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Distributed Optimization and Scaling Design for Solving Sylvester Equations

Journal of systems Science & Complexity 2024年第6期37卷 2487-2510页

作者： CHENG Songsong YU Xin ZENG Xianlin LIANG Shu HONG Yiguang Anhui Engineering Laboratory of Human-Robot Integration System and Intelligent Equipment School of Electrical Engineering and AutomationAnhui UniversityHefei 230601China Key Laboratory of Intelligent Control and Decision of Complex Systems School of AutomationBeijing Institute of TechnologyBeijing 100081China Department of Control Science and Engineering Tongji UniversityShanghai 201804China Shanghai Research Institute for Intelligent Autonomous Systems Tongji UniversityShanghai 201210China

This paper develops distributed algorithms for solving Sylvester *** authors transform solving Sylvester equations into a distributed optimization problem,unifying all eight standard distributed matrix *** the authors propose a distributed algorithm to find the least squares solution and achieve an explicit linear convergence *** results are obtained by carefully choosing the step-size of the algorithm,which requires particular information of data and Laplacian *** avoid these centralized quantities,the authors further develop a distributed scaling technique by using local information *** a result,the proposed distributed algorithm along with the distributed scaling design yields a universal method for solving Sylvester equations over a multi-agent network with the constant step-size freely chosen from configurable ***,the authors provide three examples to illustrate the effectiveness of the proposed algorithms.

关键词： Distributed optimization least squares solution linear convergence rate step-size interval Sylvester equation

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Deep Distributed Optimization for Large-Scale Quadratic Programming

arXiv

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arXiv 2024年

作者： Saravanos, Augustinos D. Kuperman, Hunter Oshin, Alex Abdul, Arshiya Taj Pacelli, Vincent Theodorou, Evangelos A. Autonomous Control and Decision Systems Laboratory Georgia Institute of Technology United States

Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue to grow, the development of efficient and reliable QP algorithms is becoming increasingly vital. In this context, this paper introduces a novel deep learning-aided distributed optimization architecture designed for tackling large-scale QP problems. First, we combine the state-of-the-art Operator Splitting QP (OSQP) method with a consensus approach to derive DistributedQP, a new method tailored for network-structured problems, with convergence guarantees to optimality. Subsequently, we unfold this optimizer into a deep learning framework, leading to DeepDistributedQP, which leverages learned policies to accelerate reaching to desired accuracy within a restricted amount of iterations. Our approach is also theoretically grounded through Probably Approximately Correct (PAC)-Bayes theory, providing generalization bounds on the expected optimality gap for unseen problems. The proposed framework, as well as its centralized version DeepQP, significantly outperform their standard optimization counterparts on a variety of tasks such as randomly generated problems, optimal control, linear regression, transportation networks and others. Notably, DeepDistributedQP demonstrates strong generalization by training on small problems and scaling to solve much larger ones (up to 50K variables and 150K constraints) using the same policy. Moreover, it achieves orders-of-magnitude improvements in wall-clock time compared to OSQP. The certifiable performance guarantees of our approach are also demonstrated, ensuring higher-quality solutions over traditional optimizers. © 2024, CC BY-NC-SA.

关键词： Quadratic programming

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A bi-level optimization approach for joint rack sequencing and storage assignment in robotic mobile fulfillment systems

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Science China(Information Sciences) 2023年第11期66卷 127-149页

作者： Xiang SHI Fang DENG Sai LU Yunfeng FAN Lin MA Jie CHEN Key Laboratory of Intelligent Control and Decision of Complex Systems Beijing Institute of Technology Beijing Institute of Technology Chongqing Innovation Center Zhejiang Cainiao Supply Chain Management Co. Ltd. Shanghai Research Institute for Intelligent Autonomous Systems

This paper studies a novel rack scheduling problem with multiple types of multiple storage locations(RS-MTMS), which can decide the retrieval sequence of racks and assign each rack a storage location after visiting a picking station. A major challenge in RS-MTMS is that the storage assignment problem and the retrieval sequence decision are closely coupled. If the RS-MTMS is solved directly, the storage assignment scheme and the retrieval sequence of racks are generally generated separately, thus resulting in poor performance. To overcome this difficulty, we propose a bi-level optimization approach for jointly optimizing the storage assignment and retrieval sequence(Bi JSR). In Bi JSR, the storage assignment problem is solved by variable neighborhood search(VNS) in the upper-level optimization. Effective candidate modes are incorporated into VNS to improve solution quality and computational efficiency. The sequencing optimization is obtained in the lower-level according to the given storage location set. A transformation strategy with sufficient problem-specific knowledge is developed to identify the lower-level optimization as the traveling salesman problem and its variants. Then these identified problems are solved using the loop-based *** results show that the proposed Bi JSR is more effective and efficient than the representative algorithms in solving the RS-MTMS problem.

关键词： rack scheduling sequence decision storage assignment bi-level optimization robotic mobile fulfillment system

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Low Frequency Sampling in Model Predictive Path Integral control

arXiv

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arXiv 2024年

作者： Vlahov, Bogdan Gibson, Jason Fan, David D. Spieler, Patrick Agha-Mohammadi, Ali-Akbar Theodorou, Evangelos A. Autonomous Control and Decision Systems Lab Georgia Institute of Technology AtlantaGA30313 United States NASA Jet Propulsion Laboratory California Institute of Technology PasadenaCA United States

Sampling-based model-predictive controllers have become a powerful optimization tool for planning and control problems in various challenging environments. In this paper, we show how the default choice of uncorrelated Gaussian distributions can be improved upon with the use of a colored noise distribution. Our choice of distribution allows for the emphasis on low frequency control signals, which can result in smoother and more exploratory samples. We use this frequency-based sampling distribution with Model Predictive Path Integral (MPPI) in both hardware and simulation experiments to show better or equal performance on systems with various speeds of input response. © 2024, CC BY.

关键词： Predictive control systems

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A Multi-step Dynamics Modeling Framework For autonomous Driving In Multiple Environments

A Multi-step Dynamics Modeling Framework For Autonomous Driv...

引用

IEEE International Conference on Robotics and Automation (ICRA)

作者： Jason Gibson Bogdan Vlahov David Fan Patrick Spieler Daniel Pastor Ali-akbar Agha-mohammadi Evangelos A. Theodorou Autonomous Control and Decision Systems Lab Georgia Institute of Technology Atlanta GA USA NASA Jet Propulsion Laboratory California Institute of Technology Pasadena CA USA

Modeling dynamics is often the first step to making a vehicle autonomous. While on-road autonomous vehicles have been extensively studied, off-road vehicles pose many challenging modeling problems. An off-road vehicle encounters highly complex and difficult-to-model terrain/vehicle interactions, as well as having complex vehicle dynamics of its own. These complexities can create challenges for effective high-speed control and planning. In this paper, we introduce a framework for multistep dynamics prediction that explicitly handles the accumulation of modeling error and remains scalable for sampling-based controllers. Our method uses a specially-initialized Long Short-Term Memory (LSTM) over a limited time horizon as the learned component in a hybrid model to predict the dynamics of a 4-person seating all-terrain vehicle (Polaris S4 1000 RZR) in two distinct environments. By only having the LSTM predict over a fixed time horizon, we negate the need for long term stability that is often a challenge when training recurrent neural networks. Our framework is flexible as it only requires odometry information for labels. Through extensive experimentation, we show that our method is able to predict millions of possible trajectories in real-time, with a time horizon of five seconds in challenging off road driving scenarios.

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Interaction and decision Making-aware Motion Planning using Branch Model Predictive control

Interaction and Decision Making-aware Motion Planning using ...

引用

IEEE Symposium on Intelligent Vehicle

作者： Rui Oliveira Siddharth H. Nair Bo Wahlberg Scania Autonomous Transport Solutions Södertälje Sweden Division of Decision and Control Systems KTH Royal Institute of Technology Stockholm Sweden Model Predictive Control Laboratory UC Berkeley Berkeley USA

Motion planning for autonomous vehicles sharing the road with human drivers remains challenging. The difficulty arises from three challenging aspects: human drivers are 1) multi-modal, 2) interacting with the autonomous vehicle, and 3) actively making decisions based on the current state of the traffic scene. We propose a motion planning framework based on Branch Model Predictive control to deal with these challenges. The multi-modality is addressed by considering multiple future outcomes associated with different decisions taken by the human driver. The interactive nature of humans is considered by modeling them as reactive agents impacted by the actions of the autonomous vehicle. Finally, we consider a model developed in human neuroscience studies as a possible way of encoding the decision making process of human drivers. We present simulation results in various scenarios, showing the advantages of the proposed method and its ability to plan assertive maneuvers that convey intent to humans.

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Lane Geometry, Compliance Levels, and Adaptive Geo-fencing in CORRIDRONE Architecture for Urban Mobility

Lane Geometry, Compliance Levels, and Adaptive Geo-fencing i...

引用

2021 International Conference on Unmanned Aircraft systems, ICUAS 2021

作者： Tony, Lima Agnel Ratnoo, Ashwini Ghose, Debasish Guidance Control and Decision Systems Laboratory Indian Institute of Science Department of Aerospace Engineering Bangalore India Autonomous Vehicles Laboratory Indian Institute of Science Department of Aerospace Engineering Bangalore India

ISBN: (纸本)9780738131153

Integrating Unmanned Aerial Vehicles (UAVs) into airspace requires a reliable framework which is robust and scalable. CORRIDRONE is one such architecture that generates corridors for point-to-point traversal of drones. This work presents details about its central features like adaptive geo-fencing, drone compliance levels, and corridor geometry. Adaptive geo-fencing guarantees vehicle safety when multiple vehicles of different hardware and software capabilities are sharing the same airspace. Compliance levels, defined based on these capabilities of the UAVs, are an essential measure for determining geo-fence bounds. The lane geometry of CORRIDRONE is designed considering the aerodynamic aspects like downwash, which ensures in-flight stability of the UAVs. These features confirm safe transit of the vehicles and also ensures efficient operation of the system. The flexibility to accommodate multiple UAVs of varying compliance levels highlight the robustness of the proposed framework. © 2021 IEEE.

关键词： Geometry

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Distributed Online Convex Optimization with Time-Varying Constraints: Tighter Cumulative Constraint Violation Bounds under Slater's Condition

引用

IEEE Transactions on Automatic control 2025年

作者： Yi, Xinlei Li, Xiuxian Yang, Tao Xie, Lihua Hong, Yiguang Chai, Tianyou Johansson, Karl H. National Key Laboratory of Autonomous Intelligent Unmanned Systems Shanghai Institute of Intelligent Science and Technology China Ministry of Education Frontiers Science Center for Intelligent Autonomous Systems China Massachusetts Institute of Technology Lab for Information & Decision Systems CambridgeMA02139 United States Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang110819 China Nanyang Technological University School of Electrical and Electronic Engineering 50 Nanyang Avenue 639798 Singapore Kth Royal Institute of Technology Division of Decision and Control Systems School of Electrical Engineering and Computer Science Sweden Digital Futures Stockholm10044 Sweden

This paper considers distributed online convex optimization with time-varying 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 static network regret and network cumulative constraint violation. A novel distributed online algorithm with a vanishing stepsize is proposed and it achieves an O(Tmax {c,1-c}) static network regret bound and an O(T1-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(T1-c). Moreover, if the loss functions are strongly convex, then static 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 tighter (network) cumulative constraint violation bounds for (distributed) online convex optimization with time-varying constraints under Slater's condition. Finally, the theoretical results are verified through numerical simulations. © 1963-2012 IEEE.

关键词： Convex optimization

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A Multi-Player Potential Game Approach for Sensor Network Localization with Noisy Measurements 63

A Multi-Player Potential Game Approach for Sensor Network Lo...

引用

63rd IEEE Conference on decision and control, CDC 2024

作者： Xu, Gehui Chen, Guanpu Fidan, Baris Hong, Yiguang Qi, Hongsheng Parisini, Thomas Johansson, Karl H. Kth Royal Institute of Technology Division of Decision and Control Systems School of Electrical Engineering and Computer Science Stockholm100 44 Sweden University of Waterloo Department of Mechanical and Mechatronics Engineering WaterlooONN2L 3G1 Canada Tongji University Department of Control Science and Engineering shanghai201804 China Shanghai Research Institute for Intelligent Autonomous Systems Shanghai201210 China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Beijing China University of Chinese Academy of Sciences School of Mathematical Sciences Beijing China Aalborg University Department of Electronic Systems Denmark Imperial College London Department of Electrical and Electronic Engineering LondonSW7 2AZ United Kingdom University of Trieste Department of Engineering and Architecture Italy

ISBN: (纸本)9798350316339

Sensor network localization (SNL) is a challenging problem due to its inherent non-convexity and the effects of noise in inter-node ranging measurements and anchor node position. We formulate a non-convex SNL problem as a multiplayer non-convex potential game and investigate the existence and uniqueness of a Nash equilibrium (NE) in both the ideal setting without measurement noise and the practical setting with measurement noise. We first show that the NE exists and is unique in the noiseless case, and corresponds to the precise network localization. Then, we study the SNL for the case with errors affecting the anchor node position and the inter-node distance measurements. Specifically, we establish that in case these errors are sufficiently small, the NE exists and is unique. It is shown that the NE is an approximate solution to the SNL problem, and that the position errors can be quantified accordingly. Based on these findings, we apply the results to case studies involving only inter-node distance measurement errors and only anchor position information inaccuracies. © 2024 IEEE.

关键词： Nash equilibrium

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A Multi-step Dynamics Modeling Framework For autonomous Driving In Multiple Environments

arXiv

引用

arXiv 2023年

作者： Gibson, Jason Vlahov, Bogdan Fan, David Spieler, Patrick Pastor, Daniel Agha-Mohammadi, Ali-Akbar Theodorou, Evangelos A. Autonomous Control and Decision Systems Lab Georgia Institute of Technology AtlantaGA30313 United States NASA Jet Propulsion Laboratory California Institute of Technology PasadenaCA United States

关键词： Off road vehicles

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