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4th Modeling, Estimation, and Control Conference (MECC)

作者： Xu, Lingyi Gajic, Zoran Rutgers State Univ Dept Elect & Comp Engn Piscataway NJ 08854 USA

This paper demonstrates that the value iteration (VI) algorithm of reinforcement learning of discrete -time (DT) linear-quadratic (LQ) optimal control problem converges very slowly mostly linearly, compared to the quadratic rate of convergence of the corresponding policy iteration (PI) algorithm. The VI algorithm produces non-monotonically decreasing or increasing sequences that converge to the optimal value either from below or from above depending on the choice of initial conditions. It is remarkable that the VI algorithm converges even in the case when the initial condition is very far from the optimal value by several orders of magnitude, and when the initial condition is not stabilizing. The PI algorithm generates a non-increasing sequence that monotonically converges from above to the optimal value assuming the initial condition (feedback gain) is stabilizing. The convergence rate for the PI algorithm is quadratic, which assures its fast convergence. It is shown in this paper that the convergence of the VI algorithm can be made quadratic by using the doubling algorithm. We precisely state a condition needed for convergence of the VI algorithm, which is milder than the corresponding convergence condition for the PI algorithm. We have also shown that the newly proposed VI algorithm requires less computational effort than the PI algorithm. Several numerical examples are solved to document the presented results.

关键词： Reinforcement learning policy iteration algorithm value iteration algorithm linear-quadratic discrete -time optimal control numerical complexity

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Convergence and numerical complexity of Policy and Value Iterations in Linear-Quadratic Discrete-Time Reinforcement Learning

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IFAC-PapersOnLine 2024年第28期58卷 96-101页

作者： Lingyi Xu Zoran Gajić Department of Electrical & Computer Engineering Rutgers The State University of New Jersey Piscataway NJ 08854 USA

This paper demonstrates that the value iteration (VI) algorithm of reinforcement learning of discrete-time (DT) linear-quadratic (LQ) optimal control problem converges very slowly mostly linearly, compared to the quadratic rate of convergence of the corresponding policy iteration (PI) algorithm. The VI algorithm produces non-monotonically decreasing or increasing sequences that converge to the optimal value either from below or from above depending on the choice of initial conditions. It is remarkable that the VI algorithm converges even in the case when the initial condition is very far from the optimal value by several orders of magnitude, and when the initial condition is not stabilizing. The PI algorithm generates a non-increasing sequence that monotonically converges from above to the optimal value assuming the initial condition (feedback gain) is stabilizing. The convergence rate for the PI algorithm is quadratic, which assures its fast convergence. It is shown in this paper that the convergence of the VI algorithm can be made quadratic by using the doubling algorithm. We precisely state a condition needed for convergence of the VI algorithm, which is milder than the corresponding convergence condition for the PI algorithm. We have also shown that the newly proposed VI algorithm requires less computational effort than the PI algorithm. Several numerical examples are solved to document the presented results.

关键词： Reinforcement learning policy iteration algorithm value iteration algorithm linear-quadratic discrete-time optimal control numerical complexity

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numerical complexity Study of Solving Hybrid Multiport Field-Circuit Problems for Diode Grids 21

Numerical Complexity Study of Solving Hybrid Multiport Field...

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21st International Conference on Electromagnetics in Advanced Applications (ICEAA)

作者： Wendt, Torben Yang, Cheng Schuster, Christian Grivet-Talocia, S. Hamburg Univ Technol Inst Electromagnet Theory Hamburg Germany Politecn Torino Dept Elect & Telecommun Turin Italy

ISBN: (纸本)9781728105635

Nonlinearly loaded multiport structures have promising features for the application of controlling scattered fields. Modelling such structures can lead to investigations up to hundreds or even thousands of ports, which poses a challenge to full-wave simulation techniques. In order to identify limitations for large scale problems, a hybrid simulation method using macromodeling and recursive convolution is adopted due to its scalability. A numerical complexity analysis is carried out for the extraction of frequency data, macromodeling of the network parameters and computation of transient responses. Of particular interest are the number of ports, load types, wave excitations and field probes. Bottlenecks are identified and possible improvements of the adopted method are proposed.

关键词： numerical complexity multiport field-circuit diode grids

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An ecological approach for skill development and performance in soccer goalkeeper training: Empirical evidence and coaching applications

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JOURNAL OF SPORTS SCIENCES 2025年第1期43卷 71-82页

作者： Bastias, Elliot Otte, Fabian W. Vaughan, James Swainston, Scott O' Sullivan, Mark AIK Fotboll Res & Dev Dept Stockholm Sweden Borussia Monchengladbach Monchengladbach Germany Univ Exeter Dept Sport & Hlth Sci Exeter England Norwegian Sch Sport Sci Dept Sport & Social Sci Oslo Norway AIK Fotboll Res & Dev Dept Evenemangsgatan 31 S-16979 Solna Sweden

Ecological approaches in sport consider that athletes adapt to properties of the task and the surrounding environment. Thus, task and environment are key constraints of performance. Yet, the influence of task and environmental constraints on athletes' performance needs empirical examination, especially in sport-specific contexts such as soccer goalkeeping. This study aimed to examine if and how task and environmental constraints influenced goalkeepers (GKs') performances. We monitored performance coefficients of two professional female GKs across 13 training tasks that varied based on 9 constraints, referring to both interactions among athletes and properties of the surrounding landscape. Results showed that constraints explain similar to 47% of the observed variability in GKs' performances. numerical complexity (i.e., the potential interactions between athletes) showed a major influence on performance, which indicates that number of interactions among athletes may constrain GKs' perceived opportunities for action. Field dimensions and landscape representativity (including elements such as penalty area(s), target goal(s) and constraints for shooting) showed positive relationships with performance, supporting that training designs retaining closer proximity to the game may benefit GKs' performances. Overall, results supported that athlete-environment couplings could be understood as a multifactorial model and hence, a combination of task constraints are necessary for designing effective learning environments.

关键词： Performance coefficients tasks constraints environmental constraints numerical complexity "periodization of skill training" (PoST) framework

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Power Amplifier Linearization in the Presence of Crosstalk and Measurement Noise in MIMO System

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2022年第10期69卷 3988-3992页

作者： Shipra Tripathi, Girish Chandra Rawat, Meenakshi Indian Inst Technol Roorkee Dept Elect & Commun Engn Roorkee 247667 Uttar Pradesh India

The crosstalk and transceiver noise is an intrinsic part of the multiple-input and multiple-output (MIMO) System, becoming more prominent in low-cost systems. Moreover, the power amplifiers (PAs) cause nonlinearity, propagating to the complete chain. The conventional techniques do not provide the joint method for crosstalk, transceiver noise, and PA nonlinearity. This results in the performance limitation of the digital predistortion (DPD). Hence we propose a wavelet multiscale principal component analysis (PCA) based technique to deal with such problems (crosstalk, transceiver noise, and system nonlinearities). It is reported using measurement and simulation that numerical stability issue is no longer an issue when wavelet multiscale PCA-based DPD is applied. The effect of wavelet multiscale PCA on bit-resolution of DPD is shown to be better than established DPD Models. On a field-programmable gate array and direct conversion transceiver-based platform, the performance of the proposed model is analyzed using PA. Parameters like normalized mean square error have shown an improvement of around 23 dB and adjacent channel error power ratio has shown an improvement of around 22 dBc for a ZX60-V63+ power amplifier using LTE-OFDM signals.

关键词： MIMO communication Principal component analysis Crosstalk Transmitters numerical models Mathematical models Wavelet analysis Adjacent channel error power ratio (ACEPR) crosstalk digital predistortion (DPD (multiple-input-multiple-output) MIMO numerical complexity power amplifier (PA) wavelet multiscale PCA (WMSPCA)

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Choosing an Adequate Convex Structure for Controller and Observer Gains in Takagi-Sugeno Control Systems 4th

Choosing an Adequate Convex Structure for Controller and Obs...

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4th IFAC Conference on Embedded Systems, Computational Intelligence and Telematics in Control (CESCIT)

作者： Ortiz, Alberto Guerra, Thierry-Marie Estrada-Manzo, Victor Lauber, Jimmy Univ Politecn Pachuca Dept Mechatron Zempoala 43830 Mexico Polytech Univ Hauts France UPHF LAMIH UMR CNRS 8201 Valenciennes France

This work presents a methodology to choose the convex structure for nonlinear gains in approaches based on Takagi-Sugeno models. The proposal faces the problem of numerical complexity in LMI-based approaches within this area;it gives a finer convex structure for controller and observer matrices depending on two criteria: less number of LMI constraints or more decision variables while keeping the same number of LMIs in traditional approaches. The advantages of the proposal are illustrated via numerical examples. Copyright (C) 2021 The Authors.

关键词： Linear matrix inequality Takagi-Sugeno model convex structures numerical complexity control systems

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Coverage Performance in MIMO-ZFBF Dense HetNets with Multiplexing and LOS/NLOS Path-Loss Attenuation

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IEEE TRANSACTIONS ON MOBILE COMPUTING 2020年第9期19卷 2044-2061页

作者： Khoshkholgh, Mohammad G. Navaie, Keivan Shin, Kang G. Leung, Victor C. M. Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 1Z4 Canada Univ Lancaster Sch Comp & Commun Lancaster LA1 4WA England Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen 518060 Peoples R China

The performance of multiple-input multiple-output (MIMO) multiplexing heterogenous cellular networks are often analyzed using a single-exponent path-loss model. Thus, the effect of the expected line-of-sight (LOS) propagation in densified settings is unaccounted for, leading to inaccurate performance evaluation and/or inefficient system design. This is due to the complexity of LOS/non-LOS models in the context of MIMO communications. We address this issue by developing an analytical framework based on stochastic geometry to evaluate the coverage performance. We focus on the zero-forcing beamforming where the maximum signal-to-interference ratio is used for cell association. We analytically derive the coverage. We then investigate the cross-stream interference correlation, and develop two approximations of the coverage: Alzer Approximation (A-A) and Gamma Approximation (G-A). The former is often used in the single antenna and single-stream MIMO. We extend A-A to a MIMO multiplexing system and evaluate its utility. We show that the inverse interference is well-fitted by a Gamma random variable, where its parameters are directly related to the system parameters. The accuracy and robustness of G-A is higher than that of A-A. We observe that depending on the multiplexing gain, it is possible to attain the best coverage probability by proper densification.

关键词： MIMO communication Multiplexing Attenuation Cellular networks Geometry Stochastic processes Correlation Area spectral efficiency coverage probability densification heterogenous cellular networks (HetNets) LOS NLOS path-loss model multiple-input multiple-output (MIMO) multiplexing numerical complexity Poisson Point Process (PPP) stochastic geometry zero-forcing beamforming (ZFBF)

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Choosing an Adequate Convex Structure for Controller and Observer Gains in Takagi-Sugeno Control Systems ⁎

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IFAC-PapersOnLine 2021年第4期54卷 206-211页

作者： Alberto Ortiz Thierry-Marie Guerra Víctor Estrada-Manzo Jimmy Lauber Dept. of Mechatronics of the Universidad Politécnica de Pachuca C.P. 43830 Zempoala Mexico Polytechnic University Hauts-de-France UPHF LAMIH UMR CNRS 8201 Valenciennes France

This work presents a methodology to choose the convex structure for nonlinear gains in approaches based on Takagi-Sugeno models. The proposal faces the problem of numerical complexity in LMI-based approaches within this area; it gives a finer convex structure for controller and observer matrices depending on two criteria: less number of LMI constraints or more decision variables while keeping the same number of LMIs in traditional approaches. The advantages of the proposal are illustrated via numerical examples.

关键词： Linear matrix inequality Takagi-Sugeno model convex structures numerical complexity control systems

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Estimation of linear operators from scattered impulse responses

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2019年第31期47卷 730-758页

作者： Bigot, Jeremie Escande, Paul Weiss, Pierre Univ Bordeaux IMB UMR5251 Inst Math Bordeaux Bordeaux France Univ Bordeaux IMB UMR5251 CNRS Bordeaux France ISAE DISC Toulouse France CNRS ITAV USR3505 Inst Technol Avancees Sci Vivant Toulouse France CNRS IMT UMR5219 Inst Math Toulouse Toulouse France Univ Toulouse Toulouse France

We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the choice of an appropriate regularization term that takes the smoothness of the operator into account. It is numerically tractable in very large dimensions. We study the estimator's robustness to noise and analyze its approximation properties with respect to the size and the geometry of the dataset. In addition, we show minimax optimality of the proposed estimator. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Integral operator Scattered approximation Estimator Convergence rate numerical complexity Radial basis functions Reproducing Kernel Hilbert Spaces Minimax

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Approximation of Integral Operators Using Product-Convolution Expansions

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2017年第3期58卷 333-348页

作者： Escande, Paul Weiss, Pierre ISAE DISC Toulouse France Univ Toulouse Inst Technol Avancees Sci Vivant ITAV USR3505 Toulouse France Univ Toulouse IMT CNRS UMR5219 Toulouse France

We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on functions is a computationally intensive problem necessary for many practical problems. We analyze a technique called product-convolution expansion: The operator is locally approximated by a convolution, allowing to design fast numerical algorithms based on the fast Fourier transform. We design various types of expansions, provide their explicit rates of approximation and their complexity depending on the time-varying impulse response smoothness. This analysis suggests novel wavelet-based implementations of the method with numerous assets such as optimal approximation rates, low complexity and storage requirements as well as adaptivity to the kernels regularity. The proposed methods are an alternative to more standard procedures such as panel clustering, cross-approximations, wavelet expansions or hierarchical matrices.

关键词： Integral operators Wavelet Spline Structured low-rank decomposition numerical complexity Approximation rate Fast Fourier transform

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