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Stabilization of Nonlinear Switched Systems with distributed time-delay: The Discrete-time Case

INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2021年第12期19卷 3843-3852页

作者： Wang, Chaochen Fang, Xiaoli Ma, Lifeng Zhang, Jie Bo, Yuming Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China

This paper investigates the stabilization problem of nonlinear switched systems subject to the distributed time-delay. The considered nonlinear switched systems are quite general whose dynamics are affected by both exogenous noises and distributed time-delay. The purpose of the addressed problem is to propose a state feedback control law such that, the closed-loop system is exponentially stable in the mean square sense and meanwhile, the required weighted L-2 gain is achieved. By resorting to the Lyapunov functional method in combination with the average dwell time approach, sufficient conditions are provided for the existence of the desired control scheme in terms of the feasibility of certain Hamilton-Jacobi inequalities (HJIs). Within the established framework, the required feedback controller gains can be obtained by solving the series of HJIs. Finally, an illustrative numerical example is provided to demonstrate the effectiveness of the developed control algorithm.

关键词： distributed time-delay Hamilton-Jacobi inequality nonlinear switched systems stabilisation

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Comparison of two different types of fractional-order COVID-19 distributed time-delay models with real data application

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INTERNATIONAL JOURNAL OF MODERN PHYSICS B 2021年第21期35卷

作者： Yang, Liangli Su, Yongmei Zhuo, Xinjian Univ Sci & Technol Beijing Sch Math & Phys Beijing 100083 Peoples R China Beijing Univ Posts & Telecommun Sch Sci Beijing 100700 Peoples R China

The outbreak of COVID-19 has a great impact on the world. Considering that there are different infection delays among different populations, which can be expressed as distributed delay, and the distributed time-delay is rarely used in fractional-order model to simulate the real data, here we establish two different types of fractional order (Caputo and Caputo-Fabrizio) COVID-19 models with distributed time-delay. Parameters are estimated by the least-square method according to the report data of China and other 12 countries. The results of Caputo and Caputo-Fabrizio model with distributed time-delay and without delay, the integer-order model with distributed delay are compared. These show that the fractional-order model can be better in fitting the real data. Moreover, Caputo order is better in short-term time fitting, Caputo-Fabrizio order is better in long-term fitting and prediction. Finally, the influence of several parameters is simulated in Caputo order model, which further verifies the importance of taking strict quarantine measures and paying close attention to the incubation period population.

关键词： COVID-19 Caputo Caputo-Fabrizio parameter estimation distributed time-delay

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Adaptive control for a class of nonlinear systems with state constraints and distributed time-varying delay 34

Adaptive control for a class of nonlinear systems with state...

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34th Chinese Control and Decision Conference (CCDC)

作者： Lei, Ming Chen, Weimin Nanjing Univ Sci & Technol Sch Math & Stat Nanjing 210094 Peoples R China

ISBN: (纸本)9781665478960

In this paper, an adaptive asymptotic tracking control method is proposed for nonlinear systems with state constraints and distributed time-varying delays. Based on back-stepping technology, a new adaptive controller is designed. In addition, we use a new inequality to compensate for the nonlinear term and distributed time-varying delay in the system;For state constraints, we use time-varying tangent Barrier Lyapunov Function (BLF) as a method to deal with state constraints. The results show that all signals in the closed-loop system are bounded, the tracking error converges near the origin, and the state constraint is not violated. Finally, the simulation results show the effectiveness of the control strategy.

关键词： time-varying tangent BLF State constraints distributed time-delay Back-stepping

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Analysis of leukaemic cells dynamics with multi-stage maturation process using a new non-linear positive model with distributed time-delay

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IET CONTROL THEORY AND APPLICATIONS 2019年第18期13卷 3052-3064页

作者： Zenati, Abdelhafid Chakir, Massaoud Tadjine, Mohamed Denai, Mouloud Natl Polytech Sch ENP Algiers Dept Engn Control Syst & Appl Math Lab Proc Control LCP 10 St Hacen Badi El Harrach Algiers Algeria Univ Hertfordshire Sch Engn & Technol Ctr Engn Res Commun & Intelligent Syst Hatfield Herts England

This study proposes a new non-linear positive model with distributed time-delay describing the dynamics of leukaemic cells lineages and their levels of maturity. The dynamic model is first reformulated into coupled non-linear equations with distributed time-delay using an appropriate transformation of the age-structured transport partial differential equations that govern the dynamics of leukaemic cell populations. After assessing the positiveness of the proposed model, the conditions for the existence of positive steady-states are established. Furthermore, the necessary and sufficient conditions for boundedness of the solutions are derived. Finally, the convergence of the proposed model to the origin is studied as this has an important biological interpretation which is the extinction of all generations of leukaemic cells following anti-leukaemia treatments. To investigate the global asymptotic stability of this important equilibrium point, both model properties (i.e. positiveness and boundedness) are used to construct a suitable Lyapunov function for the characterisation of leukaemic cells dynamics. The results demonstrate a significant improvement for the treatment of leukaemia. Some simulations are presented to illustrate the effectiveness of the proposed model.

关键词： cancer delays Lyapunov methods partial differential equations asymptotic stability distributed time-delay leukaemic cells lineages dynamic model coupled nonlinear equations age-structured transport partial differential equations leukaemic cell populations positiveness model properties leukaemic cells dynamics multistage maturation process nonlinear positive model

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Optimized design of robust resonator with distributed time-delay

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JOURNAL OF SOUND AND VIBRATION 2019年 443卷 576-590页

作者： Pilbauer, Dan Vyhlidal, Tomas Michiels, Wim Czech Tech Univ Dept Instrumentat & Control Engn Fac Mech Engn Tech 4 Prague 16607 6 Czech Republic Czech Tech Univ CIIRC Tech 4 Prague 16607 6 Czech Republic Katholieke Univ Leuven Dept Comp Sci Celestijnenlaan 200A B-3001 Heverlee Belgium

An extension of the well-known delayed resonator concept is proposed with the objective to enhance its robustness in vibration suppression under guaranteeing stability of the overall set up. The novel resonator feedback is based on an acceleration measurements passing through a delay of polynomial distribution. The feedback design is formulated as an optimization problem over the parameter set formed by the polynomial coefficients and the gain of the delay free part. The first objective is to minimize the sensitivity of the resonator performance with respect to variations of the excitation frequency, i.e. to widen its frequency stopband centered at the nominal excitation frequency. The second, equally significant objective is to guarantee that this does not lead to instability of the overall mechanical system coupled with the absorber and to ensure sufficient stability margin. The arising non-convex and nonsmooth optimization problem is widely discussed and a penalty method is developed, where the unconstrained problem in every iteration step is solved using available software tools for optimization and spectral design of time delay systems. The proposed design technique is validated by simulations for two case study examples. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： distributed time-delay Active vibration control Robust control Acceleration feedback Spectral method delayed resonator

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DCS devices based non-linear process control system design for plants with distributed time-delay using particle filter

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Journal of Central South University 2019年第12期26卷 3351-3358页

作者： DENG Ming-cong FUJII Ryohei The Graduate School of Engineering Tokyo University of Agriculture and TechnologyTokyo 184-8588Japan

Remote control process system with distributed time-delay has attracted much attention in different *** this paper,non-linear remote control of a single tank process system with wireless network is *** deal with the distributed time-delay in a large-scale plant,the time-delay compensation controller based on DCS devices is designed by using operator theory and particle *** control system(DCS)device is developed to monitor and control from the central monitoring room to each *** particle filter is a probabilistic method to estimate unobservable information from observable ***,remote control system and experimental equipment are ***,control system based on an operator theory is ***,process system with distributed time-delay using particle filter is carried ***,the actual experiment is conducted by using the proposed time-delay compensation *** estimating with the proposed method,the result is close to the case in which the distributed time-delay does not *** effectiveness of the proposed control system is confirmed by experiment results.

关键词： non-linear remote control distributed control system particle filter operator theory distributed time-delay

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Adaptive control for a class of nonlinear systems with state constraints and distributed time-varying delay

Adaptive control for a class of nonlinear systems with state...

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第34届中国控制与决策会议

作者： Ming Lei Weimin Chen School of Mathematics and Statistics Nanjing University of Science and Technology

In this paper,an adaptive asymptotic tracking control method is proposed for nonlinear systems with state constraints and distributed time-varying *** on back-stepping technology,a new adaptive controller is *** addition,we use a new inequality to compensate for the nonlinear term and distributed time-varying delay in the system;For state constraints,we use time-varying tangent B arrier Lyapunov Function(BLF) as a method to deal with state *** results show that all signals in the closed-loop system are bounded,the tracking error converges near the origin,and the state constraint is not ***,the simulation results show the effectiveness of the control strategy.

关键词： time-varying tangent BLF State constraints distributed time-delay Back-stepping

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Exponential stabilization of nonlinear switched systems with distributed time-delay: An average dwell time approach

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EUROPEAN JOURNAL OF CONTROL 2017年 37卷 34-42页

作者： Ma, Lifeng Wang, Zidong Liu, Yurong Alsaadi, Fuad E. Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Jiangsu Peoples R China Nanjing Univ Sci & Technol Minist Educ Key Lab Intelligent Percept & Syst High Dimens In Nanjing 210094 Jiangsu Peoples R China Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China Brunel Univ London Dept Comp Sci Uxbridge UB8 3PH Middx England Yangzhou Univ Dept Math Yangzhou 225002 Jiangsu Peoples R China King Abdulaziz Univ Fac Engn Commun Syst & Networks CSN Res Grp Jeddah 21589 Saudi Arabia

In this paper, the exponential stabilization problem is discussed for nonlinear switched systems subject to the distributed time-delay. Attention is focused on the design of a state feedback controller such that, the closed-loop system is exponentially stable with a guaranteed weighted L-2 gain. By resorting to the average dwell time method and the piecewise Lyapunov functional approach, sufficient conditions are derived for the solvability of the addressed problem in terms of the feasibility of certain Hamilton Jacobi inequalities (HJIs). The explicit expression of the desired controller is formulated via solving the presented set of HJIs. Furthermore, within the proposed framework, the exponential stabilization problems are investigated, respectively, for nonlinear switched systems with mixed time-delays and linear switched systems with the distributed time-delay. Finally, a simulation example is given to illustrate the effectiveness and applicability of the proposed algorithm. (C) 2017 European Control Association. Published by Elsevier Ltd. All rights reserved.

关键词： Nonlinear systems Switched systems Weighted L-2 gain Hamilton-Jacobi inequality distributed time-delay

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Improved Stability and Stabilization Criteria for T-S Fuzzy Systems with distributed time-delay 2nd

Improved Stability and Stabilization Criteria for T-S Fuzzy ...

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2nd International Conference on Data Mining and Big Data (DMBD)

作者： Ma, Qianqian Xia, Hongwei Ma, Guangcheng Xia, Yong Wang, Chong Harbin Inst Technol Harbin 150001 Heilongjiang Peoples R China Petro China Changqing Oilfield Co Nat Gas Plant 1 Jingbian 718500 Peoples R China

ISBN: (纸本)9783319618456;9783319618449

This paper investigates the stability and stabilization analysis problem of nonlinear systems with distributed time-delay. The T-S fuzzy model is employed to describe the nonlinear plant. When designing fuzzy controller, the novel imperfect premise matching method is adopted, which allows the fuzzy model and the fuzzy controller to use different premise membership functions and different number of rules. As a result, greater design flexibility can be obtained. By applying a new tighter integral inequality which involves information about the double integral of the system states, and introducing the information of membership functions, less conservative stability and stabilization conditions are derived. Finally, a numerical example is provided to clarify the effectiveness of the proposed approach.

关键词： T-S fuzzy model distributed time-delay Lyapunov stability theory Imperfect premise matching

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INCLUSION, RESTRICTION, AND OVERLAPPING DECOMPOSITIONS OF NEUTRAL SYSTEMS WITH distributed time-delay

INCLUSION, RESTRICTION, AND OVERLAPPING DECOMPOSITIONS OF NE...

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14th IFAC Symposium on Large Scale Complex Systems - Theory and Applications (IFAC LSS)

作者： Iftar, Altug Anadolu Univ Dept Elect & Elect Engn TR-26470 Eskisehir Turkey

Inclusion and restriction principles for linear time-invariant neutral distributed-time-delay systems is defined. Overlapping decompositions and expansions of such systems are then discussed. Controller design using overlapping decompositions is also presented. (C) 2016, IFAC (International Federation of Automatic. Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Large-scale systems time-delay systems neutral systems distributed time-delay overlapping decompositions controller design

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