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Computational synthesis of control barrier functions with applications in automotive lane keeping supervisory control

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IET CONTROL THEORY AND APPLICATIONS 2023年第14期17卷 1894-1908页

作者： Duan, Yue Zeng, Xiangrui Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan Hubei Peoples R China Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Hubei Peoples R China

The control barrier function (CBF) provides a good tool to design supervisory controllers for safety-critical systems. However, constructing a CBF for a general nonlinear system is a challenging task. This paper presents a general CBF computational synthesis approach for nonlinear affine systems with state constraints and input constraints using sum-of-squares (SOS) programming. System dynamics and state constraints are approximated using polynomial functions, and the input constraints are approximated using linear functions. The CBF synthesis algorithm is presented step-by-step, and tricks to deal with potential numerical issues during the SOS optimizations are discussed. The proposed algorithm is applied to an automotive lane keeping application to synthesize a CBF, and a supervisory control based on this CBF is designed. The effectiveness and resilience of this CBF-based supervisory control against disturbance are illustrated in simulation with a 14-degree-of-freedom vehicle dynamics model. Results show that this CBF-based supervisory control can improve the resilience of nominal controllers in automotive lane keeping applications.

关键词： automobiles convex programming controllers fault tolerant control optimisation

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Solving saddle point problems: a landscape of primal-dual algorithm with larger stepsizes

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JOURNAL OF GLOBAL OPTIMIZATION 2023年第4期85卷 821-846页

作者： Jiang, Fan Zhang, Zhiyuan He, Hongjin Nanjing Univ Informat Sci & Technol Sch Math & Stat Dept Informat & Comp Sci Nanjing 210044 Peoples R China Xiamen Univ Sch Math Sci Xiamen 360015 Peoples R China Ningbo Univ Sch Math & Stat Ningbo 315211 Peoples R China

We consider a class of saddle point problems frequently arising in the areas of image processing and machine learning. In this paper, we propose a simple primal-dual algorithm, which embeds a general proximal term induced with a positive definite matrix into one subproblem. It is remarkable that our algorithm enjoys larger stepsizes than many existing state-of-the-art primal-dual-like algorithms due to our relaxed convergence-guaranteeing condition. Moreover, our algorithm includes the well-known primal-dual hybrid gradient method as its special case, while it is also of possible benefit to deriving partially linearized primal-dual algorithms. Finally, we show that our algorithm is able to deal with multi-block separable saddle point problems. In particular, an application to a multi-block separable minimization problem with linear constraints yields a parallel algorithm. Some computational results sufficiently support the promising improvement brought by our relaxed requirement.

关键词： Saddle point problem Primal-dual algorithm Composite optimization convex programming Image processing RPCA

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ON MIN SUM VERTEX COVER AND GENERALIZED MIN SUM SET COVER

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SIAM JOURNAL ON COMPUTING 2023年第2期52卷 327-357页

作者： Bansal, Nikhil Batra, Jatin Farhadi, Majid Tetali, Prasad Univ Michigan Dept Comp Sci & Engn Ann Arbor MI 48109 USA Tata Inst Fundamental Res Sch Technol & Comp Sci Mumbai 400005 India Jump Trading LLC Chicago IL 60654 USA Carnegie Mellon Univ Dept Math Sci Pittsburgh PA 15213 USA

We study the Generalized Min Sum Set Cover (GMSSC) problem, wherein given a collection of hyperedges E with arbitrary covering requirements {ke \in Z+ : e \in E}, the goal is to find an ordering of the vertices to minimize the total cover time of the hyperedges;a hyperedge e is considered covered by the first time when ke and many of its vertices appear in the ordering. We give a 4.642 approximation algorithm for GMSSC, coming close to the best possible bound of 4, already for the classical special case (with all ke = 1) of Min Sum Set Cover (MSSC) studied by Feige, Lov\'asz, and Tetali, and improving upon the previous best known bound of 12.4 due to Im, Sviridenko, and van der Zwaan. Our algorithm is based on transforming the LP solution by a suitable kernel and applying randomized rounding. As part of the analysis of our algorithm, we also derive an inequality on the lower tail of a sum of independent Bernoulli random variables, which might be of independent interest and broader utility. Min Sum Vertex Cover (MSVC) is a well-known special case of MSSC in which the input hypergraph is a graph (i.e., lel = 2) and ke = 1 for every edge e \in E. We give a 16/9 \simeq 1.778 approximation for MSVC and show a matching integrality gap for the natural LP relaxation. This improves upon the previous best 1.999946 approximation of Barenholz, Feige, and Peleg. Finally, we revisit MSSC and consider the \ellp norm of cover-time of the hyperedges. Using a dual fitting argument, we show that the natural greedy algorithm achieves tight, up to NP-hardness, approximation guarantees of (p + 1)1+1/p for all p\geq 1, giving another proof of the result of Golovin, Gupta, Kumar, and Tangwongsan, and showing its tightness up to NP-hardness. For p = 1, this gives yet another proof of the 4 approximation for MSSC.

关键词： randomized algorithms approximation algorithms hardness of approximation scheduling convex programming tails of probability distributions

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Interval-Bounded Optimal Power Pattern Synthesis of Array Antenna Excitations Robust to Mutual Coupling

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2023年第11期22卷 2725-2729页

作者： Ding, Guangda Anselmi, Nicola Xu, Wanye Li, Peng Rocca, Paolo Xidian Univ Key Lab Elect Equipment Struct Design Minist Educ Xian 710071 Peoples R China Univ Trento ELEDIA Res Ctr ELEDIA UniTN DICAM Dept Civil Environm & Mech Engn I-38123 Trento Italy CNIT Univ Trento ELEDIA Res Unit I-38123 Trento Italy ELEDIA XIDIAN Xidian Univ ELEDIA Res Ctr Xian 710071 Peoples R China

A method for the optimal synthesis of linear phased arrays when calibration errors and mutual coupling are present is proposed. Starting from the knowledge of the mutual coupling model and of the calibration tolerances, the circular interval analysis (CIA) is used to derive analytic and reliable power pattern bounds used within a convex programming (CP)-based optimization, such that the lower bound of the power pattern main beam peak is maximized while the sidelobes are constrained by an arbitrary upper-bound mask. To evaluate the reliability and effectiveness of the proposed CIA-CP methodology, a set of representative numerical results is reported and compared with Monte Carlo and full-wave simulations.

关键词： Phased arrays Calibration Optimized production technology Linear antenna arrays Mutual coupling Monte Carlo methods Optimization Calibration errors circular interval analysis convex programming mutual coupling errors phased array tolerance analysis

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Scheduling with Fully Compressible Tasks: Application to Deep Learning Inference with Neural Network Compression 24

Scheduling with Fully Compressible Tasks: Application to Dee...

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24th IEEE/ACM International Symposium on Cluster, Cloud, and Internet Computing (CCGrid)

作者： Barros, Tiago da Silva Giroire, Frederic Aparicio-Pardo, Ramon Perennes, Stephane Natale, Emanuele Univ Cote Azur CNRS I3S Inria Sophia Antipolis France

ISBN: (纸本)9798350395679;9798350395662

With the advent and the growing usage of Machine Learning as a Service (MLaaS), cloud and network systems are now offering the possibility to deploy ML tasks on heterogeneous clusters. Then, network and cloud operators have to schedule these tasks, determining both when and on which devices to execute them. In parallel, several solutions, such as neural network compression, were proposed to build small models which can run on limited hardware. These solutions allow choosing the model size at inference time for any targeted processing time without having to re-train the network. In this work, we consider the Deadline Scheduling with Compressible Tasks (DSCT) problem: a novel scheduling problem with task deadlines where the tasks can be compressed. Each task can be executed with a certain compression, presenting a trade-off between its compression level (and, its processing time) and its obtained utility. The objective is to maximize the tasks utilities. We propose an approximation algorithm with proved guarantees to solve the problem. We validate its efficiency with extensive simulation, obtaining near optimal results. As application scenario, we study the problem when the tasks are Deep Learning classification jobs, and the objective is to maximize their global accuracy, but we believe that this new framework and solutions apply to a wide range of application cases.

关键词： scheduling compressible tasks neural network compression approximation algorithms convex programming

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A reweighted matrix completion algorithm for sparse inverse synthetic aperture radar imaging

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IET RADAR SONAR AND NAVIGATION 2023年第1期17卷 38-46页

作者： Lv, Mingjiu Chen, Wenfeng Ma, Jianchao Yang, Jun Ma, Xiaoyan Cheng, Qi Air Force Early Warning Acad Radar NCO Sch Wuhan Peoples R China Air Force Early Warning Acad Early Warning Technol Wuhan Peoples R China

Sparse inverse synthetic aperture radar (ISAR) imaging can be generally achieved by compressed sensing (CS) methods because sparse sampling disables the approach of conventional range Doppler. However, the CS-based methods have to convert the matrix into a vector when the random sampling is adopted, which results in huge memory usage and high computational complexity. Note that matrix completion (MC) is suitable for matrix operations, which can recover random sparse data directly based on the low-rank property of the echo matrix. In order to improve the performance of the conventional MC approaches, a novel reweighted matrix completion method for sparse ISAR imaging is proposed in this paper. To avoid using the same singular value thresholding of the traditional MC method to achieve a low-rank solution, the reweighted scheme for singular values is applied to restrain the rank. Furthermore, the weights of the current iteration are updated with their singular values obtained in the former iteration, rather than using a fixed value. Then, the alternating direction method of multipliers is utilised to alternatively optimise the proposed model, which has an improved computational efficiency. Once the full data is recovered, the ISAR image can be achieved via the conventional 2D inverse fast Fourier transform. Experimental results based on measured data validate the proposed approach that can result in improving imaging performance within several seconds, which is tens of times faster than some reported low-rank-based methods.

关键词： image segmentation Optimisation techniques high computational complexity random sampling sparse inverse synthetic aperture radar imaging imaging performance conventional 2D inverse fast Fourier singular values Radar equipment, systems and applications novel reweighted matrix completion method convex programming iterative methods synthetic aperture radar singular value thresholding traditional MC method radar imaging Optical, image and video signal processing sparse sampling reweighted matrix completion algorithm sparse ISAR imaging compressed sensing random sparse data reweighted scheme compressed sensing methods reported low-rank-based methods matrix algebra Integral transforms in numerical analysis improved computational efficiency echo matrix Interpolation and function approximation (numerical analysis) conventional MC approaches conventional range Doppler CS-based methods ISAR image Linear algebra (numerical analysis) low-rank property matrix operations low-rank solution fast Fourier transforms huge memory usage computational complexity

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A new collaborate neuro-dynamic framework for solving convex second order cone programming problems with an application in multi-fingered robotic hands

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APPLIED INTELLIGENCE 2019年第10期49卷 3512-3523页

作者： Nazemi, Alireza Shahrood Univ Technol Fac Math Sci POB ***-316 Shahrood Iran

A neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory and Lyapunov stability theory to solve convex second-order cone programming (CSOCP) problems. According to Karush-Kuhn-Tucker conditions of convex optimization, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the CSOCP problem. By employing Lyapunov function approach, it is also shown that the presented neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original optimization problem. Simulation results show that the neural network is feasible and efficient.

关键词： Neural network Second-order cone programming convex programming Convergence Stability

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Direct solution of the normal equations in interior point methods for convex transportation problems

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OPERATIONS RESEARCH LETTERS 2023年第5期51卷 469-472页

作者： Wright, Stephen E. Miami Univ Dept Stat Oxford OH 45056 USA

Recent research has shown that very large convex transportation problems can be solved efficiently with interior point methods by finding a good pre-conditioner for an iterative linear-equation solver. In this article, it is demonstrated that the specific structure of the constraints allows use of a direct method for solving those linear equations with the same order of worst-case time complexity.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： convex programming Interior point methods Network constraints

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A new sensitivity-based robust optimization of structures under bounded type uncertainty

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PROCEEDINGS OF THE INSTITUTION OF CIVIL ENGINEERS-ENGINEERING AND COMPUTATIONAL MECHANICS 2023年第3期176卷 116-131页

作者： Das, Sujit Bhattacharjya, Soumya Indian Inst Engn Sci & Technol Dept Civil Engn Sibpur W Bengal India

This paper deals with robust design optimization (RDO) of structures when uncertainty information about system parameters is limited. For such parameters, neither the statistical moments, nor the probability distribution is available. Rather, based on practical considerations, only bounds of variations of such parameters under uncertainty can be set, which is in-turn used to model them as uncertain-but-bounded (UBB) type. In recent years, convex programming (CP) approaches are used to solve RDO problem with UBB parameters. However, these approaches generally do not consider sensitivity information while formulating an RDO problem. But, it is well accepted that sensitivity is the key focus of an RDO as by definition a robust design should be least sensitive to uncertainty effects. Thus, a new sensitivity-importance based RDO formulation is proposed in this paper, where a new sensitivity index is defined and minimized along with the usual cost function subjected to a dispersion-related constraint. Then, the proposed RDO is solved through usual CP framework. The improvement by the proposed approach is demonstrated taking four application examples. The results indicate that the proposed approach yields more robust solutions compare to the conventional approaches.

关键词： uncertainty reliability & risk structural design mathematical modelling robust design optimization uncertain-but-bounded type parameters convex programming sensitivity index

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Unified Representation of the Classical Ellipsoid Method

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CYBERNETICS AND SYSTEMS ANALYSIS 2023年第5期59卷 784-793页

作者： Stetsyuk, P. I. Fischer, A. Khomiak, O. M. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine Tech Univ Dresden Inst Numer Math Dresden Germany Tech Univ Dresden Inst Numer Math Dresden Germany

A parametric version of the ellipsoid method with space scaling by a scalar parameter lambda > 0 is considered. For certain values of the parameter lambda, it is reduced to the well-known versions of the ellipsoid method, namely, the Shor, Khachiyan, Nemirovsky, and Yudin ones. The properties of two algorithmic implementations of the parameterized ellipsoid method are proved. The first algorithm is based on updating the asymmetric matrix B, and the second one updates the symmetric matrix H = BBT. The applications of the algorithms for solving convex programming problems and finding the saddle point of a convex-concave function are described.

关键词： ellipsoid method space dilation convex programming saddle point

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