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Intermittent Event-Triggered Optimal Control for Second-Order Delayed Multiagent Systems With Input Constraints

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2024年第5期54卷 2698-2710页

作者： Liu, Chen Liu, Lei Wu, Zhaojing Hohai Univ Coll Sci Nanjing 210098 Peoples R China Yantai Univ Sch Math & Informat Sci Yantai 264005 Peoples R China

In this article, the optimal leader-following consensus of nonlinear second-order delayed multiagent systems with input constraints is addressed. To begin with, a novel intermittent event-triggered (IET) control protocol is proposed, and a novel time-delay piecewise differential inequality is established to effectively integrate state delay, intermittent control, and event-triggered strategy. Then, by the proposed control protocol and inequality, two criteria for the consensus of the second-order delayed multiagent systems and its optimality under input saturation are derived successively. Furthermore, a constrained-input PI algorithm and a critic-only online RL algorithm are devised for designing IET optimal control and approximate IET optimal controller, respectively. Finally, two numerical examples are created to verify the efficacy of the basic research.

关键词： Protocols Optimal control Multi-agent systems Delays Heuristic algorithms Dynamic programming approximation algorithms ADP input constraints IET control leader-following consensus second-order delayed multiagent systems (MASs)

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Explainable AI: Efficiency Sequential Shapley Updating Approach

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IEEE ACCESS 2024年 12卷 166414-166423页

作者： Petrosian, Ovanes Zou, Jinying St Petersburg State Univ Fac Appl Math & Control Proc St Petersburg Russia

Shapley value-based explainable AI has recently attracted significant interest. However, the computational complexity of the Shapley value grows exponentially with the number of players, resulting in high computational costs that prevent its widespread practical application. To address this challenge, various approximation methods have been proposed in the literature for computing the Shapley value, such as linear Shapley computation, sampling-based Shapley computation, and several estimation-based approaches. Among these methods, the sampling approach exhibits non-zero bias and variance and is sufficiently universal to be used with almost any AI algorithm. However, it suffers from unstable interpretability results and slow convergence in high-dimensional problems. To address these problems, we propose integrating a sequential Bayesian updating framework into the Shapley sampling approach. The core idea of this method is to dynamically update probabilities based on each sample's Shapley value combined with a selection strategy. Both theoretical analysis and empirical results show that this method significantly improves the convergence speed and interpretability compared to the original sampling approach.

关键词： Bayes methods Explainable AI Mathematical models Games Forestry approximation algorithms Machine learning algorithms Resource management Game theory Anomaly detection interpretability sequential Shapley updating Shapley value sampling method Bayesian updating high-dimensional problem cancer detection game theory efficiency calculation

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Efficient 2-D DOA Estimation for Incoherently Distributed Sources With an L-Shaped Array

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IEEE WIRELESS COMMUNICATIONS LETTERS 2025年第4期14卷 1104-1108页

作者： Xu, He Liu, Wei Chen, Hua Tian, Ye Ningbo Univ Technol Sch Cyber Sci & Engn Ningbo 315211 Peoples R China Hong Kong Polytech Univ Dept Elect & Elect Engn Hong Kong Peoples R China Ningbo Univ Fac Elect Engn & Comp Sci Ningbo 315211 Peoples R China

Direction-of-arrival (DOA) estimation with sufficient accuracy and efficiency for incoherently distributed (ID) sources remains a challenging problem. To this end, a computationally efficient two-dimensional (2-D) DOA estimation algorithm for ID sources is proposed, where the generalized array manifold (GAM) of an L-shaped array established on the first-order Taylor series approximation is exploited. By extracting the first column of the array cross-covariance matrix to eliminate the impacts of additive noise and angular spreads, and further applying the conjugate symmetry operation to enlarge the effective array aperture, the proposed algorithm provides an improved estimation performance with closed-form expressions. Moreover, a proper pairing criterion is designed to avoid the ambiguity problem, and simulation results are presented to show the superiority and effectiveness of the proposed algorithm.

关键词： Direction-of-arrival estimation Estimation Vectors Manifolds Wireless communication Covariance matrices Azimuth Fading channels Apertures approximation algorithms 2-D DOA estimation ID sources generalized array manifold conjugate symmetry operation L-shaped array

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A local search 4/3-approximation algorithm for the minimum 3-path partition problem

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2022年第5期44卷 3595-3610页

作者： Chen, Yong Goebel, Randy Lin, Guohui Liu, Longcheng Su, Bing Tong, Weitian Xu, Yao Zhang, An Hangzhou Dianzi Univ Dept Math Hangzhou Peoples R China Univ Alberta Dept Comp Sci Edmonton AB T6G 2E8 Canada Xiamen Univ Sch Math Sci Xiamen Peoples R China Xian Technol Univ Sch Econ & Management Xian Peoples R China Georgia Southern Univ Dept Comp Sci Statesboro GA USA

Given a graph G = (V, E), the 3-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most 3 to cover all the vertices of V. The previous best approximation algorithm for the 3-path partition problem has a performance ratio 13/9, which is based on a simple local search strategy. We propose a more involved local search and show by an amortized analysis that it is a 4/3-approximation;we also design an instance to illustrate that the approximation ratio is tight.

关键词： Path partition Path cover Local search approximation algorithms Amortized analysis

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A Path Planning Framework Based on an Improved Weighted Heuristic RRT and Optimization Strategy

IEEE TRANSACTIONS ON INTELLIGENT VEHICLES

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IEEE TRANSACTIONS ON INTELLIGENT VEHICLES 2024年第1期9卷 1941-1952页

作者： Wang, Lihui Wang, Zhuoxuan Ying, Zehua Bai, Xiao Xu, Ninghui Southeast Univ Sch Instrument Sci & Engn Key Lab Micro Inertial Instrument & Adv Nav Techn Minist Educ Nanjing 210096 Peoples R China Purple Mt Lab Nanjing 211111 Peoples R China

This article investigates a local obstacle avoidance (LOA) problem in terms of the planning efficiency and driving safety of low-speed driving unmanned vehicles. A novel improved weighted heuristic RRT (IWH-RRT) method and an opti-mization strategy are proposed to address the LOA problem with constraints. The sampling space optimization (SPO) and vehicle non-integrity constraint detection (NICD) are first adopted to improve sampling efficiency and guide RRT tree to expand nodes that satisfy driveability towards the target point. Then a cost function combining node attribute and expanding is designed, and the parent node is reselected for the newly expanded ones to reduce the deviation from the reference line and meet the LOA requirements. Finally, the convex space is approximated according to a driving corridor generated based on the initial path, in which the optimized path is obtained by solving an optimal control problem through QP solver. The proposed framework is compared with the baselines and state-of-the-art algorithms in simulation, and real-world experiments are designed afterward. The results verify that our method has good engineering feasibility and real-time capacity in generating smooth, safe and road-shape-liked paths for LOA problems.

关键词： Planning Space vehicles approximation algorithms Collision avoidance Shape Safety Roads Local obstacle avoidance path planning path smoothing and optimization unmanned vehicles

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Relaxed Policy Iteration Algorithm for Nonlinear Zero-Sum Games With Application to H-Infinity Control

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第1期69卷 426-433页

作者： Li, Jie Li, Shengbo Eben Duan, Jingliang Lyu, Yao Zou, Wenjun Guan, Yang Yin, Yuming Tsinghua Univ Sch Vehicle & Mobil Beijing 100084 Peoples R China Univ Sci & Technol Beijing Sch Mech Engn Beijing 100083 Peoples R China

Though policy evaluation error profoundly affects the direction of policy optimization and the convergence property, it is usually ignored in policy iteration methods. This work incorporates the practical inexact policy evaluation into a simultaneous policy update paradigm to reach the Nash equilibrium of the nonlinear zero-sum games. In the proposed algorithm, the restriction of precise policy evaluation is removed by bounded evaluation error characterized by Hamiltonian without sacrificing convergence guarantees. By exploiting Frechet differential, the practical iterative process of value function with estimation error is converted into the Newton's method with variable steps, which are inversely proportional to evaluation errors. Accordingly, we construct a monotone scalar sequence that shares the same Newton's method with the value sequence to bound the error of the value function, which enjoys an exponential convergence rate. Numerical results show its convergence in affine systems, and the potential to cope with general nonlinear plants.

关键词： Game theory Games Convergence Mathematical models approximation algorithms Newton method Partial differential equations Hamilton-Jacobi-Isaacs (HJI) equation Newton's method policy iteration zero-sum game

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Computability of Optimizers

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第4期70卷 2967-2983页

作者： Lee, Yunseok Boche, Holger Kutyniok, Gitta Ludwig Maximilian Univ Munchen Math Inst D-80539 Munich Germany Tech Univ Munich Inst Theoret Informat Technol D-80333 Munich Germany Ruhr Univ Bochum Excellence Cluster Cyber Secur Age Large Scale Adv BMBF 6G Hub 6G Life D-44801 Bochum Germany Munich Ctr Quantum Sci & Technol MCQST D-80799 Munich Germany Munich Quantum Valley MQV D-80807 Munich Germany

Optimization problems are a staple of today's scientific and technical landscape. However, at present, solvers of such problems are almost exclusively run on digital hardware. Using Turing machines as a mathematical model for any type of digital hardware, in this paper, we analyze fundamental limitations of this conceptual approach of solving optimization problems. Since in most applications, the optimizer itself is of significantly more interest than the optimal value of the corresponding function, we will focus on computability of the optimizer. In fact, we will show that in various situations the optimizer is unattainable on Turing machines and consequently on digital computers. Moreover, even worse, there does not exist a Turing machine, which approximates the optimizer itself up to a certain constant error. We prove such results for a variety of well-known problems from very different areas, including artificial intelligence, financial mathematics, and information theory, often deriving the even stronger result that such problems are not Banach-Mazur computable, also not even in an approximate sense.

关键词： Optimization Hardware Computational modeling approximation algorithms Turing machines 6G mobile communication Information theory information theory artificial intelligence computability Turing machine digital computing

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1-bit Massive MIMO Signal Detector Based on Convex Integral Quadratic Programming

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2024年第5期23卷 4004-4016页

作者： Yi, Zhouwei Wei, Ping Zhu, Jiehao Zhang, Huaguo Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 610054 Peoples R China Natl Key Laboratoryof Electromagnet Space Secur Chengdu Sichuan Peoples R China

With discrete modulation techniques, such as quadrature amplitude modulation and phase-shift keying, maximum likelihood (ML) signal detection in massive multi-input multi-output (MIMO) systems fundamentally relies on convex integer programming, executed efficiently through linear operations. However, for 1-bit massive MIMO systems, the nonlinearity introduced by 1-bit quantization impedes the linear realization of the ML detector. To achieve ML detector performance with manageable computational costs, researchers have proposed a two-stage strategy consisting of relaxed continuous convex programming followed by refinement using discrete search within the candidate solution set surrounding the optimal solution of the relaxed continuous convex programming. This article specifically examines the refinement stage. We demonstrate that it is possible to approximate the ML detection's log-likelihood function using a 1-degree freedom quadratic function. We subsequently modify the decomposition algorithm for convex integer quadratic programming (CIQP) with a d -degree freedom matrix and box constraint. Finally, we employ the modified decomposition algorithm for refinement to obtain an initial candidate solution set, which is then expanded and pruned. This method is referred to as the improved CIQP-based algorithm. Numerical results indicate that the improved CIQP-based algorithm outperforms existing approaches in this domain.

关键词： Detectors Wireless communication approximation algorithms Eigenvalues and eigenfunctions Symbols Signal to noise ratio Quadrature amplitude modulation Massive MIMO 1-bit ADC convex integer quadratic programming signal detection

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Predissociation dynamics of D2 revealed by variation in fragment anisotropy parameters along the Fano profile

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JOURNAL OF CHEMICAL PHYSICS 2024年第9期160卷 094307-094307页

作者： Wang, Peng Gong, Shiyan Li, Yixuan Mo, Yuxiang Tsinghua Univ Dept Phys Beijing 100084 Peoples R China Tsinghua Univ State Key Lab Low Dimens Quantum Phys Beijing 100084 Peoples R China

We conducted a study on the variations of the fragment anisotropy parameters (beta) along the Fano profiles for the predissociation of the D2 molecule. These variations, known as beta profiles, were measured for the D(2l) fragments from the predissociation of the 4p pi D '(1)Pi(u)(upsilon ' = 1) and 4p sigma B ''(1)Sigma(+)(u)(upsilon ' = 2) states. The measured beta profiles show significant asymmetry and broader linewidths compared to the corresponding Fano profiles. By fitting the beta profiles, we were able to determine the fragment anisotropy parameters associated with the resonance state, continuum state, and the interference effect between them. Additionally, we determined the ratios of the absorption cross sections between the unperturbed and perturbed continuum states interacting with the resonance states although these ratios were found to be very small. Furthermore, we derived approximate formulas to calculate the parameters characterizing the beta profile. Despite the linewidths of the four Fano profiles being narrower than our instrumental resolution, we were still able to determine the product of the linewidth with the Fano q parameters. These findings demonstrate the utility of the beta profile as an effective tool for studying the predissociation dynamics in diatomic molecules.

关键词： approximation algorithms

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Evaluating Meta-Heuristic algorithms for Dynamic Capacitated Arc Routing Problems Based on a Novel Lower Bound Method

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IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 2024年第4期19卷 31-44页

作者： Tong, Hao Minku, Leandro L. Menzel, Stefan Sendhoff, Bernhard Yao, Xin Univ Birmingham Birmingham England Honda Res Inst Europe GmbH Offenbach Germany Lingnan Univ Hong Kong Peoples R China

Meta-heuristic algorithms, especially evolutionary algorithms, have been frequently used to find near optimal solutions to combinatorial optimization problems. The evaluation of such algorithms is often conducted through comparisons with other algorithms on a set of benchmark problems. However, even if one algorithm is the best among all those compared, it still has difficulties in determining the true quality of the solutions found because the true optima are unknown, especially in dynamic environments. It would be desirable to evaluate algorithms not only relatively through comparisons with others, but also in absolute terms by estimating their quality compared to the true global optima. Unfortunately, true global optima are normally unknown or hard to find since the problems being addressed are NP-hard. In this paper, instead of using true global optima, lower bounds are derived to carry out an objective evaluation of the solution quality. In particular, the first approach capable of deriving a lower bound for dynamic capacitated arc routing problem (DCARP) instances is proposed, and two optimization algorithms for DCARP are evaluated based on such a lower bound approach. An effective graph pruning strategy is introduced to reduce the time complexity of our proposed approach. Our experiments demonstrate that our approach provides tight lower bounds for small DCARP instances. Two optimization algorithms are evaluated on a set of DCARP instances through the derived lower bounds in our experimental studies, and the results reveal that the algorithms still have room for improvement for large complex instances.

关键词： Heuristic algorithms Metaheuristics Avalanche photodiodes Evolutionary computation Routing approximation algorithms Vehicle dynamics Time complexity Performance evaluation Benchmark testing Optimization methods

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