State Feedback Guaranteed Cost Control of Parameter Uncertain Nonlinear System

2011 ◽  
Vol 58-60 ◽  
pp. 803-809
Author(s):  
Chuan Feng Li ◽  
Yong Ji Wang ◽  
Yun Xing Shu ◽  
Zhi Shen Wang
Keyword(s):  
Nonlinear System ◽  
State Feedback ◽  
Linear Part ◽  
Nonlinear Function ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Actual System ◽  
Model Combining ◽  
Guaranteed Cost ◽  
Nonlinear Features

In an actual system, the effects of nonlinear factors are inevitable. So in real practice, when a model for complex system is being built, all the features in it will be linearized. Though simplifying the designing and analyzing process, the model being built in this way is thought to be incapable of revealing the true characteristics of the system. In order to solve this problem, the paper analyzes a model combining both linear and nonlinear features while taking the parameter perturbation of the linear part into consideration, which enables the model to retain as many characteristics of the actual system as possible. Provided that the nonlinear function satisfies the Lipschitz constraint conditions, the robust guaranteed cost state feedback control law of nonlinear system is deduced using the Lyapunov function and then converted into the feasible solutions of linear matrix inequality (LMI). The proposed method optimizes the design of controller by modifying the previous oversimplified models that fail to reveal the real characteristics of the actual system, and the effectiveness of the proposed method is being verified through an algorithm simulation example.

scholarly journals Delay-Dependent Guaranteed Cost Controller Design for Uncertain Neural Networks with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
M. Rajchakit ◽  
P. Niamsup ◽  
T. Rojsiraphisal ◽  
G. Rajchakit
Keyword(s):  
Neural Networks ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Performance Measure ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Guaranteed Cost

This paper studies the problem of guaranteed cost control for a class of uncertain delayed neural networks. The time delay is a continuous function belonging to a given interval but not necessary to be differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, a guaranteed cost controller is designed via memoryless state feedback control, and new sufficient conditions for the existence of the guaranteed cost state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

scholarly journals H∞Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
C. Emharuethai ◽  
P. Niamsup
Keyword(s):  
Nonlinear System ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Time Varying Delay ◽  
Varying Delay

H∞control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality.H∞controller is designed via memoryless state feedback control and new sufficient conditions for the existence of theH∞state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

Robust Guaranteed Cost Control of Uncertain Fuzzy Systems Under Sampled-Data Inputs

2009 ◽  
Vol 13 (2) ◽  
pp. 150-154
Author(s):  
Jun Yoneyama ◽  
Keyword(s):  
Fuzzy Systems ◽  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Input ◽  
Sampled Data ◽  
Data Control ◽  
Guaranteed Cost ◽  
Sampled Data Control

A dynamical system is usually modeled as a continuous-time system, while the control input is applied at discrete instants. This is called a sampled-data control system. This paper is concerned with robust sampled-data control with guaranteed cost for uncertain fuzzy systems. The sampled-data control input is usually the zero-order hold and hence has a piecewise-continuous delay. Thus, an input delay system approach to robust sampled-data control is introduced. Sufficient robust guaranteed cost performance conditions for the closed-loop system with a sampled-data state feedback controller are given in terms of linear matrix inequalities(LMIs). Such robust conditions are derived via descriptor approach to fuzzy time-delay systems under the assumption that a sampling interval may vary but is not greater than some prescribed number. A design method of robust sampled-data guaranteed cost controller for uncertain fuzzy systems. Numerical examples are given to illustrate our sampled-data state feedback control.

Robust H2/H∞Control Strategy for Linear Markovian Jump Systems

2014 ◽  
Vol 525 ◽  
pp. 646-652
Author(s):  
Min Bian ◽  
Qing Yun Guo
Keyword(s):  
Control Strategy ◽  
State Feedback ◽  
Control Strategies ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Bounded Real Lemma ◽  
Finite State ◽  
Linear State ◽  
Feasible Solutions ◽  
Jump Systems

The robust H2/<em>H</em>∞ control strategy for a class of linear continuous-time uncertain systems with randomly jumping parameters is investigated. The transition of the jumping parameters is decided by a finite-state Markov process. The uncertainties are supposed to be norm-bounded. It is desired to design a linear state feedback control strategies such that the closed-loop system satisfies H performance and minimizes the H2 norm of the system. A sufficient condition is first established on the existence of the robust H2/<em>H</em>∞controller bases on the bounded real lemma. Then the corresponding state-feedback law is given in terms of a set of linear matrix inequalities (LMIs). It is showed that this condition is equivalent to the feasible solutions problem of LMI. Furthermore, the control strategy design problem is converted into a convex optimization problem subject to LMI constraints, which can be easily solved by standard numerical software.

scholarly journals Stability of stochastic systems with jumps

1996 ◽  
Vol 3 (2) ◽  
pp. 173-185 ◽  
Author(s):  
E. K. Boukas ◽  
H. Yang
Keyword(s):  
Brownian Motion ◽  
Control Strategy ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
And Brownian Motion ◽  
Quadratic Stabilization ◽  
Guaranteed Cost ◽  
Linear And Nonlinear Systems

This paper deals with stochastic stability of systems with Markovian jumps and Brownian motion. Mainly, we present sufficient conditions for quadratic stabilization of Ito type stochastic linear and nonlinear systems with Markovian jumps and Brownian motion using state feedback control. We also prove the guaranteed cost property of the proposed control strategy for the linear case.

Study on Fault-Tolerant Control Scheme for a Helicopter via Adaptive H∞ Control

2013 ◽  
Vol 455 ◽  
pp. 395-401 ◽  
Author(s):  
Xi Chen ◽  
Fu Yang Chen ◽  
Bin Jiang
Keyword(s):  
State Feedback ◽  
Fault Tolerant ◽  
Adaptive Method ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Flight Performance ◽  
Actuator Faults ◽  
Stabilization Problem ◽  
Control Scheme ◽  
Tolerant State

In this paper, the stabilization problem for the 3 Degree of Freedom (3-DOF) hovering system of Quadrotor with actuator faults is investigated. To handle the helicopter system, an H robust fault-tolerant state feedback control is proposed. In addition, an adaptive method is combined with fault-tolerant H control to improve the flight performance. A more practical actuator fault is built, and the model of the system is presented. The design operates in Linear Matrix Inequality (LMI) technique. Finally, the design was verified on both MATLAB and 3-DOF platform to exam the feasibility and stability of the method.

OPTIMAL GUARANTEED COST CONTROL OF UNCERTAIN STOCHASTIC COMPLEX DELAYED DYNAMICAL NETWORKS

2010 ◽  
Vol 10 (04) ◽  
pp. 577-590 ◽  
Author(s):  
SHUKAI LI ◽  
WANSHENG TANG ◽  
JIANXIONG ZHANG
Keyword(s):  
Complex Networks ◽  
State Feedback ◽  
Cost Control ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Control Laws ◽  
Guaranteed Cost ◽  
Stochastic Complex Networks ◽  
Delayed Dynamical Networks

This paper investigates the optimal guaranteed cost control of synchronization for uncertain stochastic complex networks with time-varying delays. The aim is to design state-feedback controllers such that the complex networks are globally asymptotical mean-square synchronization, and meanwhile the optimal upper bound of cost function is guaranteed. Based on Lyapunov–Krasovskii stability theory and Itô differential rule, sufficient condition for the existence of the optimal guaranteed cost control laws is given in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document