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Regret and cumulative constraint violation analysis for online convex optimization with long term constraints

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arXiv 2021年

作者： Yi, Xinlei Li, Xiuxian Yang, Tao Xie, Lihua Chai, Tianyou Johansson, Karl H. School of Electrical Engineering and Computer Science and Digital Futures KTH Royal Institute of Technology Stockholm Sweden Department of Control Science and Engineering College of Electronics and Information Engineering Shanghai Research Institute for Intelligent Autonomous Systems Institute for Advanced Study Tongji University Shanghai China State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang China School of Electrical and Electronic Engineering Nanyang Technological University Singapore Singapore

This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to measure constraint violations, which excludes the situation that strictly feasible constraints can compensate the effects of violated constraints. A novel algorithm is first proposed and it achieves an O(Tmax{c,1-c}) bound for static regret and an O(T (1-c)/2) bound for cumulative constraint violation, where c ϵ (0, 1) is a user-defined trade-off parameter, and thus has improved performance compared with existing results. Both static regret and cumulative constraint violation bounds are reduced to O(log(T )) when the loss functions are strongly convex, which also improves existing results. In order to achieve the optimal regret with respect to any comparator sequence, another algorithm is then proposed and it achieves the optimal O( p T (1 + PT )) regret and an O(√T) cumulative constraint violation, where PT is the path-length of the comparator sequence. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results. Copyright © 2021, The Authors. All rights reserved.

关键词： Comparators (optical)

Regret and Cumulative Constraint Violation Analysis for Distributed Online Constrained Convex Optimization

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arXiv 2021年

作者： Yi, Xinlei Li, Xiuxian Yang, Tao Xie, Lihua Chai, Tianyou Johansson, Karl H. The Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm10044 Sweden The Digital Futures Stockholm10044 Sweden The Department of Control Science and Engineering College of Electronics and Information Engineering The Shanghai Research Institute for Intelligent Autonomous Systems Tongji University Shanghai 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

This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and constraint functions. At each round, each agent selects a decision from the decision set, and then only a portion of the loss function and a coordinate block of the constraint function at this round are privately revealed to this agent. The goal of the network is to minimize the network-wide loss accumulated over time. Two distributed online algorithms with full-information and bandit feedback are proposed. Both dynamic and static network regret bounds are analyzed for the proposed algorithms, and network cumulative constraint violation is used to measure constraint violation, which excludes the situation that strictly feasible constraints can compensate the effects of violated constraints. In particular, we show that the proposed algorithms achieve O(T max{κ,1-κ}) static network regret and O(T 1-κ/2) network cumulative constraint violation, where T is the time horizon and κ ∈ (0, 1) is a user-defined trade-off parameter. Moreover, if the loss functions are strongly convex, then the static network regret bound can be reduced to O(T κ). Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results. Copyright © 2021, The Authors. All rights reserved.

关键词： Economic and social effects

Operating performance assessment for industrial process with hybrid qualitative and quantitative information using modified fuzzy probabilistic rough set

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Operating performance assessment for industrial process with...

Chinese automation Congress (CAC)

作者： Xiaoyu Zou Fuli Wang Yuqing Chang Jie Pan School of Mechatronic Engineering China University of Mining and Technology Xuzhou China State Key Laboratory of Process Automation in Mining & Metallurgy Beijing China College of Information Science & Engineering Northeastern University Shenyang China School of Information and Control Engineering Xuzhou China

ISBN: (数字)9781728176871

ISBN: (纸本)9781728176888

Since satisfactory operating performance helps guarantee high comprehensive economic benefit under normal working condition for industrial processes, it is crucial to conduct accurate performance assessment on the degree of optimality for modern industry. process online assessment judges how well the process is working. However, the coexistence of the qualitative and quantitative information renders the conventional performance assessment approaches inappropriate. To solve the above problem, a modified version of fuzzy probabilistic rough set (FPRS) is proposed for performance assessment in this research. The modified FPRS is employed to establish a valid online assessment strategy of operating performance for complicated industrial processes with the coexistence of both the qualitative and quantitative information. The proposed technique is finally validated by a gold hydrometallurgy process.

关键词： Rough sets Probabilistic logic Uncertainty Production process control Indexes Gold

Output Feedback Based Iterative Learning control with Finite Frequency Range Specifications via a Heuristic Approach for Batch processes with Polytopic Uncertainties ⁎

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IFAC-PapersOnLine 2020年第2期53卷 1397-1402页

作者： Shoulin Hao Tao Liu Wojciech Paszke Hongfeng Tao Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education Dalian University of Technology Dalian 116024 China School of Control Science and Engineering Dalian University of Technology Dalian 116024 China Institute of Automation Electronic and Electrical Engineering University of Zielona Góra ul. Szafrana 2 65-516 Zielona Góra Poland Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education Jiangnan University Wuxi 214122 China

For robust control and iterative optimization of industrial batch processes with polytopic uncertainties, this paper proposes a robust output feedback based iterative learning control (ILC) design in terms of finite frequency range stability specifications. Robust stability conditions for the closed-loop ILC system along both time and batch directions are first established based on the generalized Kalman-Yakubovich-Popov lemma and linear repetitive system theory. To facilitate the ILC controller design with respect to process uncertainties described in a polytopic form, extended sufficient conditions for the system stability are then derived in terms of matrix inequalities. Correspondingly, a two-stage heuristic approach is developed to iteratively compute feasible ILC controller gains for implementation. An illustrative example is given to demonstrate the effectiveness of the proposed control design.

关键词： Batch processes polytopic uncertainties output feedback iterative learning control finite frequency range design

When Distributed Formation control Is Feasible under Hard Constraints on Energy and Time? 200

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arXiv 2020年

作者： Jia, Chunxiang Chen, Fei Xiang, Linying Lan, Weiyao Feng, Gang State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110004 China School of Control Engineering Northeastern University at Qinhuangdao Qinhuangdao066004 China Department of Automation Xiamen University Xiamen361005 China Department of Biomedical Engineering City University of Hong Kong Kowloon Hong Kong

This paper studies distributed optimal formation control with hard constraints on energy levels and termination time, in which the formation error is to be minimized jointly with the energy cost. The main contributions include a globally optimal distributed formation control law and a comprehensive analysis of the resulting closed-loop system under those hard constraints. It is revealed that the energy levels, the task termination time, the steady-state error tolerance, as well as the network topology impose inherent limitations in achieving the formation control mission. Most notably, the lower bounds on the achievable termination time and the required minimum energy levels are derived, which are given in terms of the initial formation error, the steady-state error tolerance, and the largest eigenvalue of the Laplacian matrix. These lower bounds can be employed to assert whether an energy and time constrained formation task is achievable and how to accomplish such a task. Furthermore, the monotonicity of those lower bounds in relation to the control parameters is revealed. A simulation example is finally given to illustrate the obtained results. Copyright © 2020, The Authors. All rights reserved.

关键词： Multi agent systems

Prescribed performance-based privacy-preserving quantized consensus for distributed energy dispatch optimization

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Energy 2025年 331卷

作者： Kong, Minxue Shen, Feifei Peng, Xin Li, Linlin Zhong, Weimin Li, Zhi Key Laboratory of Smart Manufacturing in Energy Chemical Process Ministry of Education East China University of Science and Technology Shanghai 200237 China School of Information Science and Engineering East China University of Science and Technology Shanghai 200237 China State Key Laboratory of Industrial Control Technology Ministry of Education East China University of Science and Technology Shanghai 200237 China School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China State Key Laboratory of Chemical Engineering and Low-Carbon Technology East China University of Science and Technology Shanghai 200237 China

To improve energy efficiency and optimize energy dispatching of combined heat and power (CHP) systems, a distributed economic optimization framework based on the equal incremental principle is established, and a distributed fixed-time quantized privacy-preserving consensus algorithm is adopted to achieve consistent incremental costs. First, a privacy mask with predetermined performance is designed to avoid the potential leakage of sensitive information in distributed communication. Based on this, fixed-time privacy-preserving leader–follower and weighted average consensus algorithms are proposed, where the setting time is independent of the initial state conditions. In contrast to existing works, the proposed algorithms can achieve complete consensus instead of converging within a small region, ensuring the global optimality of the solutions. Additionally, a quantization mechanism and time-varying gains are introduced into the algorithms, reducing transmission constraints and resource waste. Finally, the proposed algorithms are applied to the distributed economic dispatch problem, demonstrating precise convergence and excellent privacy protection effect. © 2025

关键词： Consensus Distributed economic dispatch Prescribed performance Privacy-preserving

Delay and packet-drop tolerant multi-stage distributed average tracking in mean square

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arXiv 2020年

作者： Chen, Fei Chen, Changjiang Guo, Ge Hua, Changchun Chen, Guanrong State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110004 China School of Control Engineering Northeastern University at Qinhuangdao Qinhuangdao066004 China Department of Automation Xiamen University Xiamen361005 China Institute of Electrical Engineering Yanshan University Qinhuangdao066004 China Department of Electrical Engineering City University of Hong Kong Hong Kong Hong Kong

This paper studies the distributed average tracking problem pertaining to a discrete-time linear time-invariant multi-agent network, which is subject to, concurrently, input delays, random packet-drops, and reference noise. The problem amounts to an integrated design of delay and packet-drop tolerant algorithm and determining the ultimate upper bound of the tracking error between agents' states and the average of the reference signals. The investigation is driven by the goal of devising a practically more attainable average tracking algorithm, thereby extending the existing work in the literature which largely ignored the aforementioned uncertainties. For this purpose, a blend of techniques from Kalman filtering, multi-stage consensus filtering, and predictive control is employed, which gives rise to a simple yet comepelling distributed average tracking algorithm that is robust to initialization error and allows the trade-off between communication/computation cost and stationary-state tracking error. Due to the inherent coupling among different control components, convergence analysis is significantly challenging. Nevertheless, it is revealed that the allowable values of the algorithm parameters rely upon the maximal degree of an expected network, while the convergence speed depends upon the second smallest eigenvalue of the same network's topology. The effectiveness of the theoretical results is verified by a numerical example. Copyright © 2020, The Authors. All rights reserved.

关键词： Packet loss

Off-Policy Q-Learning for Anti-Interference control of Multi-Player Systems ⁎

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IFAC-PapersOnLine 2020年第2期53卷 9189-9194页

作者： Jinna Li Zhenfei Xiao Tianyou Chai Frank. L. Lewis Sarangapani Jagannathan School of Information and Control Engineering Liaoning Shihua University Fushun 113001 China State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang 110819 China UTA Research Institute the University of Texas at Arlington Arlington TX 76118 USA Department of Electrical and Computer Engineering Missouri University of Science and Technology Rolla MO 65409 USA

This paper develops a novel off-policy game Q-learning algorithm to solve the anti-interference control problem for discrete-time linear multi-player systems using only data without requiring system matrices to be known. The primary contribution of this paper lies in that the Q-learning strategy employed in the proposed algorithm is implemented in an off-policy policy iteration approach other than on-policy learning due to the well-known advantages of off-policy Q-learning over on-policy Q-learning. All of the players work hard together for the goal of minimizing their common performance index meanwhile defeating the disturbance that tries to maximize the specific performance index, and finally they reach the Nash equilibrium of the game resulting in satisfying disturbance attenuation condition. In order to find the solution to the Nash equilibrium, the anti-interference control problem is first transformed into an optimal control problem. Then an off-policy Q-learning algorithm is proposed in the framework of typical adaptive dynamic programming (ADP) and game architecture, such that control policies of all players can be learned using only measured data. Comparative simulation results are provided to verify the effectiveness of the proposed method.

关键词： H ∞ control off-policy Q-learning game theory Nash equilibrium

control Energy of Directed Networks

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Control Energy of Directed Networks

第三十八届中国控制会议

作者： Jiajun Huang Linying Xiang Fei Chen Department of Automation Xiamen University School of Control Engineering Northeastern University at Qinhuangdao State Key Laboratory of Synthetical Automation for Process Industries Northeastern University

This work studies the control energy for directed networks which are exactly controllable. By employing Jordan transformation, we derive a simplified formula to calculate the control energy of directed networks. We show that the control energy of directed networks is a decreasing function of the terminal time, indicating that the more time to control, the less energy to cost. Additionally, we investigate the control energy for the Price network model. We show that for Price networks the control energy is a decreasing function of network heterogeneity and an increasing function of network size.

关键词： control energy Directed network Exact controllability