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arXiv 2023年

作者： Skrzypczyk, Paul Cavalcanti, Daniel

Semidefinite programs (SDPs) are a class of optimisation problems that findapplication in numerous areas of physics, engineering and *** programming is particularly suited to problems in quantum physicsand quantum information science. Following a review of the theory ofsemidefinite programming, the book proceeds to describe how it can be used toaddress a wide range of important problems from across quantum informationscience. Specific applications include quantum state, measurement, and channelestimation and discrimination, entanglement detection and quantification,quantum distance measures, and measurement incompatibility. Though SDPs havebecome an increasingly important tool in quantum information science it\'s notyet the kind of mathematics students learn routinely. Assuming only a basicknowledge of linear algebra and quantum physics and quantum information, thisgraduate-level book provides a unified and accessible presentation of one ofthe key numerical methods used in quantum information science. Copyright © 2023, The Authors. All rights reserved.

关键词： linear algebra

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Quantised control of delayed Markovian jump systems with partly known transition probabilities

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IET CONTROL theory AND applications 2021年第3期15卷 372-389页

作者： Yang, Ning Chen, Dongyan Hu, Jun Harbin Univ Sci & Technol Dept Math Harbin 150080 Peoples R China Univ South Wales Sch Engn Pontypridd M Glam Wales

This paper is devoted to solve the quantised control problem of the continuous-time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities. For the Markov chain, the transition rates are assumed to be partly known. The involved mixed time delays comprise both time-varying delays and distributed delays. The logarithmic quantiser is introduced in the design of the state feedback controller and the uncertainty is entered into the quantization error matrix represented by an interval matrix. Based on the generalised Ito's formula, the free-connection weighting matrix method and the stochastic analysis theory, several novel sufficient conditions are derived to guarantee that the trivial solution of the closed-loop system is robustly exponentially stable in the mean square. Then, the concrete expression form of the desired controller gain is obtained via the solutions to a set of linear matrix inequalities. In addition, the corresponding stability criteria are given for three special situations of Markovian jump systems. Finally, a numerical example and a practical example (the wheeled mobile manipulator) are provided to show the feasibility and availability of the proposed theoretical results.

关键词： algebra Markov processes Other topics in statistics linear control systems Control system analysis and synthesis methods Stability in control theory Discrete control systems Time-varying control systems Distributed parameter control systems

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An Efficient Single-pass Online Computation of Higher-Order Bivariate Statistics

An Efficient Single-pass Online Computation of Higher-Order ...

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IEEE International conference on Big Data

作者： Ilya Stupakov Anton Kochepasov Novosibirsk State Technical University Novosibirsk Russia Non Academic San Francisco California United States

ISBN: (数字)9798350362480

ISBN: (纸本)9798350362497

Bivariate statistical moments are widely used in many areas of academic research and industry, beyond covariance matrices. Relationships between pairs of random variables can be further used to test hypotheses, which require higher-order bivariate moments. To reveal subtle patterns and differences, the processing of millions of observations across numerous variables may be necessary, posing significant challenges, especially for streaming data. This study introduces an efficient, single-pass methodology to compute central statistical co-moments of arbitrary order on large, continuous data streams. Our approach employs two key steps: (1) constructing a dense memory layout for input data batches enabling a single-pass matrix transformation, and (2) performing intermediate accumulation using optimized linear algebra subprograms (BLAS), resulting in a fast and scalable streaming solution. This method accelerates computation, essential for real-time analytics at scale. At any point, the accumulated data can be transformed to yield the desired higher-order bivariate moments. We also address numerical stability issues and propose a solution to maintain accuracy across millions of observations. Experimental results show that our method outperforms current streaming methods by more that an order of magnitude, advancing the extraction of bivariate statistical insights for data-intensive and time-sensitive applications.

关键词： Performance evaluation Industries Accuracy Scalability Layout linear algebra Real-time systems Random variables numerical stability Streams

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The Reachable Set Estimation for Continuous-time Delayed Nonlinear Switched Systems with Impulsive Perturbation

The Reachable Set Estimation for Continuous-time Delayed Non...

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Fully Actuated System theory and applications (CFASTA), conference on

作者： Qingzheng Guo Zhiguang Feng College of Intelligent Systems Science and Engineering Harbin Engineering University Harbin P. R. China

ISBN: (数字)9798350373691

ISBN: (纸本)9798350373707

In this paper, we mainly study the reachable set estimation problem of the continuous-time delayed nonlinear switched systems with impulsive perturbation under the condition of zero initial state and bounded peak disturbances. The purpose is to acquire a set of bounded ellipsoids that can include all the states starting from the origin. By adopting the real bounded lemma, integral inequality techniques, the free weight matrix method, we get a sufficient condition in the form of linear matrix inequality (LMI) for the continuous-time delayed nonlinear switched system with impulsive perturbation, so as to insure that all the state trajectories of the studied system are restricted to a closed bounded set. Eventually, a specific numerical example is given to illustrate the effectiveness and correctness of the results obtained in this paper.

关键词： Switched systems Sufficient conditions Perturbation methods Integral equations Estimation Control systems linear matrix inequalities

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Finite-horizon optimal tracking control for constrained-input nonlinear interconnected system using aperiodic distributed nonzero-sum games

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IET CONTROL theory AND applications 2021年第9期15卷 1199-1213页

作者： Duan, Dandan Liu, Chunsheng Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing 210016 Jiangsu Peoples R China

This paper proposes a distributed adaptive dynamic programming scheme to investigate the optimal tracking control problem for finite-horizon non-linear interconnected systems with constraint inputs under aperiodic sampling. A N-player nonzero-sum differential game system is constructed with the presented non-linear interconnected system and the tracking error system by introducing the augment vectors. To address the problems of constrained-input and finite-horizon control, a non-quadratic utility function and a finite-horizon cost function are utilized which will arise in the time-varying Hamilton-Jacobi (HJ) equation. Then, a periodic event-triggered scheme is designed to realize aperiodic sampling, where the consumption of communication resources is reduced and the Zeno behavior is avoided. Under the designed periodic event-triggered scheme, the time-varying HJ equation is almost impossible to get an analytical solution due to its hybrid properties and non-linearity. Therefore, the critic neural networks are used to estimate the optimal solution of the HJ equation, and the weight update law is constructed to guarantee the uniformly ultimate bounded of approximated errors. Further, the hybrid nonzero-sum differential game is confirmed to be uniformly ultimate bounded by using the Lyapunov theory. Finally, the obtained distributed PET control strategy is successfully applied to dispose the missile-target intercepter problem.

关键词： Optimisation techniques Interpolation and function approximation (numerical analysis) algebra Game theory Other topics in statistics Combinatorial mathematics Control system analysis and synthesis methods Stability in control theory Optimal control Multivariable control systems Discrete control systems Self-adjusting control systems Nonlinear control systems

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Bayesian Graph Signal Estimation in Nonlinear GSP Models with Multiple Topologies

Bayesian Graph Signal Estimation in Nonlinear GSP Models wit...

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Annual conference on Information Sciences and Systems (CISS)

作者： Eyal Zeltzer Tirza Routtenberg School of ECE Ben-Gurion University of the Negev Beer-Sheva Israel

ISBN: (数字)9798331513269

ISBN: (纸本)9798331513276

Dynamic systems with evolving graph topologies arise in applications such as power grids and sensor networks. Conventional graph signal estimation methods often assume fixed topologies, limiting their applicability in dynamic environments. In this paper, we address the problem of Bayesian graph signal estimation in nonlinear models with varying networks by leveraging graph filters from graph signal processing (GSP) theory. We use the criterion of averaged mean-squared error (AMSE) across topologies, and develop the GSP-minimum linear AMSE (GSP-MLAMSE) estimator, which minimizes the AMSE among graph-filter-based estimators. We demonstrate that the GSP-MLAMSE estimator extends the GSP linear minimum mean-squared-error (GSP-LMMSE) estimator [1] to the case of multiple topologies. In addition, we prove that it achieves the minimum linear AMSE estimator for orthogonal graph frequencies. We also develop its parametric version via the Chebyshev graph filter, which ensures numerical stability and scalability while maintaining robustness to topology variations. Simulations of power system state estimation demonstrate significant improvements in the AMSE and robustness across varying signal-to-noise ratios (SNRs) compared to existing methods.

关键词： Filters Network topology Scalability Power system stability Robustness Topology Bayes methods numerical models State estimation Signal to noise ratio

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Beyond PCA: A Gram-Schmidt Approach to Feature Extraction

Beyond PCA: A Gram-Schmidt Approach to Feature Extraction

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Annual Allerton conference on Communication, Control, and Computing

作者： Bahram Yaghooti Netanel Raviv Bruno Sinopoli Department of Electrical and Systems Engineering Washington University in St. Louis St. Louis MO USA Department of Computer Science and Engineering Washington University in St. Louis St. Louis MO USA

ISBN: (数字)9798331541033

ISBN: (纸本)9798331541040

linear feature extraction at the presence of nonlinear dependencies among the data is a fundamental challenge in unsupervised learning. We propose using a Gram-Schmidt (GS) type orthogonalization process over function spaces in order to detect and remove redundant dimensions. Specifically, by applying the GS process over a family of functions which presumably captures the nonlinear dependencies in the data, we construct a series of covariance matrices that can either be used to identify new large-variance directions, or to remove those dependencies from the principal components. In the former case, we provide information-theoretic guarantees in terms of entropy reduction. In the latter, we prove that under certain assumptions the resulting algorithms detect and remove nonlinear dependencies whenever those dependencies lie in the linear span of the chosen function family. Both proposed methods extract linear features from the data while removing nonlinear redundancies. We provide simulation results on synthetic and real-world datasets which show improved performance over state-of-the-art feature extraction algorithms.

关键词： numerical analysis Simulation Redundancy linear algebra Feature extraction Entropy Data mining Unsupervised learning Principal component analysis Information theory

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Response Estimation and Reference Model-free Controller Design Approach for 2-DOF Control Systems

Response Estimation and Reference Model-free Controller Desi...

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Fully Actuated System theory and applications (CFASTA), conference on

作者： Ruirui Yang Kazuhiro Yubai Satoshi Komada Daisuke Yashiro Weijie Ren Department of Electrical and Electronic Engineering Mie University Kurimamachiya Tsu Japan Shenzhen Key Laboratory of Control Theory and Intelligent Systems Southern Uni. of Sci. and Tech Shenzhen China

ISBN: (数字)9798350373691

ISBN: (纸本)9798350373707

In this paper, we adopt a linear time-invariant (LTI) two-degree-of-freedom (2-DOF) control system as our subject of control. An input-output response estimation method and a controller design method based on response estimation are proposed. First, using the initial input-output data of a closed-loop system to estimate the response when updating controller parameters. Second, the controller parameters are updated by optimizing the objective function based on the estimated response data. Finally, numerical examples verify the effectiveness of the proposed method. Unlike traditional data-driven design methods based on reference models, the proposed controller design method does not require a reference model, which solves the problem of the difficulty of selecting a suitable reference model. Additionally, the response after the controller update can be estimated in advance before being applied to the real machine system. Avoiding the wear and tear or damage of the machine caused by the direct real machine test when the designed controller is not ideal, meanwhile saving the experimental cost.

关键词： linear systems Design methodology Noise Estimation 2-DOF Process control numerical models

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Hierarchic distributed stabilization of a class of three-dimensional formations for underactuated agents

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IET CONTROL theory AND applications 2021年第3期15卷 472-488页

作者： El-Hawwary, Mohamed I. Cairo Univ Fac Engn Dept Elect Dept Elect Power Engn Giza 12613 Egypt KTH Royal Inst Technol Div Decis & Control Syst Stockholm Sweden

The paper presents a distributed hierarchic control design solving a formations problem in three dimension. The agents are modelled as thrust-underactuated rigid bodies. The class of formations addressed encompasses path following of closed convex paths with shape, size, orientation, relative displacements and relative agents' on-path angular positions all seen as formation parameters. This problem can be seen as a generalization of circular formation problems which acquired particular attention in the field of multi-agents, and the agents model used is one that usually models certain unmanned aerial vehicles and other autonomous vehicles. The solution relies on reduction-based set stabilization where the problem is broken down into simpler nested sub-problems. The results illustrate how addressing complex control problems using hierarchical set stabilization is natural, simplifies the solution, and provides useful properties. The results are illustrated via simulations.

关键词： Spatial variables control Aerospace control Mobile robots linear algebra (numerical analysis) Combinatorial mathematics Control system analysis and synthesis methods Stability in control theory Multivariable control systems

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An Overview of applications of Gaussian numerical methods 2

An Overview of Applications of Gaussian Numerical Methods

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2nd International conference on Smart Electronics and Communication, ICOSEC 2021

作者： Tewari, Yogya Hadap, Arti Soni, Payal Sharma, Muskan Shukla, Daksh Malanker, Shreya NMIMS MPSTME Dept. of Computer Engineering Mumbai India

ISBN: (纸本)9781665433686

numerical methods have widespread applications in Engineering and the Gaussian methods are extensively used for solving complex equations as these methods arrive at a solution without the need for matrix inversion, they save on computation cost and time. The various methods namely Gauss Elimination, Gauss Seidel and Gauss Jordan have vast applications in fluid chemistry, massive MIMO technology, puzzle solving, resolving RFID in wireless network, Real time character inverse kinematics, and many more. The paper explores various applications of Gaussian methods as well as compares them based on performance, speed and efficiency. © 2021 IEEE.

关键词： linear algebra

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