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Adaptive Critic for Event-Triggered Unknown Nonlinear Optimal Tracking Design With Wastewater Treatment Applications

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第9期34卷 6276-6288页

作者： Wang, Ding Hu, Lingzhi Zhao, Mingming Qiao, Junfei Beijing Univ Technol Fac Informat Technol Beijing Key Lab Computat Intelligence & Intellige Beijing Lab Smart Environm Protect Beijing 100124 Peoples R China Beijing Univ Technol Beijing Inst Artificial Intelligence Beijing 100124 Peoples R China

In this article, an event-based near-optimal tracking control algorithm is developed for a class of nonaffine systems. First, in order to gain the tracking control strategy, the costate function is established through the iterative dual heuristic dynamic programming (DHP) algorithm. Then, the event-based control method is employed to improve the utilization efficiency of resources and ensure that the closed-loop system has an excellent control performance. Meanwhile, the input-to-state stability (ISS) is proven for the event-based tracking plant. In addition, three kinds of neural networks are used in the event-based DHP algorithm, which aims to identify the nonaffine nonlinear system, estimate the costate function, and approximate the tracking control law. Finally, a numerical experimental simulation is conducted to verify the effectiveness of the proposed scheme. Moreover, in order to further validate the feasibility, the algorithm is applied to the wastewater treatment plant to effectively control the concentrations of dissolved oxygen and nitrate nitrogen.

关键词： Heuristic algorithms Control systems Trajectory Wastewater treatment approximation algorithms Trajectory tracking Nonlinear dynamical systems Event-triggered mechanism iterative adaptive critic neural networks nonaffine nonlinear systems optimal tracking control

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Exact and Approximate Squarers for Error-Tolerant Applications

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IEEE TRANSACTIONS ON COMPUTERS 2023年第7期72卷 2120-2126页

作者： Chen, Ke Xu, Chenyu Waris, Haroon Liu, Weiqiang Montuschi, Paolo Lombardi, Fabrizio Nanjing Univ Aeronaut & Astronaut Coll Elect Informat & Engn Nanjing 210016 Jiangsu Peoples R China Politecn Torino DAUIN I-10129 Turin Italy Northeastern Univ Dept Elect & Comp Engn Boston MA 02115 USA

Approximate computing is considered an innovative paradigm with wide applications to high performance and low power systems. These applications have relaxed requirements for accuracy, so they can tolerate errors in results and achieve high performance. In approximate computing, multipliers have been widely studied, but squarers (as similar schemes) have not received much attention. In this paper, an accurate squarer is designed based on a Radix-8 Booth-folding square algorithm to reduce the number of partial products and the depth of the partial product array. Several approximate squarers (R8AS1, R8AS2 and R8AS3) are proposed based on the exact squarer to reduce power and delay. Two approximate partial product generators are also designed to simplify the Radix-8 Booth square encoder in R8AS1 and R8AS2. In addition, approximate compressors with compensation are used in the partial product compression stage to reduce additional area and power consumption in R8AS3. Synthesis results for power, area, and delay at 28nm CMOS technology are presented. Compared with designs in the technical literature with the same accuracy, the proposed 16-bit designs reduce the PDP by 37%;in general, the PDP is decreased by up to 51%. Finally, the proposed approximate squarers are implemented in a square-law detector as a communication application and achieve an SNR close to 30dB. Also, the three proposed approximate squarers are applied to the k-means clustering algorithm for machine learning to accomplish high performance in classification.

关键词： Encoding Generators Compressors Hardware approximation algorithms Clustering algorithms Machine learning algorithms Radix-8 booth-folding square algorithm low power approximate squarers approximate compressors square-law detector k-means clustering

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Fast MSE-Based Sampling of Bandlimited Graph Signals via Low-Pass Impulse Responses

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2023年 71卷 4207-4223页

作者： Wang, Fen Cheung, Gene Ye, Minxiang Li, Taihao Feng, Yi-Tian Zhejiang Lab Hangzhou 311121 Peoples R China York Univ Dept EECS Toronto ON M3J 1P3 Canada

Sampling is a fundamental problem in graph signal processing that selects a node subset to collect samples, so that data in the remaining nodes can be well recovered. Existing eigen-decomposition-free (ED-free) graph sampling schemes are not designed to minimize mean square error (MMSE) of reconstructed bandlimited graph signals, often resulting in sub-par MSE performance. In this paper, we propose a lightweight ED-free algorithm to minimize an approximate MSE objective using per-node impulse responses of an ideal low-pass graph filter. Specifically, we first derive a proxy of the MMSE greedy sampling objective without matrix inverse. We then define node-dependent impulse responses of an ideal low-pass graph filter-analogous to the sinc function in traditional signal processing-which can be approximated very fast without ED. We use these response vectors to reformulate our derived sampling objective, then show that the optimal sampling set has supported low-pass impulse responses that are as orthogonal as possible-defaulting to uniform sampling for 1D regular kernels when the graph Fourier basis is DFT. For optimization, we propose a fast sampling algorithm to evaluate candidates via vector-vector multiplications by reusing previous greedy results. For faster sampling, we relax the MMSE-based greedy objective to a bounded approximation, so that candidate nodes can be easily appraised using simple scalar multiplications. Extensive experiments show that our sampling method achieved state-of-the-art sampling speed and had the best MSE performance among deterministic ED-free sampling methods in various scenarios.

关键词： Laplace equations Complexity theory Signal processing algorithms Sampling methods Matrix decomposition Eigenvalues and eigenfunctions approximation algorithms Graph sampling graph signal processing optimality design eigen-decomposition

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Optimal scenario reduction for one- and two-stage robust optimization with discrete uncertainty in the objective

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第2期310卷 529-551页

作者： Goerigk, Marc Khosravi, Mohammad Univ Siegen Network & Data Sci Management Unteres Schloss 3 D-57072 Siegen Germany

Robust optimization typically follows a worst-case perspective, where a single scenario may determine the objective value of a given solution. Accordingly, it is a challenging task to reduce the size of an uncer-tainty set without changing the resulting objective value too much. On the other hand, robust optimiza-tion problems with many scenarios tend to be hard to solve, in particular for two-stage problems. Hence, a reduced uncertainty set may be central to find solutions in reasonable time. We propose scenario re-duction methods that give guarantees on the performance of the resulting robust solution. Scenario re-duction problems for one-and two-stage robust optimization are framed as optimization problems that only depend on the uncertainty set and not on the underlying decision making problem. Experimental results indicate that objective values for the reduced uncertainty sets are closely correlated to original objective values, resulting in better solutions than when using general-purpose clustering methods such as K-means. (c) 2023 Elsevier B.V. All rights reserved.

关键词： Robustness and sensitivity analysis Robust optimization Scenario reduction Clustering approximation algorithms

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How heavy independent sets help to find arborescences with many leaves in DAGs

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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2023年 135卷 158-174页

作者： Fernandes, Cristina G. Lintzmayer, Carla N. Univ Sao Paulo Comp Sci Dept Sao Paulo Brazil Univ Fed ABC Ctr Matemat Computacao & Cognicao Santo Andre Brazil

Trees with many leaves have applications for broadcasting a message to all recipients simultaneously. Internal nodes of a broadcasting tree require more expensive technology to forward the messages received. We address a problem that captures the main goal: finding spanning trees with few internal nodes in a given network. The MAXIMUM LEAF SPANNING ARBORESCENCE problem consists of, given a directed graph D, finding a spanning arborescence of D, if one exists, with the maximum number of leaves. This problem is NP-hard in general and MaxSNP-hard in the rooted directed acyclic graphs class. This paper explores a relationship between MAXIMUM LEAF SPANNING ARBORESCENCE in rooted directed acyclic graphs and maximum weight set packing. The latter problem is related to independent sets on particular classes of intersection graphs. Exploiting this relation, we derive a 7/5-approximation for MAXIMUM LEAF SPANNING ARBORESCENCE on rooted directed acyclic graphs, improving on the previous 3/2-approximation.(c) 2023 Elsevier Inc. All rights reserved.

关键词： approximation algorithms Maximum leaf spanning arborescence Weighted independent sets Directed acyclic graphs

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AVERAGE SENSITIVITY OF GRAPH algorithms

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SIAM JOURNAL ON COMPUTING 2023年第4期52卷 1039-1081页

作者： Varma, Nithin Yoshida, Yuichi Chennai Math Inst Chennai 603103 Tamil Nadu India Natl Inst Informat Chiyoda Ku Tokyo 1018430 Japan

Modern applications of graph algorithms often involve the use of the output sets (usually, a subset of edges or vertices of the input graph) as inputs to other algorithms. Since the input graphs of interest are large and dynamic, it is desirable for an algorithm's output to not change drastically when a few random edges are removed from the input graph, so as to prevent issues in postprocessing. Alternately, having such a guarantee also means that one can revise the solution obtained by running the algorithm on the original graph in just a few places in order to obtain a solution for the new graph. We formalize this feature by introducing the notion of average sensitivity of graph algorithms, which is the average earth mover's distance between the output distributions of an algorithm on a graph and its subgraph obtained by removing an edge, where the average is over the edges removed and the distance between two outputs is the Hamming distance. In this work, we initiate a systematic study of average sensitivity of graph algorithms. After deriving basic properties of average sensitivity such as composition, we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the minimum s-t cut problem, and the maximum matching problem. In addition, we prove that the average sensitivity of our global minimum cut algorithm is almost optimal, by showing a nearly matching lower bound. We also show that every algorithm for the 2-coloring problem has average sensitivity linear in the number of vertices. One of the main ideas involved in designing our algorithms with low average sensitivity is the following fact: if the presence of a vertex or an edge in the solution output by an algorithm can be decided locally, then the algorithm has a low average sensitivity, allowing us to reuse the analyses of known sublineartime algorithms and local computation algorith

关键词： average sensitivity graph algorithms sublinear algorithms approximation algorithms

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A Learning Based Hierarchical Control Framework for Human-Robot Collaboration

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2023年第1期20卷 506-517页

作者： Jin, Zhehao Liu, Andong Zhang, Wen-An Yu, Li Su, Chun-Yi Zhejiang Univ Technol Coll Informat Engn Hangzhou 310032 Peoples R China Concordia Univ Dept Mech & Ind Engn Montreal PQ H3B 1R6 Canada

In this paper, using the ball and beam system as an illustration, a control scheme is developed on human-robot collaboration, i.e., a two-level hierarchical framework is proposed to establish a robust human-robot collaboration (HRC) policy. On the high level, a deep reinforcement learning (DRL) algorithm is presented to plan the desired beam rotational velocity. The low level is constructed by a human-intention perception module and a robust collaboration policy design module. For the first module, a probabilistic model is fitted by using the Gaussian process regression (GPR) approach to predict human-hand velocities, and prediction results follow Gaussian distributions where mean values and variances represent predicted human-hand velocities and corresponding prediction confidences, respectively. For the second module, a robust collaboration policy is established by fusing a proactive policy and a conservative policy, where the proactive policy is used to control the robot to achieve the desired beam rotational velocity by using the predicted human-hand velocities. The conservative policy is designed to ensure the collaboration safety. The weighted parameters for fusion are adaptively tuned based on the prediction precision and confidence. Experiments are conducted on controlling ball position on a beam jointly by a human and a robot with vision data, and experimental results show the effectiveness of the designed robust collaboration policy.

关键词： Robots Collaboration Task analysis Prediction algorithms Predictive models Q-learning approximation algorithms Human-robot collaboration human-intention perception deep reinforcement learning Gaussian process regression hierarchical control

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A Macro-Micro Population-Based Co-Evolutionary Multi-Objective Algorithm for Community Detection in Complex Networks

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IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 2023年第3期18卷 69-86页

作者： Zhang, Lei Yang, Haipeng Yang, Shangshang Zhang, Xingyi Anhui Univ Hefei Peoples R China

Recently, multi-objective evolutionary algorithms (MOEAs) have shown promising performance in terms of community detection in complex networks. However, most studies have focused on designing different strategies to achieve good community detection performance based on a single population. Unlike these studies, this study proposes a macro-micro population-based co-evolutionary multi-objective algorithm called MMCoMO for community detection in complex networks to obtain a better trade-off between exploration and exploitation. This algorithm employs two populations, i.e., macro-population and micro-population, for co-evolution to obtain better community structures. In particular, the macro-population prefers exploration and is responsible for quickly determining approximate partitions of the network to obtain good rough community structures as early as possible, whereas the micro-population favors exploitation and is responsible for searching for good fine community structures through the local search process. Thus, these two populations can be used to improve each other through interactions in the co-evolutionary process. In particular, a guiding strategy is designed using the elite (non-dominated) solutions of the macro-population to guide the micro-population, and an influencing strategy is further designed using the elite solutions of the micro-population to positively influence the macro-population. Experiments on synthetic networks and 14 real-world networks demonstrate the superiority of the proposed algorithm over several state-of-the-art community detection algorithms.

关键词： Sociology Complex networks Evolutionary computation approximation algorithms Partitioning algorithms Statistics Detection algorithms

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Improving Quantum Computation by Optimized Qubit Routing

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第3期197卷 1161-1194页

作者： Wagner, Friedrich Baermann, Andreas Liers, Frauke Weissenbaeck, Markus Fraunhofer Inst Integrated Circuits IIS Erlangen Germany Univ Erlangen Nurnberg Dept Data Sci Erlangen Germany

In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms formulated in the circuit model of computation onto specific quantum hardware. Our approach decomposes the routing problem into an allocation subproblem and a set of token swapping problems. This allows us to tackle the allocation part and the token swapping part separately. Extracting the allocation part from the qubit routing model of Nannicini et al. (Optimal qubit assignment and routing via integer programming, 2021, ), we formulate the allocation subproblem as a binary linear program. Herein, we employ a cost function that is a lower bound on the overall routing problem objective. We strengthen the linear relaxation by novel valid inequalities. For the token swapping part we develop an exact branch-and-bound algorithm. In this context, we improve upon known lower bounds on the token swapping problem. Furthermore, we enhance an existing approximation algorithm which runs much faster than the exact approach and typically is able to determine solutions close to the optimum. We present numerical results for the fully integrated allocation and token swapping problem. Obtained solutions may not be globally optimal due to the decomposition and the usage of an approximation algorithm. However, the solutions are obtained fast and are typically close to optimal. In addition, there is a significant reduction in the number of artificial gates and output circuit depth when compared to various state-of-the-art heuristics. Reducing these figures is crucial for minimizing noise when running quantum algorithms on near-term hardware. As a consequence, using the novel decomposition approach leads to compiled algorithms with improved quality. Indeed, when compiled with the novel routing procedure and executed on real hardware, our experimental results for quantum approximate optimization algorithms show a

关键词： Combinatorial optimization Integer programming approximation algorithms Quantum compilation

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Discovery of Approximate Lexicographical Order Dependencies

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2023年第4期35卷 3684-3698页

作者： Jin, Yifeng Tan, Zijing Chen, Jixuan Ma, Shuai Fudan Univ Sch Comp Sci Shanghai 200433 Peoples R China Beihang Univ Sch Comp Sci & Engn SKLSDE Lab Beijing 200433 Peoples R China

Lexicographical order dependencies (LODs) specify orders between list of attributes, and are proven useful in optimizing SQL queries with order by clauses. To discover hidden dependencies from dirty data in practice, approximate dependency discoveries are actively studied, aiming at automatically discovering dependencies that hold on data with some exceptions. In this paper we study the discovery of approximate LODs. (1) We adapt two error measures, namely g(1) and g(3), to LODs. We prove their desirable properties, present efficient algorithms for computing the measures and related lower and upper bounds, and study the relationship between the two measures. (2) We present an efficient approximate LOD discovery algorithm that is well suited to the two error measures, with a set of pruning rules, optimization techniques and ranking functions. (3) We study techniques for estimating g1 by sampling, with high accuracy and far less time. (4) We conduct extensive experiments to verify the effectiveness and scalability of our methods, using both real-life and synthetic data.

关键词： Measurement uncertainty approximation algorithms Remuneration Optimization Time measurement Sorting Estimation Data profiling data dependency metadata

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