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Weighted Null Space Fitting (WNSF): A Link between The Prediction Error Method and Subspace Identification

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arXiv 2024年

作者： He, Jiabao Hjalmarsson, Håkan Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm100 44 Sweden

— Subspace identification method (SIM) has been proven to be very useful and numerically robust for estimating state-space models. However, it is in general not believed to be as accurate as prediction error method (PEM). Conversely, PEM, although more accurate, comes with non-convex optimization problems and requires local non-linear optimization algorithms and good initialization points. This contribution proposes a weighted null space fitting (WNSF) method to identify a state-space model, combining some advantages of the two mainstream approaches aforementioned. It starts with the estimate of a nonparametric model using least-squares, and then the reduction to a state-space model in the observer canonical form is a multi-step least-squares procedure where each step consists of the solution of a quadratic optimization problem. Unlike SIM, which focuses on the range space of the extended observability matrix, WNSF estimates its null space, avoiding the need for singular value decomposition. Moreover, the statistically optimal weighting for the null space fitting problem is derived. It is conjectured that WNSF is asymptotically efficient, which is supported by a simulation study. Copyright © 2024, The Authors. All rights reserved.

关键词： State space methods

Uncertainty-Informed Model Selection Method for Nonlinear System Identification and Interpretable Machine Learning

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Uncertainty-Informed Model Selection Method for Nonlinear Sy...

Mediterranean Conference on control and Automation (MED)

作者： Yuanlin Gu Hua-Liang Wei Division of Computer Science and Maths University of Stirling Stirling United Kingdom Department of Automatic Control and Systems Engineering University of Sheffield Sheffield

ISBN: (数字)9798350395440

ISBN: (纸本)9798350395457

Modeling uncertainty has been an active and important topic in the fields of data-driven modeling and machine learning. Uncertainty ubiquitously exists in any data modeling process, making it challenging to identify the optimal models among many potential candidates. This article proposes an uncertainty-informed method to address the model selection problem. The performance of the proposed method is evaluated on a dataset generated from a complex system model. The experimental results demonstrate the effectiveness of the proposed method and its superiority over conventional approaches. This method has minimal requirements for the length of training data and model types, making it applicable for various modeling frameworks.

关键词： Data-driven modeling Adaptation models Uncertainty Recurrent neural networks Training data Machine learning Data models

A Weighted Least-Squares Method for Non-Asymptotic Identification of Markov Parameters from Multiple Trajectories

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arXiv 2024年

作者： He, Jiabao Rojas, Cristian R. Hjalmarsson, Håkan Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm100 44 Sweden

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step least-squares algorithms, such as Weighted Null-Space Fitting. Recently, there has been an increasing interest in non-asymptotic analysis of estimation algorithms. In this contribution we identify the Markov parameters using weighted least-squares and present non-asymptotic analysis for such estimator. To cover both stable and unstable systems, multiple trajectories are collected. We show that with the optimal weighting matrix, weighted least-squares gives a tighter error bound than ordinary least-squares for the case of non-uniformly distributed measurement errors. Moreover, as the optimal weighting matrix depends on the system’s true parameters, we introduce two methods to consistently estimate the optimal weighting matrix, where the convergence rate of these estimates is also provided. Numerical experiments demonstrate improvements of weighted least-squares over ordinary least-squares in finite sample settings. Copyright © 2024, The Authors. All rights reserved.

关键词： Asymptotic analysis

Benchmarking Semantic Communications for Image Transmission Over MIMO Interference Channels

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Benchmarking Semantic Communications for Image Transmission ...

International Conference on Wireless Communications and Signal Processing (WCSP)

作者： Yanhu Wang Shuaishuai Guo Anming Dong Hui Zhao School of Control Science and Engineering Shandong University School of Computer Science and Technology Qilu University of Technology Communication Systems Department EURECOM

ISBN: (数字)9798350390643

ISBN: (纸本)9798350390650

Semantic communications offer promising prospects for enhancing data transmission efficiency. However, existing schemes have predominantly concentrated on point-to-point transmissions. In this paper, we aim to investigate the validity of this claim in interference scenarios compared to baseline approaches. Specifically, our focus is on general multiple-input multiple-output (MIMO) interference channels, where we propose an interference-robust semantic communication (IRSC) scheme. This scheme involves the development of transceivers based on neural networks (NNs), which integrate channel state information (CSI) either solely at the receiver or at both transmitter and receiver ends. Moreover, we establish a composite loss function for training IRSC transceivers, along with a dynamic mechanism for updating the weights of various components in the loss function to enhance system fairness among users. Experimental results demonstrate that the proposed IRSC scheme effectively learns to mitigate interference and outperforms baseline approaches, particularly in low signal-tonoise (SNR) regimes.

关键词： Wireless communication Training Transmitters Receivers Artificial neural networks Signal processing Semantic communication Transceivers Interference channels Signal to noise ratio

Accelerating Distributed Nash Equilibrium Seeking

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Accelerating Distributed Nash Equilibrium Seeking

European control Conference (ECC)

作者： Tatiana Tatarenko Angelia Nedić Department of Control Theory and Intelligent Systems TU Darmstadt German School of Electrical Computer and Energy Engineering Arizona State University USA

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to solve variational inequalities, we develop the algorithm converging to Nash equilibria in games, where players have no access to the full information but are able to communicate with neighbors over some communication graph. The convergence rate is demonstrated to be geometric and improves the rates obtained by the previously presented procedures seeking Nash equilibria in the class of games under consideration.

关键词： Extrapolation Europe Games Nash equilibrium Topology Convergence

Coherence-based Input Design for Sparse System Identification

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arXiv 2024年

作者： Parsa, Javad Rojas, Cristian R. Hjalmarsson, Håkan Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm100 44 Sweden

The maximum absolute correlation between regressors, which is called mutual coherence, plays an essential role in sparse estimation. A regressor matrix whose columns are highly correlated may result from optimal input design, since there is no constraint on the mutual coherence, so when this regressor is used to estimate sparse parameter vectors of a system, it may yield a large estimation error. This paper aims to tackle this issue for fixed denominator models, which include Laguerre, Kautz, and generalized orthonormal basis function expansion models, for example. The paper proposes an optimal input design method where the achieved Fisher information matrix is fitted to the desired Fisher matrix, together with a coordinate transformation designed to make the regressors in the transformed coordinates have low mutual coherence. The method can be used together with any sparse estimation method and in a numerical study we show its potential for alleviating the problem of model order selection when used in conjunction with, for example, classical methods such as AIC and BIC. © 2024, CC BY.

关键词： Fisher information matrix

On final opinions of the Friedkin-Johnsen model over random graphs with partially stubborn community

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On final opinions of the Friedkin-Johnsen model over random ...

IEEE Conference on Decision and control

作者： Lingfei Wang Yu Xing Karl H. Johansson Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology and with Digital Futures Stockholm Sweden

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

This paper studies the formation of final opinions for the Friedkin-Johnsen (FJ) model with a community of partially stubborn agents. The underlying network of the FJ model is symmetric and generated from a random graph model, in which each link is added independently from a Bernoulli distribution. It is shown that the final opinions of the FJ model will concentrate around those of an FJ model over the expected graph as the network size grows, on the condition that the stubborn agents are well connected to other agents. Probability bounds are proposed for the distance between these two final opinion vectors, respectively for the cases where there exist non-stubborn agents or not. Numerical experiments are provided to illustrate the theoretical findings. The simulation shows that, in presence of non-stubborn agents, the link probability between the stubborn and the non-stubborn communities affect the distance between the two final opinion vectors significantly. Additionally, if all agents are stubborn, the opinion distance decreases with the agent stubbornness.

关键词： Vectors Numerical models

Weighted Least-Squares PARSIM

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arXiv 2024年

Subspace identification methods (SIMs) have proven very powerful for estimating linear state-space models. To overcome the deficiencies of classical SIMs, a significant number of algorithms has appeared over the last two decades, where most of them involve a common intermediate step, that is to estimate the range space of the extended observability matrix. In this contribution, an optimized version of the parallel and parsimonious SIM (PARSIM), PARSIMopt, is proposed by using weighted least-squares. It not only inherits all the benefits of PARSIM but also attains the best linear unbiased estimator for the above intermediate step. Furthermore, inspired by SIMs based on the predictor form, consistent estimates of the optimal weighting matrix for weighted least-squares are derived. Essential similarities, differences and simulated comparisons of some key SIMs related to our method are also presented. Copyright © 2024, The Authors. All rights reserved.

关键词： State space methods

A Moreau Envelope Approach for LQR Meta-Policy Estimation

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A Moreau Envelope Approach for LQR Meta-Policy Estimation

IEEE Conference on Decision and control

作者： Ashwin Aravind Mohammad Taha Toghani César A. Uribe Centre for Systems and Control IIT Bombay Mumbai MH India Department of Electrical and Computer Engineering Rice University Houston TX USA

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

We study the problem of policy estimation for the Linear Quadratic Regulator (LQR) in discrete-time linear timeinvariant uncertain dynamical systems. We propose a Moreau Envelope-based surrogate LQR cost, built from a finite set of realizations of the uncertain system, to define a meta-policy efficiently adjustable to new realizations. Moreover, we design an algorithm to find an approximate first-order stationary point of the meta-LQR cost function. Numerical results show that the proposed approach outperforms naive averaging of controllers on new realizations of the linear system. We also provide empirical evidence that our method has better sample complexity than Model-Agnostic Meta-Learning (MAML) approaches.

关键词： Linear systems Uncertain systems Costs Uncertainty System realization Estimation Cost function Numerical models Trajectory Convergence