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Sign Hessian-Weighted Gradient Algorithms for Distributed time-varying Convex optimization

IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2025年第1期12卷 474-484页

作者： Huang, Bomin Yang, Chengqian Chen, Fei Lan, Weiyao Jimei Univ Coll Comp Engn Xiamen 361021 Peoples R China Northeastern Univ Qinhuangdao Sch Control Engn Qinhuangdao 066004 Peoples R China Nankai Univ Coll Artificial Intelligence Tianjin 300350 Peoples R China Xiamen Univ Dept Automat Xiamen 361005 Peoples R China

In this article, we initiate our exploration with a time-varying optimization problem, featuring linear equality constraints. To address this complex problem, we introduce a novel continuous-time sign Hessian-weighted gradient algorithm. Remarkably, our proposed approach is capable of handling the time-varying nature of the problem, all without the need for the invertibility of the Hessian matrix associated with the cost function. We present two distinct distributed algorithms: the edge-based and node-based variations. To underscore the practical effectiveness of our methodology, we provide some numerical examples, offering compelling evidence to validate our research findings.

关键词： Cost function Heuristic algorithms Vectors Network systems time-varying systems Distributed algorithms Control systems Convergence Transportation Surges Distributed algorithm Hessian matrix sign function time-varying optimization

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time-varying optimization of Networked Systems With Human Preferences

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2023年第1期10卷 503-515页

作者： Ospina, Ana M. M. Simonetto, Andrea Dall'Anese, Emiliano Univ Colorado Boulder Dept Elect Comp & Energy Engn Boulder CO 80309 USA Inst Polytech Paris UMA ENSTA Paris F-91120 Palaiseau France

This article considers a time-varying optimization problem associated with a network of systems, with each of the systems shared by (and affecting) a number of individuals. The objective is to minimize cost functions associated with the individuals' preferences, which are unknown, subject to time-varying constraints that capture physical or operational limits of the network. To this end, this article develops a distributed online optimization algorithm with concurrent learning of the cost functions. The cost functions are learned on-the-fly based on the users' feedback (provided at irregular intervals) by leveraging tools from the shape-constrained Gaussian process. The online algorithm is based on a primal-dual method and acts effectively in a closed-loop fashion where: First, users' feedback is utilized to estimate the cost, and second, measurements from the network are utilized in the algorithmic steps to bypass the need for sensing of (unknown) exogenous inputs of the network. The performance of the algorithm is analyzed in terms of dynamic network regret and constraint violation. Numerical examples are presented in the context of real-time optimization of distributed energy resources.

关键词： Costs Cost function time-varying systems Heuristic algorithms Network systems Gaussian processes Convex functions Feedback Gaussian process (GP) Index Terms networked systems regret analysis time-varying optimization

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time-varying optimization-Based Approach for Distributed Formation of Uncertain Euler-Lagrange Systems

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第7期52卷 5984-5998页

作者： Sun, Chao Feng, Zhi Hu, Guoqiang Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

We investigate a distributed time-varying formation control problem for an uncertain Euler-Lagrange system. A time-varying optimization-based approach is proposed. Based on this approach, the robots can achieve the expected formation configuration and meanwhile optimize a global objective function using only neighboring and local information. We consider the time-varying optimization where the objective functions can change in real time. In this case, the consensus-based formation tracking control issues and formation containment tracking control issues in the literature can be solved by the proposed approach. By a penalty-based method, the robots' states asymptotically converge to the estimated optimal solution to an equivalent time-varying optimization problem, whose optimal solution can achieve simultaneous formation and optimization. Furthermore, we consider two more general scenarios: 1) the local objective functions can have non-neighbor's information and 2) the optimization problems can have inequality constraints.

关键词： optimization Robots Linear programming time-varying systems Sun Trajectory Task analysis Distributed formation control Euler-Lagrange systems time-varying optimization

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Distributed time-varying optimization-An Output Regulation Approach

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IEEE TRANSACTIONS ON CYBERNETICS 2024年第4期54卷 2155-2165页

作者： Ding, Zhengtao Univ Manchester Dept Elect & Elect Engn Manchester M13 9PL England

This article deals with distributed algorithm design for time-varying optimization problems, which include unconstrained time-varying optimization and a special constrained problem commonly known as a resource allocation problem. The time-varying nature exists in the individual cost functions and the demand functions, and they are then captured by neutrally stable linear dynamic systems known as exosystems. To address the time-varying nature, new distributed algorithm structures are developed and two algorithms are designed for distributed time-varying optimization (DTVO) and distributed time-varying optimal resource allocation (DTVORA) to ensure that there exist time-varying solutions and the solution states will converge to the time-varying solutions. The driving terms for tracking the variation in the solutions are designed using exosystem dynamics. Rigorous convergence analyses are carried out using Lyapunov theory, and the examples are included to demonstrate the potential applications of the two proposed algorithms.

关键词： Distributed optimization (DOP) optimal resource allocation time-varying optimization

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Distributed Continuous-time Algorithm for time-varying optimization With Affine Formation Constraints

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第4期68卷 2615-2622页

作者： Wu, Chu Fang, Hao Zeng, Xianlin Yang, Qingkai Wei, Yue Chen, Jie Beijing Inst Technol Sch Automat Beijing Peoples R China Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Frontier Res Ctr Peng Cheng Lab Shenzhen Peoples R China Tongji Univ Coll Elect & Informat Engn Shanghai 200092 Peoples R China

In this article, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functions, each of which is known by only one individual agent. The optimal solution is a time-varying affine transformation of a nominal configuration rather than some constants. To tackle the difficulty caused by the dynamic aspect of the local cost functions and handle affine formation constraints, the fixed-time distributed estimator and distributed gradient tracking technique are developed, respectively, to compensate the time variation of solution trajectory and calculate the weighted sum of local gradients to eliminate the tracking error. The time-varying optimal solution trajectory is thus accurately tracked with the proposed estimator-based gradient tracking algorithm. Using appropriately chosen coefficients, the tracking error is guaranteed to vanish at an exponential rate. The proposed estimator-based gradient tracking algorithm is further validated through numerical simulations.

关键词： Cost function Stress Laplace equations time-varying systems Costs Trajectory Standards Affine formation fixed-time estimator gradient tracking time-varying optimization

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Prediction-Correction Splittings for time-varying optimization With Intermittent Observations

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IEEE CONTROL SYSTEMS LETTERS 2020年第2期4卷 373-378页

作者： Bastianello, Nicola Simonetto, Andrea Carli, Ruggero Univ Padua Dept Informat Engn I-35131 Padua Italy IBM Res Ireland Optimizat & Control Grp Dublin D15 HN66 Ireland

We study the solution of a time-varying optimization problem which is observed, i.e., it is known, only intermittently. We propose three approaches based on the prediction-correction scheme for solving this problem by exploiting splitting methods. We present convergence results in mean to a bounded asymptotical error, and show-case them in a numerical example featuring a regression problem.

关键词： time-varying optimization prediction-correction splitting methods intermittent observations

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PREDICTION-CORRECTION FOR NONSMOOTH time-varying optimization VIA FORWARD-BACKWARD ENVELOPES 44

PREDICTION-CORRECTION FOR NONSMOOTH TIME-VARYING OPTIMIZATIO...

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44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Bastianello, Nicola Simonetto, Andrea Carli, Ruggeri Univ Padua Dept Informat Engn Padua Italy IBM Res Ireland Dublin Ireland

ISBN: (纸本)9781479981311

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward envelope, and we are able to prove the convergence of the solutions to a neighborhood of the optimizer that depends on the sampling time. Numerical simulations for a time-varying regression problem with elastic net regularization highlight the effectiveness of the algorithm.

关键词： time-varying optimization prediction-correction methods forward-backward envelope convex optimization

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Implicit Trajectory Planning for Feedback Linearizable Systems: A time-varying optimization Approach

Implicit Trajectory Planning for Feedback Linearizable Syste...

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American Control Conference (ACC)

作者： Zheng, Tianqi Simpson-Porco, John Mallada, Enrique Johns Hopkins Univ Dept Elect & Comp Engn Baltimore MD 21218 USA Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

ISBN: (纸本)9781538682661

We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to, e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-object or multi-agent tracking problems with constraints.

关键词： time-varying optimization motion planning feedback linearization

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General Third-Order-Accuracy Formulas for time Discretization Applied to time-varying optimization

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IEEE ACCESS 2020年 8卷 224235-224245页

作者： Xuan, Hejun Zhu, Xinhui Li, Jian Guo, Huaping Li, Yanling Xinyang Normal Univ Sch Comp & Informat Technol Xinyang 464000 Peoples R China Xinyang Normal Univ Henan Key Lab Anal & Applicat Educ Big Data Xinyang 464000 Peoples R China

time discretization is an important part of time-varying problems solving that determines convergence, real-time performance and accuracy for solution models. It is a challenging work compared with relatively simple derivative approximation due to unknown future information and stability constraint. To the best of the authors's knowledge, no effective time discretization was developed other than Euler finite difference formula before recently development of ZeaD formulas. Existing work presents some ZeaD formulas including specific time-discretization formulas having third order accuracy. In this work, N-instant general third-order-accuracy formula is proposed, and it leads to different general third-order-accuracy formulas when different instant number N is considered. Stability and convergence are analyzed, and effective domains for parameters in 5-instant and 6-instant general third-order-accuracy formula are given to guarantee effective time discretization. Furthermore, N-instant general third-order-accuracy formula is employed to solve time-varying optimization, and N-instant general solution model is proposed. Finally, comparative experimental results are presented to substantiate the effectiveness and superiority of proposed general formulas and models.

关键词： time discretization general third-order-accuracy formulas time-varying optimization 0-stability

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Prediction-Correction Splittings for Nonsmooth time-varying optimization 18

Prediction-Correction Splittings for Nonsmooth Time-Varying ...

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18th European Control Conference (ECC)

作者： Bastianello, Nicola Simonetto, Andrea Carli, Ruggero Univ Padua Dept Informat Engn Padua Italy IBM Res Ireland Dublin Ireland

ISBN: (纸本)9783907144008

We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on prediction-correction, which employs splitting methods to solve the sampled instances of the time-varying problem. We describe the prediction-correction scheme and two splitting methods, the forward-backward and the Douglas-Rachford. Then by using a result for generalized equations, we prove convergence of the generated sequence of approximate optimizers to a neighborhood of the optimal solution trajectory. Simulation results for a leader following formation in robotics assess the performance of the proposed algorithm.

关键词： time-varying optimization prediction-correction splitting methods forward-backward Douglas-Rachford generalized equations

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