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Asymptotic Equivalence of Evolution Equations Governed by Cocoercive Operators and Their Forward Discretizations

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2019年第1期182卷 30-48页

作者： Contreras, Andres Peypouquet, Juan Univ Chile Dept Ingn Matemat FCFM Beauchef 851 Santiago Chile Univ Chile FCFM Dept Ingn Matemat Beauchef 851 Santiago Chile Univ Chile FCFM Ctr Modelamiento Matemat CNRSUMI2807 Beauchef 851 Santiago Chile

The purpose of this work is to study discrete approximations of evolution equations governed by cocoercive operators by means of Euler iterations, both in a finite and in an infinite time horizon. On the one hand, we give precise estimations for the distance between iterates of independently generated Euler sequences and use them to obtain bounds for the distance between the state, given by the continuous-time trajectory, and the discrete approximation obtained by the Euler iterations. On the other hand, we establish the asymptotic equivalence between the continuous- and discrete-time systems, under a sharp hypothesis on the step sizes, which can be removed for operators deriving from a potential. As a consequence, we are able to construct a family of smooth functions for which the trajectories/sequences generated by basic first-order methods converge weakly but not strongly, extending the counterexample of Baillon. Finally, we include a few guidelines to address the problem in smooth Banach spaces.

关键词： Asymptotic equivalence Cocoercive operators Euler iterations gradient algorithm

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2 CLASSES LINEAR DISCRIMINATION - A MIN-MAX APPROACH

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PATTERN RECOGNITION LETTERS 1989年第5期10卷 281-287页

作者： CASTAGLIOLA, P DUBUISSON, B Université de Technologie de Compiègne URA CNRS. 817 B.P. 649 60206 Compiegne Cedex France

In this paper we propose a new dichotomic linear discrimination algorithm based on a criterion recursively defined from the min and max functions. This criterion allows us, using a gradient algorithm, to find two hype... 详细信息

关键词： gradient algorithm Linear discrimination min and max function

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Improving the performance analysis of a gradient-based adaptive IIR notch filter

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2002年第9期85卷 25-34页

作者： Takeshita, Y Xiao, Y Shida, K Saga Univ Grad Sch Sci & Engn Saga 8408502 Japan Hiroshima Prefectural Womens Univ Fac Human Life & Environm Sci Hiroshima 7348558 Japan

improvement of performance analysis is discussed for the plain gradient-type adaptive IIR bilinear notch filters often used in the areas of communication, control, radar, and so on. Specifically, instead of the gradient linearization in the conventional analysis, nonlinear terms are introduced in the approximate expression of the gradient and an explicit expression of the estimation variance of the gradient algorithm in the steady state is derived. In regard to the step size, the convergence condition is derived that guarantees convergence of the algorithm. Its effectiveness and limitation are clarified. (C) 2002 Wiley Periodicals, Inc.

关键词： gradient-type IIR notch filter gradient algorithm performance analysis estimation variance convergence condition

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A note on "Solving the general Sylvester discrete-time periodic matrix equations via the gradient based iterative method"

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APPLIED MATHEMATICS LETTERS 2021年 119卷 107149-107149页

作者： Chen, Zebin Chen, Xuesong Guangdong Univ Technol Sch Appl Math Guangzhou 510006 Peoples R China

In this note, we point out that the value range of iterative factor delta in Hajarian (2016) is not enough to guarantee the convergence result. We have rederived the proof process and got the correct value range of iterative factor delta. A new scaling is given and then the value range of delta is greatly increased. (C) 2021 Elsevier Ltd All rights reserved.

关键词： Sylvester matrix equations gradient algorithm Iterative method

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Sequential versus concurrent gradient-based optimal algorithms for the robust control of quantum systems

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JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS 2022年第18期55卷 184006-184006页

作者： Dionis, E. Sugny, D. Univ Bourgogne Franche Comte CNRS UMR 6303 Lab Interdisciplinaire Carnot Bourgogne BP 47870 F-21078 Dijon France

We investigate two different formulations of gradient-based algorithms for the robust control of quantum systems. We consider the simultaneous control of an ensemble of systems which differ by the value of a constant Hamiltonian parameter. The two versions of the iterative algorithm, called concurrent and sequential, correspond respectively to a joint update of the control at each iteration for all the elements of the ensemble or to a successive correction of the control in which the control law is different for each system. We analyze the relative efficiency of the two optimization procedures on two benchmark examples, namely the control of two-level quantum systems and Bose-Einstein condensates in a one-dimensional optical lattice. Intensive numerical simulations show the superiority of the sequential-update formulation with respect to the concurrent one for a similar numerical cost.

关键词： optimal control theory gradient algorithm quantum control robust control two-level quantum systems Bose-Einstein condensates

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Test Cycle Simulation of Bench Based on Deep Reinforcement Learning

SAE INTERNATIONAL JOURNAL OF PASSENGER VEHICLE SYSTEMS

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SAE INTERNATIONAL JOURNAL OF PASSENGER VEHICLE SYSTEMS 2024年第3期17卷

作者： Gong, Xiaohao Li, Xu Hu, Xiong Li, Wenli Chongqing Univ Technol Chongqing Peoples R China China Merchants Testing Vehicle Technol Res Inst C Shanghai Peoples R China Chongqing Univ Technol Key Lab Adv Manufacture Technol Automobile Parts Minist Educ Chongqing Peoples R China

Test cycle simulation is an essential part of the vehicle-in-the-loop test, and the deep reinforcement learning algorithm model is able to accurately control the drastic change of speed during the simulated vehicle driving process. In order to conduct a simulated cycle test of the vehicle, a vehicle model including driver, battery, motor, transmission system, and vehicle dynamics is established in MATLAB/Simulink. Additionally, a bench load simulation system based on the speed-tracking algorithm of the forward model is established. Taking the driver model action as input and the vehicle gas/brake pedal opening as the action space, the deep deterministic policy gradient (DDPG) algorithm is used to update the entire model. This process yields the dynamic response of the output end of the bench model, ultimately producing the optimal intelligent driver model to simulate the vehicle's completion of the World Light Vehicle Test Cycle (WLTC) on the bench. The results indicate that the algorithm exhibits good convergence in the simulation, throughout the WLTC simulation, the driver always kept the vehicle speed error within 1 km/h, and the response time is less than 0.5 s under the vehicle's starting condition. In comparison to the PID control algorithm and the model predictive control (MPC) algorithm, it demonstrates smaller speed error and response time, ensuring accuracy, high efficiency, and safety during the indoor vehicle-in-the-loop test.

关键词： RPM tracking Bench load simulation Working condition simulation Deep reinforcement learning Deep deterministic policy gradient algorithm

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Demand-Side Energy Management Considering Price Oscillations for Residential Building Heating and Ventilation Systems

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2019年第8期15卷 4742-4752页

作者： Ma, Kai Yu, Yangqing Yang, Bin Yang, Jie Yanshan Univ Sch Elect Engn Qinhuangdao 066004 Hebei Peoples R China Xian Univ Architecture & Technol Sch Bldg Serv Sci & Engn Xian 710055 Shaanxi Peoples R China

This paper presents an energy management method to optimally control the energy supply and the temperature settings of distributed heating and ventilation systems for residential buildings. The control model attempts to schedule the supply and demand simultaneously with the purpose of minimizing the total costs. Moreover, the Predicted Percentage of Dissatisfied (PPD) model is introduced into the consumers' cost functions and the quadratic fitting method is applied to simplify the PPD model. An energy management algorithm is developed to seek the optimal temperature settings, the energy supply, and the price. Furthermore, due to the ubiquity of price oscillations in electricity markets, we analyze and examine the effects of price oscillations on the performance of the proposed algorithm. Finally, the theoretical analysis and simulation results both demonstrate that the proposed energy management algorithm with price oscillations can converge to a region around the optimal solution.

关键词： Demand response (DR) energy management gradient algorithm heating and ventilation price oscillations

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Source and Sink Transitions Controllers for Continuous Petri Nets: A gradient-Based Approach

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IFAC Proceedings Volumes 2003年第6期36卷 193-198页

作者： Dimitri Lefebvre Edouard Leclercq Fabrice Druaux Philippe Thomas GREAH - Université Le Havre -76063 - Le Havre - France UTBM- SeT Belfort Technopôle 90010 Belfort France

This paper is about the control design of hybrid dynamical systems modeled with Petri nets. For this purpose, continuous Petri nets with variable speeds are described as state space representations. In this context, the marking vector is considered as a state space vector, the model outputs are defined by subnets, and the transitions are divided into internal ones and external ones (i.e. source and sink transitions) that correspond to the model inputs. gradient-based controllers are proposed in order to adapt the firing speeds of the source and sink transitions according to a desired trajectory of the output marking.

关键词： Continuous Petri nets control design gradient algorithm

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Peak Searching for Multimodal Optimization through gradient-based Stochastic Extremum Seeking Technique

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Energy Procedia 2017年 105卷 2589-2594页

作者： Chun Yin Shanshan Wu Shiwei Zhou Wei Wang Yuhua Cheng Xuegang Huang School of Automation Engineering University of Electronic Science and Technology of China Chengdu 611731 China China Aerodynamics Research and Development Center Mianyang 621000 China

In this paper, a global peak searching algorithm is proposed for multimodal optimization problem. The proposed algorithm is built through combining gradient-based stochastic extremum seeking method with iterative approach. By increasing the initial search point, the gradient-based stochastic extremum seeking algorithm with different initial condition is iteratively operated to seek a list of the local extreme values near different initial points. Then, the global peak can be found by comparing the list of the local extreme values. The stability anlysis and working process of the global peak searching algorithm is proven. Simulation results are given to show the effectiveness of the proposed control method.

关键词： Global searching gradient algorithm Initial point

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Overlapping Blocks in Reconstruction of Sparse Images 40

Overlapping Blocks in Reconstruction of Sparse Images

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40th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO)

作者： Stankovic, Isidora Dakovic, Milos Orovic, Irena Univ Montenegro Fac Elect Engn Podgorica 20000 Montenegro

ISBN: (纸本)9789532330922

Images are commonly analysed by the discrete cosine transform (DCT) on a number of blocks of smaller size. The blocks are then combined back to the original size image. Since the DCT of blocks have a few nonzero coefficients, the images can be considered as sparse in this transformation domain. The theory of compressive sensing states that some corrupted pixels within blocks can be reconstructed by minimising the blocks sparsity in the DCT domain. Block edges can affect the quality of the reconstruction. In some blocks, a few pixels from an object which mostly belongs to the neighbouring blocks may appear at the edges. Compressive sensing reconstruction algorithm can recognise these pixels as disturbance and perform their false reconstruction in order to minimise the sparsity of the considered block. To overcome this problem, a method with overlapping blocks is proposed. Images are analysed with partially overlapping blocks and then reconstructed using their non-overlapped parts. We have demonstrated the improvements of overlapping blocks on images corrupted with combined noise. A comparison between the reconstructions with non-overlapping and overlapping blocks is presented using the structural similarity index.

关键词： compressive sensing image reconstruction overlapping blocks gradient algorithm noisy image

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