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Quantized Distributed Nonconvex Optimization with Linear Convergence

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Quantized Distributed Nonconvex Optimization with Linear Con...

IEEE Conference on Decision and control

作者： Lei Xu Xinlei Yi Jiayue Sun Yang Shi Karl Henrik Johansson Tao Yang State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang China Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Digital Futures Stockholm Sweden Department of Mechanical Engineering University of Victoria Victoria Canada

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

This paper considers distributed nonconvex op-timization for minimizing the average of local cost functions, by using local information exchange over undirected communication networks. Since the communication channels often have limited bandwidth or capacity, we first introduce a quantization rule and an encoder/decoder scheme to reduce the transmission bits. By integrating them with a distributed algorithm, we then propose a distributed quantized nonconvex optimization algorithm. Assuming the global cost function satisfies the Polyak– Łojasiewicz condition, which does not require the global cost function to be convex and the global minimizer is not necessarily unique, we show that the proposed algorithm linearly converges to a global optimal point. Moreover, a low data rate is shown to be sufficient to ensure linear convergence when the algorithm parameters are properly chosen. The theoretical results are illustrated by numerical simulation examples.

关键词： Quantization (signal) Communication channels Bandwidth Cost function Numerical simulation Communication networks Distributed algorithms

Nonlinear Cooperative Output Regulation with Input Delay Compensation

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arXiv 2024年

作者： Zheng, Shiqi Ahn, Choon Ki Jiang, Xiaowei Yan, Huaicheng Shi, Peng The School of Automation China University of Geosciences Wuhan430079 China Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems Wuhan430074 China The Engineering Research Center of Intelligent Technology for Geo-Exploration Ministry of Education Wuhan430074 China The Shaoyang Institute of Advanced Manufacturing Technology Shaoyang422000 China The School of Electrical Engineering Korea University Seoul136-701 Korea Republic of The Key Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education East China University of Science and Technology Shanghai200237 China The School of Electrical and Mechanical Engineering The University of Adelaide AdelaideSA5005 Australia

This paper investigates the cooperative output regulation (COR) of nonlinear multi-agent systems (MASs) with long input delay based on periodic event-triggered mechanism. Compared with other mechanisms, periodic event-triggered control can automatically guarantee a Zeno-free behavior and avoid the continuous monitoring of triggered conditions. First, a new periodic event-triggered distributed observer, which is based on the fully asynchronous communication data, is proposed to estimate the leader information. Second, a new distributed predictor feedback control method is proposed for the considered nonlinear MASs with input delay. By coordinate transformation, the MASs are mapped into new coupled ODE-PDE target systems with some disturbance-like terms. Then, we show that the COR problem is solvable. At last, to further save the communication resource, a periodic event-triggered mechanism is considered in the sensor-to-controller transmission in every agent. A new periodic event-triggered filter is proposed to deal with the periodic event-triggered feedback data. The MASs with input delay are mapped into coupled ODE-PDE target systems with sampled data information. Then, Lyapunov-Krasovskii functions are constructed to demonstrate the exponential stability of the MASs. Simulations verify the validity of the proposed results. © 2024, CC BY-NC-ND.

关键词： Feedback control

Teaching MPC: Which way to the promised land?

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arXiv 2021年

作者： Faulwasser, Timm Lucia, Sergio Darup, Moritz Schulze Mönnigmann, Martin Institute of Energy Systems Energy Efficiency and Energy Economics TU Dortmund University Dortmund Germany Laboratory of Process Automation Systems TU Dortmund University Dortmund Germany Control and Cyberphysical Systems TU Dortmund University Dortmund Germany Automatic Control and Systems Theory Ruhr University Bochum Bochum Germany

Since the earliest conceptualizations by Lee and Markus, and Propoi in the 1960s, Model Predictive control (MPC) has become a major success story of systems and control with respect to industrial impact and with respect to continued and wide-spread research interest. The field has evolved from conceptually simple linear-quadratic (convex) settings in discrete and continuous time to nonlinear and distributed settings including hybrid, stochastic, and infinite-dimensional systems. Put differently, essentially the entire spectrum of dynamic systems can be considered in the MPC framework with respect to both-system theoretic analysis and tailored numerics. Moreover, recent developments in machine learning also leverage MPC concepts and learning-based and data-driven MPC have become highly active research areas. However, this evident and continued success renders it increasingly complex to live up to industrial expectations while enabling graduate students for state-of-the-art research in teaching MPC. Hence, this position paper attempts to trigger a discussion on teaching MPC. To lay the basis for a fruitful debate, we subsequently investigate the prospect of covering MPC in undergraduate courses;we comment on teaching textbooks;and we discuss the increasing complexity of research-oriented graduate teaching of MPC. Copyright © 2021, The Authors. All rights reserved.

关键词： Model predictive control

Compressed Gradient Tracking Algorithms for Distributed Nonconvex Optimization

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arXiv 2023年

作者： Xu, Lei Yi, Xinlei Wen, Guanghui Shi, Yang Johansson, Karl H. Yang, Tao The State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 China The Lab for Information & Decision Systems Massachusetts Institute of Technology CambridgeMA02139 United States The Department of Systems Science School of Mathematics Southeast University Nanjing210096 China The Department of Mechanical Engineering University of Victoria VictoriaBCV8W 2Y2 Canada The Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm100 44 Sweden

In this paper, we study the distributed nonconvex optimization problem, aiming to minimize the average value of the local nonconvex cost functions using local information exchange. To reduce the communication overhead, we introduce three general classes of compressors, i.e., compressors with bounded relative compression error, compressors with globally bounded absolute compression error, and compressors with locally bounded absolute compression error. By integrating them, respectively, with the distributed gradient tracking algorithm, we then propose three corresponding compressed distributed nonconvex optimization algorithms. Motivated by the state-of-the-art BEER algorithm proposed in [1], which is an efficient compressed algorithm integrating gradient tracking with biased and contractive compressors, our first proposed algorithm extends this algorithm to accommodate both biased and non-contractive compressors. For each algorithm, we design a novel Lyapunov function to demonstrate its sublinear convergence to a stationary point if the local cost functions are smooth. Furthermore, when the global cost function satisfies the Polyak–Lojasiewicz (P–L) condition, we show that our proposed algorithms linearly converge to a global optimal point. It is worth noting that, for compressors with bounded relative compression error and globally bounded absolute compression error, our proposed algorithms’ parameters do not require prior knowledge of the P–L constant. The theoretical results are illustrated by numerical examples, demonstrating the effectiveness of the proposed algorithms in significantly reducing the communication burden while maintaining the convergence performance. Moreover, simulation results show that the proposed algorithms outperform the state-of-the-art compressed distributed nonconvex optimization algorithms. Copyright © 2023, The Authors. All rights reserved.

关键词： Cost functions

Distributed Online Convex Optimization with Adversarial Constraints: Reduced Cumulative Constraint Violation Bounds under Slater’s Condition

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arXiv 2023年

作者： Yi, Xinlei Li, Xiuxian Yang, Tao Xie, Lihua Hong, Yiguang Chai, Tianyou Johansson, Karl H. Lab for Information & Decision Systems Massachusetts Institute of Technology CambridgeMA02139 United States Department of Control Science and Engineering College of Electronics and Information Engineering Tongji University Shanghai201804 China Shanghai Research Institute for Intelligent Autonomous Systems China The State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 China School of Electrical and Electronic Engineering Nanyang Technological University 50 Nanyang Avenue Singapore639798 Singapore Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Sweden Digital Futures Stockholm10044 Sweden

This paper considers distributed online convex optimization with adversarial constraints. In this setting, a network of agents makes decisions at each round, and then only a portion of the loss function and a coordinate block of the constraint function are privately revealed to each agent. The loss and constraint functions are convex and can vary arbitrarily across rounds. The agents collaborate to minimize network regret and cumulative constraint violation. A novel distributed online algorithm is proposed and it achieves an O(T max{c,1−c}) network regret bound and an O(T 1−c/2) network cumulative constraint violation bound, where T is the number of rounds and c ∈ (0, 1) is a user-defined trade-off parameter. When Slater’s condition holds (i.e, there is a point that strictly satisfies the inequality constraints), the network cumulative constraint violation bound is reduced to O(T 1−c). Moreover, if the loss functions are strongly convex, then the network regret bound is reduced to O(log(T)), and the network cumulative constraint violation bound is reduced to O(√log(T)T) and O(log(T)) without and with Slater’s condition, respectively. To the best of our knowledge, this paper is the first to achieve reduced (network) cumulative constraint violation bounds for (distributed) online convex optimization with adversarial constraints under Slater’s condition. Finally, the theoretical results are verified through numerical simulations. Copyright © 2023, The Authors. All rights reserved.

关键词： Economic and social effects

Communication Compression for Distributed Nonconvex Optimization

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arXiv 2022年

作者： Yi, Xinlei Zhang, Shengjun Yang, Tao Chai, Tianyou Johansson, Karl H. Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Digital Futures Stockholm100 44 Sweden Department of Electrical Engineering University of North Texas DentonTX76203 United States State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 China

This paper considers distributed nonconvex optimization with the cost functions being distributed over agents. Noting that information compression is a key tool to reduce the heavy communication load for distributed algorithms as agents iteratively communicate with neighbors, we propose three distributed primal–dual algorithms with compressed communication. The first two algorithms are applicable to a general class of compressors with bounded relative compression error and the third algorithm is suitable for two general classes of compressors with bounded absolute compression error. We show that the proposed distributed algorithms with compressed communication have comparable convergence properties as state-of-the-art algorithms with exact communication. Specifically, we show that they can find first-order stationary points with sublinear convergence rate O(1/T) when each local cost function is smooth, where T is the total number of iterations, and find global optima with linear convergence rate under an additional condition that the global cost function satisfies the Polyak–Lojasiewicz condition. Numerical simulations are provided to illustrate the effectiveness of the theoretical results. Copyright © 2022, The Authors. All rights reserved.

关键词： Iterative methods

Recursive Weighted Null-Space Fitting Method for Identification of Multivariate systems ⁎

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IFAC-PapersOnLine 2021年第7期54卷 345-350页

作者： Mengyuan Fang Miguel Galrinho Håkan Hjalmarsson Zhejiang Engineering Laboratory of Industrial Internet Communication Technology Zhejiang Sci-Tech University Hangzhou China. State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang China OHB Sweden AB Kista Sweden Centre for Advanced Bio Production and Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Sweden

Recursive identification of structured multivariate models is known to be difficult due to the general non-convexity of the likelihood function. In this work, we propose a recursive multivariate weighted null-space fitting method for identification of structured multivariate models. The proposed method first uses recursive least squares to estimate a high order non-parametric model, then a parametric model is obtained through weighted least squares from the non-parametric model. In this way, the method avoids directly optimizing a non-convex likelihood function and has guaranteed global convergency. Moreover, the proposed method is flexible in model structures and has the same finite sample performance as its off-line counterpart. We use simulation examples to illustrate the performance.

关键词： Recursive system identification multivariate systems weighted null-space fitting

Adaptive Neural Network-Based Asynchronous control for Switching Cyber-Physical systems With Unknown Dead Zone

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IEEE transactions on cybernetics 2025年 PP卷 PP页

作者： Jun Cheng Junhui Wu Huaicheng Yan Dan Zhang Zheng-Guang Wu Ying Zhai Guangxi Normal University School of Mathematics and Statistics Guilin541006 China East China University of Science and Technology Key Laboratory of Advanced Control and Optimization for Chemical Process of Ministry of Education Shanghai200237 China Zhejiang University of Technology Department of Automation Hangzhou310014 China Zhejiang University Institute of Cyber-Systems and Control Hangzhou310027 China

This study investigates the problem of adaptive neural network asynchronous control for switching cyber-physical systems under unknown dead zones. A generalized switching rule, instead of a Markov/semi-Markov process, is utilized to scrutinize the switching behavior of subsystems. This approach characterizes the dynamic nature of sojourn probabilities using single-mode-based sojourn time, aiming to decrease computational load while meeting the demands of real-world scenarios. Considering the intricacies of network environments, the unknown dead zone inputs are considered, which can be effectively implemented via the adaptive neural network-based control law. To counteract the adverse effects of unforeseen information, a saturation-based observer is developed, in which the saturation level is dynamically adjusted with the hope of providing greater flexibility. Utilizing a Lyapunov function that correlates with the detected mode and the system mode, sufficient criteria are established to ensure that the closed-loop system remains bounded in probability. Eventually, the practicality and effectiveness of the proposed control methodology are verified through two simulated examples.

关键词： Markov processes

Rule-Based Energy Management Strategy of Fuel Cell/Ultracapacitor/Battery Vehicles: winner of the IEEE VTS Motor Vehicles Challenge 2020

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Rule-Based Energy Management Strategy of Fuel Cell/Ultracapa...

IEEE Conference on Vehicle Power and Propulsion (VPPC)

作者： Alessandro Ferrara Christoph Hametner Division of Process Control and Automation TU Wien Institute of Mechanics and Mechatronics Vienna Austria Christian Doppler Laboratory for Innovative Control and Monitoring of Automotive Powertrain Systems TU Wien Vienna Austria

ISBN: (数字)9781728189598

ISBN: (纸本)9781728189604

This paper focuses on the energy management of fuel cell/ultracapacitor/battery hybrid vehicles. A robust rule-based strategy is proposed to effectively reduce hydrogen consumption, increase vehicle lifetime, and handle multiple constraints. This strategy won the IEEE VTS Motor Vehicles Challenge 2020. The formulation of the control rules is heavily based on the vehicle model and the analysis of the assigned cost function. A stochastic generation of driving scenarios is proposed to deal with the limited information provided by the challenge, guarantying a robust design of the energy management strategy. The results are analyzed on a large set of synthetic driving cycles.

关键词： Hydrogen Stochastic processes Fuel cells Supercapacitors Propulsion Batteries Fuels