H 2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach

2011 ◽  
Author(s):  
Xin Wang ◽  
Edwin E. Yaz ◽  
Susan C. Schneider ◽  
Yvonne I. Yaz
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Time Step ◽  
Control Approach ◽  
The Difference

A novel H2–H∞ State Dependent Riccati Equation control approach is presented for providing a generalized control framework to discrete time nonlinear system. By solving a generalized Riccati Equation at each time step, the nonlinear state feedback control solution is found to satisfy mixed performance criteria guaranteeing quadratic optimality with inherent stability property in combination with H∞ type of disturbance attenuation. Two numerical techniques to compute the solution of the resulting Riccati equation are presented: The first one is based on finding the steady state solution of the difference equation at every step and the second one is based on finding the minimum solution of a linear matrix inequality. The effectiveness of the proposed techniques is demonstrated by simulations involving the control of an inverted pendulum on a cart, a benchmark mechanical system.

Modeling and Fuzzy Control for Complex Flexible Nonlinear Systems with Time-Delay

2014 ◽  
Vol 602-605 ◽  
pp. 920-923
Author(s):  
Ji Xiang Chen
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
Fuzzy State

A time-delay discrete-time fuzzy singularly perturbed modeling and fuzzy state feedback control approach are presented for a class of complex flexible nonlinear systems with time-delay. The considered flexible nonlinear system is firstly described by a time-delay standard discrete-time fuzzy singular perturbation model. A fuzzy state feedback control law is secondly design. By using a matrix spectral norm and linear matrix inequalities approach, the sufficient conditions of the controller existence are divided. The provided controller not only can stabilize the resulting closed-loop system but also overcome the effects caused by both time-delay and external disturbances. A simulation example is given to illustrate the effectiveness of the developed result.

scholarly journals The Robust Consensus of a Noisy Deffuant-Weisbuch Model

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Jiangbo Zhang ◽  
Yiyi Zhao
Keyword(s):  
Discrete Time ◽  
Model Parameters ◽  
Positive Probability ◽  
Noise Strength ◽  
Opinion Formation ◽  
Time Step ◽  
Absolute Value ◽  
The Difference ◽  
Robust Consensus

We construct a new opinion formation of the Deffuant-Weisbuch model with the interference of the outer noise, where there are finite n agents and the evolution is discrete-time. The opinion interaction occurs by one randomly chosen pair at each time step. The difference to the original Deffuant-Weisbuch model is that communications of any selected pairs will be affected by noises. The aim of this paper is to study the robust consensus of this noisy Deffuant-Weisbuch model. We first define the noise strength as the maximum noise absolute value. We will then show that when the noise strength is less than a certain threshold, this noisy model will achieve T-robust consensus when t is sufficiently large; next we prove that the noisy model achieves robust consensus with a positive probability; finally, we demonstrate these results and provide numerical relations among the noise strength and some model parameters.

Discrete Time-Coupled State-Dependent Riccati Equation Control of Nonlinear Mechatronic Systems

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Xin Wang
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Disturbance Attenuation ◽  
Infinite Time ◽  
Mechatronic Systems ◽  
Feedback Controllers ◽  
Control Laws ◽  
State Dependent ◽  
Time Optimal ◽  
Nonlinear Plant

Abstract A discrete-time-coupled state-dependent Riccati equation (CSDRE) control strategy is structured in this paper for synthesizing state feedback controllers satisfying the combined nonlinear quadratic regulator (NLQR) and H∞ robust control performance objectives. Under smoothness assumptions, the nonlinear plant dynamics can be formulated into state-dependent coefficient form through direct parameterization. By solving a pair of coupled state-dependent Riccati equations, the optimal stabilizing solutions can achieve inherent stability, nonlinear quadratic optimality, and H∞ disturbance attenuation performance. The established two-player Nash's game theory is utilized for developing both of the finite and infinite time optimal control laws. Furuta swing-up pendulum, a representative nonholonomic underactuated nonlinear system, is stabilized in real-time for validating the robustness and potential of proposed approach in mechatronics applications.

scholarly journals Robust Moving HorizonH∞Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
F. Yıldız Tascikaraoglu ◽  
I. B. Kucukdemiral ◽  
J. Imura
Keyword(s):  
Discrete Time ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Delayed Systems ◽  
State Delays ◽  
Delay Dependent

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.

scholarly journals Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Chang Che ◽  
Jiayao Peng ◽  
Tao Zhao ◽  
Jian Xiao ◽  
Jie Zhou
Keyword(s):  
Nonlinear Systems ◽  
Integral Inequality ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
State Delays ◽  
Lyapunov Stability Criterion ◽  
Takagi Sugeno

This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S) fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs) are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

scholarly journals Design of a Preview Controller for Discrete-Time Systems Based on LMI

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Reference Signal ◽  
Original System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Time Systems

A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.

scholarly journals StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yong Zhao ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

Composite attitude control for flexible spacecraft with simultaneous disturbance attenuation and rejection performance

2011 ◽  
Vol 226 (2) ◽  
pp. 154-161 ◽  
Author(s):  
H Liu ◽  
L Guo ◽  
Y Zhang
Keyword(s):  
Model Uncertainty ◽  
Attitude Control ◽  
Disturbance Observer ◽  
State Feedback ◽  
Flexible Spacecraft ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Space Environment ◽  
Control Approach ◽  
Measurement Noises

In this paper, a composite attitude control approach for orbiting spacecraft with rigid central hubs and flexible appendages is presented. The established attitude control model consists of the vibration modes excited by the rigid body, the space environment disturbances, the measurement noises, and the model uncertainty. The model is formulated into a dynamic system with two types of disturbance inputs. A composite control law with the simultaneous disturbance attenuation and rejection performance is presented for the flexible spacecraft system subject to multiple disturbances. The disturbance-observer-based control is designed for feedforward compensation of the elastic vibration. The H∞ state-feedback controller is designed to perform the robust attitude control in the presence of the space environment disturbances, measurement noises, and the model uncertainty. Numerical simulations show that the performance of the attitude control systems can be improved by combining the disturbance observer with H∞ state-feedback control.

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