scholarly journals Robust Finite-Time H-Infinity Control with Transients for Dynamic Positioning Ship Subject to Input Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Xiaogong Lin ◽  
Kun Liang ◽  
Heng Li ◽  
Yuzhao Jiao ◽  
Jun Nie
Keyword(s):  
Finite Time ◽  
External Disturbance ◽  
Fixed Time ◽  
Input Delay ◽  
Linear Matrix ◽  
Time Interval ◽  
Dynamic Positioning ◽  
Initial Condition ◽  
Transient Performance ◽  
Zero Initial Condition

This paper presents the problem of robust finite-time H∞ control with transients for ocean surface vessels equipped with dynamic positioning (DP) system in presence of input delay. The main objective of this work is to design a finite-time H∞ state feedback controller, which ensures that all states of ship do not exceed a given threshold over a fixed time interval, with better robustness and transient performance subject to time-varying disturbance. Based on a novel augmented Lyapunov-Krasovskii-like function (LKLF) with triple integral terms and a method combining the Wirtinger inequality and reciprocally convex approach, a less conservative result is derived. In particular, an H∞ performance index with nonzero initial condition is introduced to attenuate the overconservatism caused by the assumption of zero initial condition and enhance the transient performance of ship subject to external disturbance. More precisely, the controller gain matrix for the DP system can be achieved by solving the linear matrix inequalities (LMIs), which can be easily facilitated by using some standard numerical packages. Finally, a numerical simulation for a ship is proposed to verify the effectiveness and less conservatism of the controller we designed.

Finite-Time Stabilization of Stochastic Systems With Partially Known Transition Probabilities

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Xiao-li Luan ◽  
Fei Liu ◽  
Peng Shi
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Fixed Time ◽  
Linear Matrix ◽  
Time Interval ◽  
Markov Jump ◽  
Stabilizing Controller ◽  
Finite Time Stabilization

In this paper, the problem of finite-time stabilization for a class of uncertain Markov jump systems with partially known transition probabilities is investigated. The main aim of this paper is to derive the finite-time stabilization criteria for the underlying systems when the transition probabilities are partially known and to design a state feedback stabilizing controller such that the trajectories of the system stay within a given bound in a fixed time interval. Sufficient conditions for the existence of the desired controller are established with the linear matrix inequalities framework. A numerical example is used to illustrate the effectiveness of the developed theoretic results.

On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval

2011 ◽  
Vol 34 (7) ◽  
pp. 841-849 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Non Linear ◽  
Robust Controllability ◽  
Jump Systems ◽  
Takagi Sugeno

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

scholarly journals Finite-Time H2/H∞ Control Design for Stochastic Poisson Systems with Applications to Clothing Hanging Device

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yan Qi ◽  
Shiyu Zhong ◽  
Zhiguo Yan
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Control Design ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Transient Performance ◽  
Definition Of

In this paper, the design of finite-time H2/H∞ controller for linear Itô stochastic Poisson systems is considered. First, the definition of finite-time H2/H∞ control is proposed, which considers the transient performance, H2 index, and H∞ index simultaneously in a predetermined finite-time interval. Then, the state feedback and observer-based finite-time H2/H∞ controllers are presented and some new sufficient conditions are obtained. Moreover, an algorithm is given to optimize H2 and H∞ index, simultaneously. Finally, a simulation example indicates the effectiveness of the results.

scholarly journals RobustL2-L∞Filtering of Time-Delay Jump Systems with Respect to the Finite-Time Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Delayed Systems ◽  
Markov Jump Linear Systems

This paper studied the problem of stochastic finite-time boundedness and disturbance attenuation for a class of linear time-delayed systems with Markov jumping parameters. Sufficient conditions are provided to solve this problem. TheL2-L∞filters are, respectively, designed for time-delayed Markov jump linear systems with/without uncertain parameters such that the resulting filtering error dynamic system is stochastically finite-time bounded and has the finite-time interval disturbance attenuationγfor all admissible uncertainties, time delays, and unknown disturbances. By using stochastic Lyapunov-Krasovskii functional approach, it is shown that the filter designing problem is in terms of the solutions of a set of coupled linear matrix inequalities. Simulation examples are included to demonstrate the potential of the proposed results.

scholarly journals Finite-Time Stability Analysis for a Class of Continuous Switched Descriptor Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Pan Tinglong ◽  
Yang Kun ◽  
Shen Yanxia ◽  
Gao Zairui ◽  
Ji Zhicheng
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Interval ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability has more practical application values than the classical Lyapunov asymptotic stability over a fixed finite-time interval. The problems of finite-time stability and finite-time boundedness for a class of continuous switched descriptor systems are considered in this paper. Based on the average dwell time approach and the multiple Lyapunov functions technique, the concepts of finite-time stability and boundedness are extended to continuous switched descriptor systems. In addition, sufficient conditions for the existence of state feedback controllers in terms of linear matrix inequalities (LMIs) are obtained with arbitrary switching rules, which guarantee that the switched descriptor system is finite-time stable and finite-time bounded, respectively. Finally, two numerical examples are presented to illustrate the reasonableness and effectiveness of the proposed results.

A new measure of the degree of controllability for linear system with external disturbance and its application to wind turbines

2016 ◽  
Vol 24 (4) ◽  
pp. 739-759 ◽  
Author(s):  
Yaping Xia ◽  
Minghui Yin ◽  
Chenxiao Cai ◽  
Baoyong Zhang ◽  
Yun Zou
Keyword(s):  
Linear System ◽  
Wind Turbines ◽  
Structural Parameters ◽  
External Disturbance ◽  
Minimum Energy ◽  
Fixed Time ◽  
Speed Ratio ◽  
Initial Condition ◽  
Design And Optimization ◽  
Mass Spring

This paper is concerned with the measure of degree of controllability (DOC) for linear system with external disturbance. A new measure of DOC, in which the initial condition is regarded as a random vector, is proposed in this paper by solving the fixed-time expected minimum-energy transfer control problem. Since this new measure is dependent on the statistical information of initial condition rather than its estimated value, it is more suitable to apply the proposed measure in the design and optimization of the structural parameters of controlled plants. Furthermore, the simulations on the NREL (National Renewable Energy Laboratory) CART3 wind turbine demonstrate that the relation of the proposed measure to turbine parameters (including rotor inertia and optimum tip speed ratio) coincides with that of the MPPT efficiency to turbine parameters. This indicates that the proposed measure is applicable to guide the design and optimization of the structural parameters of wind turbines. Meanwhile, a mass-spring-damper system is also simulated to validate the proposed measure.

Finite-time H∞ sliding mode control of uncertain T-S fuzzy system with time-varying delay based on observer

2021 ◽  
Vol 40 (1) ◽  
pp. 983-999
Author(s):  
Huan Li ◽  
Pengyi Tang ◽  
Yuechao Ma
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Time Interval ◽  
Sliding Mode Controller ◽  
Time Varying ◽  
Sliding Surface ◽  
State Estimator ◽  
Mode Control

In this paper, a class of observer-based sliding mode controller is designed, and the finite-time H∞ control problem of uncertain T-S fuzzy systems with time-varying is studied. Firstly, an integral-type sliding surface function with time-delay is devised based on the state estimator, and sufficient criteria of finite-time bounded and finite-time H∞ bounded can be obtained for the T-S systems. Moreover, the proposed sliding mode control law is integrated to ensure the dynamics of controlled system into the sliding surface in a finite-time interval. Then, according to the linear matrix inequalities (LMIs), the desired gain matrices of fuzzy sliding mode controller and state estimator are derived. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.

Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters

2016 ◽  
Vol 71 (4) ◽  
pp. 289-304 ◽  
Author(s):  
R. Sakthivel ◽  
M. Sathishkumar ◽  
B. Kaviarasan ◽  
S. Marshal Anthoni
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Regulatory Networks ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Time Interval ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping

AbstractThis article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.

scholarly journals Global Finite-Time and Fixed-Time Synchronization for Discontinuous Complex Dynamical Networks with Semi-Markovian Switching and Mixed Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Lina Yu ◽  
Jingchao Zhang ◽  
Yunfei Ma ◽  
Xinhua Tan ◽  
Chunwei Wang
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Fixed Time ◽  
Functional Method ◽  
Markovian Switching ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Dynamical Networks ◽  
Analysis Technique

This paper is concerned with the global finite-time and fixed-time synchronization for a class of discontinuous complex dynamical networks with semi-Markovian switching and mixed time-varying delays. The novel state-feedback controllers, which include integral terms and discontinuous facts, are designed to realize the global synchronization between the drive system and response system. By applying the Lyapunov functional method and matrix inequality analysis technique, the global finite-time and fixed-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.

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