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Dynamic Event-Triggering Neural Learning Control for Partially Unknown Nonlinear Systems

IEEE TRANSACTIONS ON CYBERNETICS 2022年第4期52卷 2200-2213页

作者： Mu, Chaoxu Wang, Ke Qiu, Tie Tianjin Univ Sch Elect & Informat Engn Tianjin 300072 Peoples R China Tianjin Univ Coll Intelligence & Comp Sch Comp Sci & Technol Tianjin 300350 Peoples R China

This article presents an event-sampled integral reinforcement learning algorithm for partially unknown nonlinear systems using a novel dynamic event-triggering strategy. This is a novel attempt to introduce the dynamic triggering into the adaptive learning process. The core of this algorithm is the policy iteration technique, which is implemented by two neural networks. A critic network is periodically tuned using the integral reinforcement signal, and an actor network adopts the event-based communication to update the control policy only at triggering instants. For overcoming the deficiency of static triggering, a dynamic triggering rule is proposed to determine the occurrence of events, in which an internal dynamic variable characterized by a first-order filter is defined. Theoretical results indicate that the impulsive system driven by events is asymptotically stable, the network weight is convergent, and the Zeno behavior is successfully avoided. Finally, three examples are provided to demonstrate that the proposed dynamic triggering algorithm can reduce samples and transmissions even more, with guaranteed learning performance.

关键词： Heuristic algorithms Artificial neural networks approximation algorithms Nonlinear dynamical systems Indexes Optimal control Event triggering internal dynamic variable integral reinforcement learning (IRL) neural networks (NNs) nonlinear systems policy iteration (PI)

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Collaborative Optimization Model of Highway Network with Tourism Resources as the Target Node

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MOBILE INFORMATION SYSTEMS 2022年第1期2022卷

作者： Niu, Wei Global Inst Software Technol Int Business Sch Suzhou 215163 Peoples R China

In order to improve the collaborative optimization effect of tourism resources and highway network, this paper combines deep learning algorithm to construct a collaborative optimization model of tourism resources and highway network, and adopts an algorithm based on continuous convex approximation. By iterating the optimal solution obtained each time, a high-quality approximate beamforming matrix and artificial noise covariance matrix can finally be obtained, which eliminates the problem that the traditional algorithm cannot solve the noise. Moreover, this paper introduces artificial noise to prove that the rank relaxation is compact by considering the corresponding minimization power problem. The simulation results show that the proposed scheme and approximation algorithm can obtain better system security and speed than the existing literature, and there are certain improvements compared with the traditional method, so the effectiveness of the method in this paper is verified by simulation experiments.

关键词： approximation algorithms

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Hypothesis Test and Confidence Analysis With Wasserstein Distance on General Dimension

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NEURAL COMPUTATION 2022年第6期34卷 1448-1487页

作者： Imaizumi, Masaaki Ota, Hirofumi Hamaguchi, Takuo Univ Tokyo Meguro Ku Tokyo 1530041 Japan RIKEN Ctr Adv Intelligence Project Chuo Ku Tokyo 1030027 Japan Rutgers State Univ Piscataway NJ 08854 USA

We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its excellent properties. However, hypothesis tests and a confidence analysis for it have not been established in a general multivariate setting. This is because the limit distribution of the empirical distribution with the Wasserstein distance is unavailable without strong restriction. To address this problem, in this study, we develop a novel nonasymptotic gaussian approximation for the empirical 1-Wasserstein distance. Using the approximation method, we develop a hypothesis test and confidence analysis for the empirical 1-Wasserstein distance. We also provide a theoretical guarantee and an efficient algorithm for the proposed approximation. Our experiments validate its performance numerically.

关键词： approximation algorithms

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Wideband Beampattern Synthesis Using Single Digital Beamformer With Integer Time Delay Filters

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2022年第5期70卷 3437-3449页

作者： Lu, Qinghui Cui, Guolong Liu, Ruitao Yu, Xianxiang Wang, Xiangrong Kong, Lingjiang Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

Existing wideband beampattern synthesis methods usually require multiple beamformers, each corresponding to one frequency bin, which results in excessive resource consumption in engineering practice. To alleviate the resource consumption of wideband array beamforming, we propose a novel time-domain wideband digital beamformer that can control the beam shape over the whole bandwidth for interference mitigation by using only one set of amplitude-phase weights and integer time delay filters. To tackle the resultant optimization problem, two effective algorithms are introduced, and both can solve the problem within polynomial time. One is an alternating optimization algorithm that decomposes the original problem into multiple tractable subproblems iteratively. The other is the convex approximation algorithm that transforms the original problem into a series of second-order cone programming problems iteratively. The two algorithms exhibit their respective advantages in terms of convergence and computational complexity. Extensive numerical examples are presented to evaluate the proposed time-domain wideband beamforming strategy, highlighting that it can form a deep notch in any interested spatial-spectral region to suppress the strong interferences.

关键词： Wideband Optimization Array signal processing approximation algorithms White noise Time-domain analysis Time-frequency analysis Alternating optimization (AO) algorithm convex approximation (CA) algorithm interference nulling nonconvex optimization wideband digital beamformer (DBF)

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algorithms for Intersection Graphs of t-Intervals and t-Pseudodisks

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THEORY OF COMPUTING 2022年 18卷

作者： Chekuri, Chandra Inamdar, Tanmay Univ Illinois Dept Comp Sci Urbana IL 61801 USA Univ Bergen Dept Informat Bergen Norway Univ Iowa Iowa City IA 52242 USA

Intersection graphs of planar geometric objects such as intervals, disks, rectangles and pseudodisks are well-studied. Motivated by various applications, in intersection graphs of t-intervals. A t-interval is a union of t intervals???these graphs are also referred to as multiple-interval graphs. Subsequent work by Kammer et al. (APPROX-RANDOM 2010) considered intersection graphs of t-disks (union of t disks), and other geometric objects. In this paper we revisit some of these algorithmic questions via more recent developments in computational geometry. For the minimum-weight dominating set problem in t-interval graphs, we obtain a polynomial-time 0 (t log t)-approximation algorithm, improving upon the previously known polynomial-time t2-approximation by Butman et al. (op. cit.). In the same class of graphs we show that it is NP-hard to obtain a (t ??? 1 ??? e)-approximation for any fixed t ??? 3 and e > 0. The approximation ratio for dominating set extends to the intersection graphs of a collection of t-pseudodisks (nicely intersecting t-tuples of closed Jordan domains). We obtain an 0(1/t)-approximation for the maximum-weight independent set in the

关键词： Key words and phrases approximation algorithms computational geometry multiple interval graphs geometric set cover dominating set independent set

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Dual Heuristic Programming for Optimal Control of Continuous-Time Nonlinear Systems Using Single Echo State Network

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第3期52卷 1701-1712页

作者： Liu, Chong Zhang, Huaguang Luo, Yanhong Su, Hanguang Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110004 Peoples R China

This article presents an improved online adaptive dynamic programming (ADP) algorithm to solve the optimal control problem of continuous-time nonlinear systems with infinite horizon cost. The Hamilton-Jacobi-Bellman (HJB) equation is iteratively approximated by a novel critic-only structure which is constructed using the single echo state network (ESN). Inspired by the dual heuristic programming (DHP) technique, ESN is designed to approximate the costate function, then to derive the optimal controller. As the ESN is characterized by the echo state property (ESP), it is proved that the ESN can successfully approximate the solution to the HJB equation. Besides, to eliminate the requirement for the initial admissible control, a new weight tuning law is designed by adding an alternative condition. The stability of the closed-loop optimal control system and the convergence of the out weights of the ESN are guaranteed by using the Lyapunov theorem in the sense of uniformly ultimately bounded (UUB). Two simulation examples, including linear system and nonlinear system, are given to illustrate the availability and effectiveness of the proposed approach by comparing it with the polynomial neural-network scheme.

关键词： Optimal control approximation algorithms Artificial neural networks Nonlinear systems Tuning Convergence Stability analysis Adaptive dynamic programming (ADP) echo state network (ESN) Hamilton-Jacobi-Bellman (HJB) nonlinear systems optimal control

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Optimal intervention in economic networks using influence maximization methods

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期300卷 1136-1148页

作者： Klages-Mundt, Ariah Minca, Andreea Cornell Univ Ctr Appl Math 657 Rhodes Hall Ithaca NY 14853 USA Cornell Univ Sch Operat Res & Informat Engn 222 Rhodes Hall Ithaca NY 14853 USA

We consider optimal intervention in the Elliott-Golub-Jackson network model (Elliott, Golub, and Jackson, 2014) and we show that it can be transformed into an influence maximization-like form, interpreted as the reverse of a default cascade. Our analysis of the optimal intervention problem extends well-established targeting results to the economic network setting, which requires additional theoretical steps. We prove several results about optimal intervention: it is NP-hard and cannot be approximated to a constant factor in polynomial time. In turn, we show that randomizing failure thresholds leads to a version of the problem which is monotone submodular, for which existing powerful approximations in polynomial time can be applied. In addition to optimal intervention, we also show practical consequences of our analysis to other economic network problems: (1) it is computationally hard to calculate expected values in the economic network, and (2) influence maximization algorithms can enable efficient importance sampling and stress testing of large failure scenarios. We illustrate our results on a network of firms connected through input-output linkages inferred from the World Input Output Database. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Risk analysis Economic networks NP hardness approximation algorithms Influence maximization

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Azimuth-Invariant Motion Compensation and Imaging Chirp Scaling Algorithm for Multiple-Receiver Synthetic Aperture Sonar

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IEEE ACCESS 2022年 10卷 114060-114076页

作者： Tian, Zhen Zhong, Heping Tang, Jinsong Zhang, Jiafeng Naval Univ Engn Naval Inst Underwater Acoust Technol Wuhan 430030 Hubei Peoples R China

To improve the imaging quality of conventional imaging algorithms without motion compensation (MOCO) and the efficiency of point-by-point MOCO algorithms for multiple-receiver synthetic aperture sonar (SAS) with azimuth-invariant six-degree of freedom (DOF) motion errors, an azimuth-invariant MOCO and imaging chirp scaling (CS) algorithm is presented in this paper. Taylor series approximation is used to process the range history in double square root form, while considering the fourth-order and inner terms with respect to the azimuth time. Using the method of series reversion and Fourier transform (FT) properties, the analytical two-dimensional frequency spectrum of the point target response of each receiver is derived. On this basis, the azimuth-invariant MOCO and imaging CS algorithm is proposed for six-DOF motion error compensation and multiple-receiver SAS imaging. Because it considers the azimuth-invariant six-DOF motion errors, the proposed algorithm has better imaging quality than conventional imaging algorithms without MOCO. Additionally, it has a significantly higher efficiency than point-by-point MOCO algorithms because the CS algorithm is a fast FT-based algorithm and does not require interpolation processing. The imaging simulation and experimental results verified the effectiveness and efficiency of the proposed algorithm.

关键词： Imaging Synthetic aperture sonar Receivers Chirp modulation Transmitters approximation algorithms Taylor series Underwater communication Sonar navigation Sonar equipment Chirp scaling algorithm motion compensation series reversion synthetic aperture sonar underwater imaging technology

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Aligning Points to Lines: Provable approximations

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2022年第1期34卷 138-149页

作者： Jubran, Ibrahim Feldman, Dan Univ Haifa Comp Sci Dept Robot & Big Data Lab IL-3498838 Haifa Israel

We suggest a new optimization technique for minimizing the sum Sigma(n)(i=1) g(i)(x) of n non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational geometry, combinatorics and convex optimization. As an example application, we provide the first constant-factor approximation algorithms whose running-times are polynomial in n for the fundamental problem of Points-to-Lines alignment: Given n points p(1),...,p(n) and n lines l(1),...,l(n) on the plane and z > 0, compute the matching pi : [n] -> [n] and alignment (rotation matrix R and translation vector t) that minimize the sum of euclidean distances Sigma(n)(i=1) dist(Rp(i) - t, l(pi(i)))z between each point to its corresponding line. This problem is non-trivial even if z = 1 and the matching p is given. If p is given, our algorithms run in O(n(3)) time, and even near-linear in n using core-sets that support: streaming, dynamic, and distributed parallel computations in poly-logarithmic update time. Generalizations for handling e.g., outliers or pseudo-distances such as M-estimators for the problem are also provided. Experimental results and open source code show that our algorithms improve existing heuristics also in practice. A companion demonstration video in the context of Augmented Reality shows how such algorithms may be used in real-time systems .

关键词： approximation algorithms non-convex optimization visual tracking points-to-lines alignment coresets

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Nuisance Parameter Estimation algorithms for Separable Nonlinear Models

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第11期52卷 7236-7247页

作者： Chen, Long Chen, Jia-Bing Chen, Guang-Yong Gan, Min Chen, C. L. Philip Univ Macau Fac Sci & Technol Macau Peoples R China Fujian Med Univ Union Hosp Dept Gastroenterol Fuzhou 350001 Peoples R China Fuzhou Univ Coll Comp & Data Sci Fuzhou 350116 Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China

Many inverse problems in machine learning, system identification, and image processing include nuisance parameters, which are important for the recovering of other parameters. Separable nonlinear optimization problems fall into this category. The special separable structure in these problems has inspired several efficient optimization strategies. A well-known method is the variable projection (VP) that projects out a subset of the estimated parameters, resulting in a reduced problem that includes fewer parameters. The expectation maximization (EM) is another separated method that provides a powerful framework for the estimation of nuisance parameters. The relationships between EM and VP were ignored in previous studies, though they deal with a part of parameters in a similar way. In this article, we explore the internal relationships and differences between VP and EM. Unlike the algorithms that separate the parameters directly, the hierarchical identification algorithm decomposes a complex model into several linked submodels and identifies the corresponding parameters. Therefore, this article also studies the difference and connection between the hierarchical algorithm and the parameter-separated algorithms like VP and EM. In the numerical simulation part, Monte Carlo experiments are performed to further compare the performance of different algorithms. The results show that the VP algorithm usually converges faster than the other two algorithms and is more robust to the initial point of the parameters.

关键词： Jacobian matrices Autoregressive processes Convergence Monte Carlo methods Inverse problems Ear approximation algorithms Expectation-maximization (EM) algorithm hierarchical identification algorithm separable nonlinear optimization problem variable projection (VP) algorithm

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