Robust Sampled-Data Fuzzy Control of Nonlinear Systems with Parametric Uncertainties: Its Application to Depth Control of Autonomous Underwater Vehicles

김도완,이호재,김문환,이상영,김태영 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.6

This paper presents a new direct discrete-time design methodology of a robust sampled-data fuzzy controller for a class of nonlinear system with parametric uncertainties that is exactly represented by Takagi?Sugeno (T?S) fuzzy model. Based on an exact discrete-time fuzzy model in an integral form, sufficient conditions for a robust asymptotic stabilization of the nonlinear system are investigated in the discrete-time Lyapunov sense. It is shown that the resulting sampled-data controller indeed robustly asymptotically stabilizes the nonlinear plant. To illustrate the effectiveness of the proposed methodology, an example, a sampled-data depth control of autonomous underwater vehicles (AUVs) is provided.

시간 종속적인 리아프노프 함수를 이용한 모바일 로봇의 선도-추종 샘플 데이터 제어

예동희,한승용,이상문,Ye, Donghee,Han, Seungyong,Lee, Sangmoon 대한임베디드공학회 2021 대한임베디드공학회논문지 Vol.16 No.4

The aim of this paper is to propose a less conservative stabilization condition for leader-following sampled-data control of wheeled mobile robot (WMR) systems by using a clock-dependent Lyapunov function (CDLF) with looped functionals. In the leader-following WMR system, the state and input of the leader robot are measured by digital devices mounted on the following robot, and they are utilized to construct the sampled-data controller of the following robot. To design the sampled-data controller, a stabilization condition is derived by using the CDLF with looped functionals, and formulated in terms of sum of squares (SOS). The considered Lyapunov function is a polynomial form with respect to the clock related to the transmitted sampling instants. As the degree of the Lyapunov function increases, the stabilization condition becomes less conservative. This ensures that the designed controller is able to stabilize the system with a larger maximum sampling interval. The simulation results are provided to demonstrate the effectiveness of the proposed method.

Dissipative Based Adaptive Reliable Sampled-data Control of Time-varying Delay Systems

Santra, Srimanta,Karimi, Hamid Reza,Sakthivel, Rathinasamy,Anthoni, S. Marshal Institute of Control, Robotics and Systems 2016 International Journal of Control, Automation, and Vol.14 No.1

This paper is concerned with the problem of dissipative based adaptive reliable controller for a class of time delay systems subject to actuator failures and time-varying sampling with a known upper bound on the sampling intervals. By constructing a proper Lyapunov-Krasovskii functional which fully uses the available information about the actual sampling pattern and time delays, a new set of sufficient conditions is derived to obtain the required result. Then, a dissipative based adaptive sampled-data controller is designed such that the resulting closed-loop system is reliable in the sense that it is asymptotically stable and has the prescribed dissipative performance under given constraints. The existence condition of the desired dissipative based adaptive reliable sampled-data controller is obtained in terms of linear matrix inequalities. Further, the performance of the proposed controller is implemented on a liquid propellant rocket motor with a pressure feeding system model. The simulation results show the effectiveness and better performance of the proposed adaptive reliable sampled-data controller over conventional reliable controller.

The Ultimate Bound of a Sampled-Data Sliding Mode Control System with Short Sampling Period

Heum-Yong Park,Young-Hun Jo,Kang-Bak Park 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8

Almost all of control methods proposed so far have been designed in the continuous-time domain. Actual systems, however, have been implemented in the discrete-time domain since MCU and/or microprocessors have been used for the control system, that is, the overall system turned to be a sampled-data system. In this case, the ultimate error cannot converge to zero in the actual system even though the proposed control algorithm showed the asymptotic stability in the continuous-time domain. In this paper, therefore, the ultimate error bound of a sampled data system has been investigated. The ultimate error is shown to be related in the sampling period.

Time-variant Feedback Stabilization of Constrained Delayed Boolean Networks Under Nonuniform Sampled-data Control

Xiangshan Kong,Haitao Li 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.5

This paper investigates the time-variant state feedback stabilization of constrained delayed Boolean control networks under nonuniform sampled-data control. Firstly, using the augmented algebraic form of constrained delayed Boolean control networks, the constrained nonuniform sampled-data controllability matrix is constructed. Secondly, based on the controllability matrix, a necessary and sufficient condition is proposed for the nonuniform sampled-data reachability of constrained delayed Boolean control networks. Thirdly, by virtue of the nonuniform sampled-data reachability, a new procedure is established to design time-variant state feedback sampled-data stabilizers via reachable set approach. The obtained results are applied to the cell survival regulation of apoptosis networks.

Event-triggering Formation Control for Second-order Multi-agent Systems With Sampled Position Data

Jing Liu,Zhen Li,Jia-Bao Liu,Jian-an Fang 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.4

This paper addresses the problem of event-triggering formation control (ETFC) for second-order multiagent systems (MASs) with sampled position data. Firstly, two types of distributed control strategies based on the sampled position data are proposed to solve the observer-based formation control problems. These novel formation control strategies allow the event-triggering conditions to be intermittently examined at random sampling instants, where the data transmission is driven by an event-triggering control protocol. Under this framework, both timeinvariant and time-varying formation controls are considered. Then, based on the algebraic graph theory and matrix theory, some sufficient conditions are given to ensure that the second- order MASs achieve the specified formation shape. Finally, simulation results are provided to show the effectiveness of the theoretical analysis.

An Observer Based Sampled-data Control for Class of Scalar Nonlinear Systems Using Continualized Discretization Method

Triet Nguyen-Van 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.2

A new observer based sampled-data feedback control is proposed for a class of scalar nonlinear affine systems, where the control distribution is constant, in the presence of noise. The discrete-time states are estimated by a nonlinear state observer, and used for designing the sampled-data control. The discrete-time model used for controller and state observer design is derived using continualizated discretization method. This discretization method is based on the new concept of continualization of discrete-time models, and is applicable to any system whose Jacobian matrix is defined. In this work, it is shown that for the system without the presence of noise, the proposed sampled-data control preserves the equilibria and dynamics of the desired system, while the conventional control, which is based on forward difference method, does not. Simulations are carried out for the scalar Riccati system with the presence of noise to demonstrate the better performances of the proposed method not only in sampled-data control design, but also in system states estimation than the conventional method for both high and low sampling frequencies.

Synchronization criteria for delayed Lur’e systems and randomly occurring sampled-data controller gain

Lee, S.H.,Park, M.J.,Kwon, O.M. Elsevier 2019 Communications in nonlinear science & numerical si Vol.68 No.-

<P><B>Abstract</B></P> <P>In this paper, the synchronization problem for delayed Lur’e systems with sampled-data control is investigated. To reflect noises and perturbations of a designed controller gain, Bernoulli sequence and random variables are applied to sampled-data scheme. By constructing some novel Lyapunov-Krasovskii functionals and utilizing some mathematical techniques such as Wirtinger-based integral inequalities, a sampled-data synchronization method for delayed Lur’e systems under a sampled-data control with randomly occurring perturbations is proposed as the framework of linear matrix inequalities. As a special case of the first result, a sampled-data synchronization criterion without considering randomly occurring perturbations is derived. Finally, via three numerical examples, the superiority and validity of the proposed results will be verified through comparing with the existing results.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A concept of stochastic parameter uncertainties is applied to a sampled-data control method to present a realistic system. </LI> <LI> A novel <I>t<SUB>k</SUB> </I>-dependent double integral term of LKFs, ( <SUB> t k + 1 </SUB> − t ) ∫ <SUB> t k </SUB> t ∫ s t ω 3 T ( u ) R <SUB> ω 3 </SUB> ( u ) d u d s , is proposed and a bound of its time derivative is estimated by utilizing Wirtinger-based double inequality and a maximum value of a function. </LI> <LI> Two novel LKFs, 2 ( <SUB> t k + 1 </SUB> − t ) ∑ i = 1 l ∫ 0 d i T x ( t ) [ <SUB> k 1 , i </SUB> ( <SUB> ψ i </SUB> ( s ) − γ i − s ) + <SUB> k 2 , i </SUB> ( γ i + s − <SUB> ψ i </SUB> ( s ) ) ] d s , and 2 ( t − <SUB> t k </SUB> ) ∑ i = 1 l ∫ 0 d i T x ( t ) [ <SUB> k 3 , i </SUB> ( <SUB> ψ i </SUB> ( s ) − γ i − s ) + <SUB> k 4 , i </SUB> ( γ i + s − <SUB> ψ i </SUB> ( s ) ) ] d s , are proposed for the first time through a condition of a nonlinear function to enhance the feasible region of synchronization criteria. </LI> <LI> The effectiveness and less conservatism of our results are illustrated via three numerical examples. </LI> </UL> </P>

Sampled-data Fuzzy Control of Two-wheel Inverted Pendulums Based on Passivity Theory

Rongjun Liu,Junfeng Wu,Dan Wang 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.5

In this paper, an aperiodically sampled-data control scheme is detailed for the two-wheel inverted pendulum using Takagi-Sugeno (T-S) fuzzy models. The passivity theory is applied in the presence of the disturbances in the actuator channel. A two-rule fuzzy model is utilized to represent the two-wheel inverted pendulum. By using the pendulum angle as the antecedent variable of the fuzzy rule, a passive sampled-data controller is established using the pendulum inclination angle and the mean value of the rim motors’ rotary angles. A Lyapunov-like function based on the two fuzzy rules is constructed to develop criteria of passivity, by the utilization of very-strict passivity in terms of the pendulum angle. Then a solution to the gains of sampled-data controller is synthesized to ensure the very-strict passivity of the pendulum system. By the illustrative examples, the effectiveness of the variable-sampling control scheme is validated for the two-wheel inverted pendulum.

Sampled-data Robust H∞ Control for T-S Fuzzy Time-delay Systems with State Quantization

Xiaojing Han,Yuechao Ma 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.1

This paper investigates the sampled-data robust H∞ control for T-S fuzzy time-delay systems with statequantization. Based on a modified Lyapunov-Krasovskii function(LKF), which is fully considered the characteristicsof sample-data and state quantization, a sample-data and state quantized controller is designed. By introducingthe free weighting matrices, some integral techniques and modified inequalities, the results in this paper are lessconservative than other existing results. At the end of the paper, two examples are given to show the effectivenessand superiority of the proposed methods.