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KKL Observer Synthesis for Nonlinear systems via Physics-Informed Learning

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arXiv 2025年

作者： Niazi, M.B. Umar Cao, John Barreau, Matthieu Johansson, Karl Henrik Division of Decision and Control Systems Digital Futures KTH Royal Institute of Technology StockholmSE-100 44 Sweden Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Department of Electrical Engineering Stanford University StanfordCA94305 United States

This paper proposes a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems. The design of a KKL observer involves finding an injective map that transforms the system state into a higher-dimensional observer state, whose dynamics is linear and stable. The observer’s state is then mapped back to the original system coordinates via the inverse map to obtain the state estimate. However, finding this transformation and its inverse is quite challenging. We propose to sequentially approximate these maps by neural networks that are trained using physics-informed learning. We generate synthetic data for training by numerically solving the system and observer dynamics. Theoretical guarantees for the robustness of state estimation against approximation error and system uncertainties are provided. Additionally, a systematic method for optimizing observer performance through parameter selection is presented. The effectiveness of the proposed approach is demonstrated through numerical simulations on benchmark examples and its application to sensor fault detection and isolation in a network of Kuramoto oscillators using learned KKL observers. © 2025, CC BY.

关键词： State estimation

Output Feedback Position Tracking control of Marine Vessels Subject to Periodic Disturbances

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Output Feedback Position Tracking Control of Marine Vessels ...

American control Conference (ACC)

作者： Deniz Kurtoglu Enver Tatlicioglu Erkan Zergeroglu Department of Mechanical Engineering Laboratory for Autonomy Control Information and Systems (LACIS) University of South Florida Tampa FL United States of America Department of Electrical Electronics Engineering Ege University Izmir Turkey Department of Computer Engineering Gebze Technical University Gebze Kocaeli Turkey

ISBN: (数字)9798350382655

ISBN: (纸本)9798350382662

This work deals with the design and implementation of a novel output feedback position tracking controller for marine vessels subject to uncertainties in their dynamical parameters and periodic external disturbance. Specifically, an adaptive controller that does not make use of velocity measurements has been presented which can compensate for uncertainties in the system's dynamical parameters and periodic external disturbance. A filtered based velocity surrogate formulation in conjunction with a periodic noise estimator and a desired model compensation based adaptive parameter estimator have been utilized to tackle the problem. Boundedness of the closed loop system and convergence of the position tracking error to the origin are proven via Lyapunov-type arguments. Comparative numerical simulations are presented to illustrate the effectiveness of the proposed controller.

关键词： Uncertain systems Uncertainty Noise Estimation Numerical simulation Filtering theory Numerical models

Multisensor fusion estimation of nonlinear systems with intermittent observations and heavy-tailed noises

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Science China(Information Sciences) 2022年第09期65卷 173-190页

作者： Bo XIAO Q.M.Jonathan WU Liping YAN School of Artificial Intelligence Beijing University of Posts and Telecommunications Department of Electrical and Computer Engineering University of Windsor Key Laboratory of Intelligent Control and Decision of Complex Systems School of AutomationBeijing Institute of Technology

Inspired by the robust student t-distribution based nonlinear filter(RSTNF), a student tdistribution and unscented transform(UT) based filter for state estimation of heavy-tailed nonlinear dynamic systems, a modified RSTNF for intermittent observations is derived. The fusion estimation for nonlinear multisensor systems with intermittent observations and heavy-tailed measurement and process noises is *** this work, the centralized fusion, the sequential fusion, and the na¨?ve distributed fusion algorithms are presented, respectively. Theoretical analysis shows that the presented algorithms are effective, which are the efficient extension of the classical unscented Kalman filter(UKF) or the cubature Kalman filter(CKF) based algorithms with Gaussian noises. Simulation results show that the presented algorithms are effective and feasible.

关键词： state fusion estimation nonlinear systems heavy-tailed noise intermittent observations multivariate t-distribution

Worst-Case Integrity Attacks and Resilient State Estimation With Partially Secured Measurements

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IEEE Transactions on control of Network systems 2025年

作者： Zhou, Jing Shang, Jun Chen, Tongwen University of Alberta Department of Electrical and Computer Engineering EdmontonABT6G 1H9 Canada Tongji University Department of Control Science and Engineering Shanghai Institute of Intelligent Science and Technology National Key Laboratory of Autonomous Intelligent Unmanned Systems Frontiers Science Center for Intelligent Autonomous Systems Shanghai200092 China

This paper examines the problem of optimal deception attacks against state estimation with partially secured measurements, where smart sensors transmit innovation sequences to the remote end for information fusion. Due to resource limitations or defensive countermeasures, the adversary can only modify data packets transmitted through unreliable channels. Meanwhile, the attack should be synthesized with sophistication to deceive an anomaly detector. To investigate the vulnerabilities of such estimation systems without feedback links and enhance security performance, the optimal attack policy is derived by formulating and explicitly solving a convex optimization problem, with the goal of maximizing the sum of estimation errors. Subsequently, a novel attack detection and resilient state estimation algorithm is proposed to ensure an acceptable level of estimation accuracy. The theoretical performance metrics, including false alarm rates for the proposed detector, are provided. Finally, the effectiveness of the results is confirmed through numerical examples. © 2014 IEEE.

关键词： Optimal detection

Learning a Better control Barrier Function

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arXiv 2022年

作者： Dai, Bolun Krishnamurthy, Prashanth Khorrami, Farshad Control/Robotics Research Laboratory Electrical & Computer Engineering Department Tandon School of Engineering New York University BrooklynNY11201 United States

control barrier functions (CBFs) are widely used in safety-critical controllers. However, constructing a valid CBF is challenging, especially under nonlinear or non-convex constraints and for high relative degree systems. Meanwhile, finding a conservative CBF that only recovers a portion of the true safe set is usually possible. In this work, starting from a "conservative" handcrafted CBF (HCBF), we develop a method to find a CBF that recovers a reasonably larger portion of the safe set. Since the learned CBF controller is not guaranteed to be safe during training iterations, we use a model predictive controller (MPC) to ensure safety during training. Using the collected trajectory data containing safe and unsafe interactions, we train a neural network to estimate the difference between the HCBF and a CBF that recovers a closer solution to the true safe set. With our proposed approach, we can generate safe controllers that are less conservative and computationally more efficient. We validate our approach on two systems: a second-order integrator and a ball-on-beam. © 2022, CC BY.

关键词： controllers

Carbon-Aware Computing in a Network of Data Centers: A Hierarchical Game-Theoretic Approach

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arXiv 2024年

作者： Breukelman, Enno Hall, Sophie Belgioioso, Giuseppe Dörfler, Florian The KTH Royal Institute of Technology School of Electrical Engineering and Computer Science Division of Decision and Control Systems Malvinas väg 10 StockholmSE-100 44 Sweden The Automatic Control Laboratory Department of Electrical Engineering and Information Technology ETH Zurich Physikstrasse 3 Zürich8092 Switzerland

Over the past decade, the continuous surge in cloud computing demand has intensified data center workloads, leading to significant carbon emissions and driving the need for improving their efficiency and sustainability. This paper focuses on the optimal allocation problem of batch compute loads with temporal and spatial flexibility across a global network of data centers. We propose a bilevel game-theoretic solution approach that captures the inherent hierarchical relationship between supervisory control objectives, such as carbon reduction and peak shaving, and operational objectives, such as priority-aware scheduling. Numerical simulations with real carbon intensity data demonstrate that the proposed approach successfully reduces carbon emissions while simultaneously ensuring operational reliability and priority-aware scheduling. © 2024, CC BY-NC-ND.

关键词： Carbon

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

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

IEEE Conference on Decision and control

作者： Gehui Xu Guanpu Chen Baris Fidan Yiguang Hong Hongsheng Qi Thomas Parisini Karl H. Johansson Department of Electrical and Electronic Engineering Imperial College London London UK Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden Department of Mechanical and Mechatronics Engineering University of Waterloo Waterloo ON Canada Department of Control Science and Engineering Tongji University shanghai China Shanghai Research Institute for Intelligent Autonomous Systems Shanghai China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Beijing China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing China Department of Electronic Systems Aalborg University Denmark Department of Engineering and Architecture University of Trieste Italy

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

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.

关键词： Location awareness Noise Games Position measurement Nash equilibrium Distance measurement Noise measurement

Performance Analysis of Distributed Filtering under Mismatched Noise Covariances

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arXiv 2024年

作者： Lyu, Xiaoxu Wen, Guanghui Shi, Ling Duan, Peihu Duan, Zhisheng The Department of Electronic and Computer Engineering Hong Kong University of Science and Technology Hong Kong The Laboratory of Security Operation and Control for Intelligent Autonomous Systems Department of Systems Science School of Mathematics Southeast University Nanjing211189 China School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering Science College of Engineering Peking University Beijing100871 China

This paper systematically investigates the performance of consensus-based distributed filtering under mismatched noise covariances. First, we introduce three performance evaluation indices for such filtering problems, namely the standard performance evaluation index, the nominal performance evaluation index, and the estimation error covariance. We derive difference expressions among these indices and establish one-step relations among them under various mismatched noise covariance scenarios. We particularly reveal the effect of the consensus fusion on these relations. Furthermore, the recursive relations are introduced by extending the results of the one-step relations. Subsequently, we demonstrate the convergence of these indices under the collective observability condition, and show this convergence condition of the nominal performance evaluation index can guarantee the convergence of the estimation error covariance. Additionally, we prove that the estimation error covariance of the consensus-based distributed filter under mismatched noise covariances can be bounded by the Frobenius norms of the noise covariance deviations and the trace of the nominal performance evaluation index. Finally, the effectiveness of the theoretical results is verified by numerical simulations. Copyright © 2024, The Authors. All rights reserved.

关键词： Wiener filtering

Data-Driven Learning and control with Event-Triggered Measurements

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IEEE Transactions on Automatic control 2025年

作者： Feng, Shilun Shi, Dawei Chen, Tongwen Shi, Ling Beijing Institute of Technology State Key Laboratory of Intelligent Control and Decision of Complex Systems MIIT Key Laboratory of Servo Motion System Drive and Control School of Automation Beijing100081 China University of Alberta Department of Electrical and Computer Engineering EdmontonABT6G 1H9 Canada Hong Kong University of Science and Technology Department of Electronic and Computer Engineering Clear Water Bay Kowloon Hong Kong

Event-triggered control has attracted considerable attention for its effectiveness in resource-restricted applications. To make event-triggered control as an end-to-end solution, a key issue is how to effectively learn unknown system dynamics from event-triggered measurements and consequently, develop a learning-based event-triggered controller. Existing works learn system dynamics based on periodic time-triggered measurements, and it is yet to know how to learn a controller with performance guarantee based on event-triggered measurements. To address this issue, we consider the problem of learning an event-triggered state feedback controller for an unknown linear system based on event-triggered state measurements in this work. In particular, we first analyze the event-triggered measurements within a set-membership framework. We prove that the estimation error belongs to a bounded ellipsoid determined by the historical measurements and the event-triggering condition. Subsequently, we demonstrate that all admissible systems compatible with the collected data samples can be explicitly represented in the form of quadratic matrix inequalities using the state estimates. With the acquired set of admissible systems, a co-design problem for the data-driven controller and event-triggering condition is solved using the linear matrix inequality technique, with guaranteed closed-loop stability and L2-gain performance. Finally, numerical examples and comparisons are provided to illustrate the effectiveness of the proposed event-triggered learning and control approach. © 1963-2012 IEEE.

关键词： Networked control systems