In order to compute the smallest eigenvalue and its corresponding eigenvector of a large-scale, real, and symmetric matrix, we propose a class of greedy randomized coordinate updating iteration methods based on the principle that the indices of larger entries in absolute value of the current residual are selected with a higher probability and, with respect to this index set, the next iterate is updated from the current iterate along with the selected coordinate such that the corresponding entry of the residual is annihilated, resulting in fast convergence rates of the proposed iteration methods. Under appropriate conditions, we prove the convergence of both sequences of the Rayleigh-quotients and the acute angles between the iterates and the eigenvector in terms of the expectation. By numerical experiments, we show that this class of greedy randomized coordinate updating iteration methods are advantageous over the parameterized power method and the coordinate descent method in both iteration counts and computing times. Moreover, with theoretical analysis and computational performance, we confirm that the convergence property of this class of iteration methods can be improved significantly by suitably choosing the arbitrary nonnegative parameter involved in the greedy probability criterion. © 2025 IMACS

关键词： Eigenvalues and eigenfunctions

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Cherenkov Radiation:A Stochastic Differential Model Driven by Brownian Motions

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Computer Modeling in engineering & Sciences 2023年第4期135卷 155-168页

作者： Qingqing Li Zhiwen Duan Dandan Yang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

With the development of molecular imaging,Cherenkov optical imaging technology has been widely *** studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion *** this paper,time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic *** on the original steady-state diffusion equation,we first propose a stochastic partial differential *** numerical solution to the stochastic partial differential model is carried out by using the finite element *** the time resolution is high enough,the numerical solution of the stochastic diffusion equation is better than the numerical solution of the steady-state diffusion equation,which may provide a new way to alleviate the problem of Cherenkov luminescent imaging *** addition,the process of generating Cerenkov and penetrating in vitro imaging of 18 F radionuclide inmuscle tissue are also first proposed by GEANT4Monte *** result of the GEANT4 simulation is compared with the numerical solution of the corresponding stochastic partial differential equations,which shows that the stochastic partial differential equation can simulate the corresponding process.

关键词： Cherenkov radiation stochastic partial differential equations numerical approximation and analysis GEANT4 Monte Carlo simulation

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Fair k-Center Problem with Outliers on Massive Data

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Tsinghua Science and Technology 2023年第6期28卷 1072-1084页

作者： Fan Yuan Luhong Diao Donglei Du Lei Liu Beijing Institute for Scientific and Engineering Computing Faculty of ScienceBeijing University of TechnologyBeijing 100124China Faculty of Management University of New BrunswickFrederictonE3B 5A3Canada

The clustering problem of big data in the era of artificial intelligence has been widely *** of the huge amount of data,distributed algorithms are often used to deal with big data *** distributed computing model has an attractive feature:it can handle massive datasets that cannot be put into the main *** the other hand,since many decisions are made automatically by machines in today’s society,algorithm fairness is also an important research area of machine *** this paper,we study two fair clustering problems:the centralized fair k-center problem with outliers and the distributed fair k-center problem with *** these two problems,we have designed corresponding constant approximation ratio *** theoretical proof and analysis of the approximation ratio,and the running space of the algorithm are given.

关键词： machine learning distributed algorithm fairness constraints outlier constraints k-center problem

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ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS

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Acta Mathematica Scientia 2023年第4期43卷 1865-1880页

作者：韩豪张诚坚 School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous ***,for the analytical solutions of the equations,we derive their expressions and asymptotical stability ***,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically ***,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.

关键词： neutral reaction-diffusion equations piecewise continuous arguments asymptotical stability finite element methods numerical experiment

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A Derivative-free Trust-region Method for Optimization on the Ellipsoid

A Derivative-free Trust-region Method for Optimization on th...

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2023 International Conference on Advances in Computer Science and engineering Technology, ACSE 2023

作者： Xie, Pengcheng State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences ZhongGuanCun East Road No. 55 Beijing China

Optimization methods play a crucial role in various fields and applications. In some optimization problems, the derivative information of the objective function is unavailable. Such black-box optimization problems need to be solved by derivative-free optimization methods. At the same time, optimization problems with ellipsoidal constraints are important and have widespread applications in various fields as well. Following the development of the late professor M. J. D. Powell's efficient derivative-free trust-region optimization methods, this paper considers solving derivative-free optimization problems on the ellipsoid. Our new optimization solver EC-NEWUOA for problems on the ellipsoid in ., n is designed based on Powell's derivative-free software NEWUOA for unconstrained optimization problems. The proposed techniques for our new method mainly include using the Courant penalty function, the augmented Lagrangian method, and the projection technique. Details about the method and theoretical analysis are included in this paper. We also compare our new method with other algorithms by solving test problems and then show the numerical advantages of our new method. © Published under licence by IOP Publishing Ltd.

关键词： Lagrange multipliers

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Linearized Transformed L1 Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schr¨odinger Equations

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Numerical Mathematics(Theory,Methods and Applications) 2023年第2期16卷 348-369页

作者： Wanqiu Yuan Dongfang Li Chengjian Zhang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

A linearized transformed L1 Galerkin finite element method(FEM)is presented for numerically solving the multi-dimensional time fractional Schr¨odinger *** optimal error estimates of the fully-discrete scheme are *** error estimates are obtained by combining a new discrete fractional Gr¨onwall inequality,the corresponding Sobolev embedding theorems and some inverse *** the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting *** examples are presented to confirm the theoretical results.

关键词： Optimal error estimates time fractional Schr¨odinger equations transformed L1 scheme discrete fractional Gr¨onwall inequality

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Improving Performance of Virtual Machine Covert Timing Channel Through Optimized Run-Length Encoding

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Journal of Computer Science & Technology 2023年第4期38卷 793-806页

作者：王翀陈荣亮古亮 Shenzhen Institute of Advanced Technology Chinese Academy of SciencesShenzhen 518055China Sangfor Technologies Inc. Shenzhen 518055China Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen 518055China

With its wider acceptability,cloud can host a diverse set of data and applications ranging from entertainment to personal to *** foundation of cloud computing is based on virtual machines where boundaries among the application data are very thin,and the potential of data leakage exists all the *** instance,a virtual machine covert timing channel is an aggressive mechanism to leak confidential information through shared components or networks by violating isolation and security policies in *** performance of a covert timing channel(covert channel)is crucial to adversaries and attempts have been made to improve the performance of covert timing channels by advancing the encoding mechanism and covert information *** promising,the redundancy of the covert message is mainly *** paper applies three encoding schemes namely run-length,Huffman,and arithmetic encoding schemes for data compression of a virtual machine covert timing channel by exploiting ***,the paper studies the performance of such channels according to their ***,we show that these encoding schemes still contain redundancy in a covert channel scenario,and thereby a new encoding scheme namely optimized Runlength encoding(OptRLE)is presented that greatly enhances the performance of a covert timing *** optimizations schemes adopted by OptRLE are also discussed,and a mathematical model of the behavior of an OptRLE-based covert timing channel is *** theoretical capacity of a channel can be obtained using the proposed *** analysis reveals that OptRLE further improves the performance of a covert timing channel,in addition to the effects of the *** result shows how OptRLE affects the size of covert data and the capacity of covert timing channels,and why the performance of the covert timing channel is improved.

关键词： covert storage channel information security covert channel threat evaluation anti-detection criterion covert channel restriction

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The exactness of the l_(1)penalty function for a class of mathematical programs with generalized complementarity constraints

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Fundamental Research 2024年第6期4卷 1459-1464页

作者： Yukuan Hu Xin Liu State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable *** includes the traditional mathematical program with complementarity constraints(MPCC)as a special *** account of the disjunctive feasible region,MPCC and MPGCC are generally difficult to *** l_(1)penalty method,often adopted in computation,opens a way of circumventing the *** it remains unclear about the exactness of the l_(1)penalty function,namely,whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original *** this paper,we consider a class of MPGCCs that are of multi-affine objective *** problem class finds applications in various fields,e.g.,the multi-marginal optimal transport problems in many-body quantum physics and the pricing problems in network *** first provide an instance from this class,the exactness of whose l_(1)penalty function cannot be derived by existing *** then establish the exactness results under rather mild *** results cover those existing ones for MPCC and apply to multi-block contexts.

关键词： Mathematical program with generalized complementarity constraints l_(1)penalty function Exact penalty Multi-affine objective function Error bound

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Human-Machine Pilot Navigation Method Using Nonlinear Model Predictive Control, Simulation and Inflight Testing 43

Human-Machine Pilot Navigation Method Using Nonlinear Model ...

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43rd AIAA DATC/IEEE Digital Avionics Systems Conference, DASC 2024

作者： Bertoncini, Jeremy Dudek, Adrian Ostler, Johannes Russ, Martin Gerdts, Matthias Institute of Applied Mathematics and Scientific Computing Institute of Flight Systems University of the Bundeswehr Munich Department of Aerospace Engineering Neubiberg85577 Germany

ISBN: (纸本)9798350349610

In military or civil aviation, depending on the mission to be accomplished, an aircraft may need to avoid prohibited or dangerous areas that are not always within line of sight. However, these areas can be identified by external information and communicated from a ground station. The aim of this work is to provide an optimal control method that generates trajectories and assists the pilot in navigating. Using a human-machine interface, the pilot has access to a digital twin of the actual airspace, where the route is modeled using a tunnel-in-the-sky method. The research can be applied to airborne mission management, airport maneuver management or military operations. The path planning task is formulated as an optimal control problem and solved on a fixed time horizon using a nonlinear model predictive controller (NMPC) [5]. © 2024 IEEE.

关键词： Motion planning

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