On Controlling an Uncertain System With Polynomial Chaos and H2 Control Design

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Brian A. Templeton ◽  
David E. Cox ◽  
Sean P. Kenny ◽  
Mehdi Ahmadian ◽  
Steve C. Southward
Keyword(s):  
Polynomial Chaos ◽  
State Space Model ◽  
Uncertain System ◽  
Lyapunov Equation ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
H2 Control ◽  
Physical Systems ◽  
Lqr Problem ◽  
Galerkin Projections

This paper applies the H2 norm along time and parameter domains. The norm is related to the probabilistic H2 problem. It is calculated using polynomial chaos to handle uncertainty in the plant model. The structure of expanded states resulting from Galerkin projections of a state space model with uncertain parameters is used to formulate cost functions in terms of mean performances of the states, as well as covariances. Also, bounds on the norm are described in terms of linear matrix inequalitys. The form of the gradient of the norm, which can be used in optimization, is given as a Lyapunov equation. Additionally, this approach can be used to solve the related probabilistic LQR problem. The legitimacy of the concept is demonstrated through two mechanical oscillator examples. These controllers could be easily implemented on physical systems without observing uncertain parameters.

Robust Weighted Measurement Fusion Kalman Predictor with Uncertain Parameters and Noise Variances

2014 ◽  
Vol 701-702 ◽  
pp. 538-543
Author(s):  
Chuan Shan Yang ◽  
Xue Mei Wang ◽  
Wen Juan Qi ◽  
Zi Li Deng
Keyword(s):  
Uncertain System ◽  
Lyapunov Equation ◽  
Conservative System ◽  
Upper Bounds ◽  
Uncertain Parameters ◽  
Invariant System ◽  
Worst Case ◽  
Kalman Predictor ◽  
Time Invariant ◽  
Time Invariant System

For the multisensor time-invariant system with uncertainties of both the noise variances and parameters, by introducing a fictitious white noise to compensate the uncertain parameters, the uncertain system can be converted into the conservative system with known parameters and uncertain noise variances. Using the minimax robust estimation principle, and the Lyapunov equation approach, a robust weighted measurement fusion Kalman predictor is presented based on the worst-case conservative system with the conservative upper bounds of noise variances. A Monte-Carlo simulation example shows its effectiveness.

Determining Human Control Intent Using Inverse LQR Solutions

2013 ◽  
Author(s):  
M. Cody Priess ◽  
Jongeun Choi ◽  
Clark Radcliffe
Keyword(s):  
Human Subjects ◽  
Optimal Solution ◽  
Linear Matrix ◽  
Minimization Method ◽  
Human Control ◽  
Balance Task ◽  
Lqr Problem ◽  
Seated Balance ◽  
Gradient Based ◽  
Time Invariant

In this paper, we have developed a method for determining the control intention in human subjects during a prescribed motion task. Our method is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? We describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. We develop a model for an upright seated-balance task which will be suitable for identification of human control intent once experimental data is available.

Bounding the Dynamic Behavior of an Uncertain System via Polynomial Chaos-based Simulation

SIMULATION ◽  
2009 ◽  
Vol 86 (1) ◽  
pp. 31-40 ◽  
Author(s):  
A. H. C. Smith ◽  
F. Ponci ◽  
A. Monti
Keyword(s):  
Dynamic Behavior ◽  
Polynomial Chaos ◽  
Uncertain System

Turbofan Engine Robust H-∞ Dynamical Output Feedback Control Design Based on LMI Method

2005 ◽  
Author(s):  
Xi Wang ◽  
Daoliang Tan ◽  
Tiejun Zheng
Keyword(s):  
Output Feedback ◽  
Linear Models ◽  
Nonlinear Models ◽  
Design Method ◽  
State Space Model ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Turbofan Engine ◽  
Engine Simulation ◽  
Linear State

This paper presents an approach to turbofan engine dynamical output feedback controller (DOFC) design in the framework of LMI (Linear Matrix Inequality)-based H∞ control. In combination with loop shaping and internal model principle, the linear state space model of a turbofan engine is converted into that of some augmented plant, which is used to establish the LMI formulations of the standard H∞ control problem with respect to this augmented plant. Furthermore, by solving optimal H∞ controller for the augmented plant, we indirectly obtain the H∞ DOFC of turbofan engine which successfully achieves the tracking of reference instructions and effective constraints on control inputs. This design method is applied to the H∞ DOFC design for the linear models of an advanced multivariate turbofan engine. The obtained H∞ DOFC is only in control of the steady state of this turbofan engine. Simulation results from the linear and nonlinear models of this turbofan engine show that the resulting controller has such properties as good tracking performance, strong disturbance rejection, and satisfying robustness.

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

scholarly journals Robust Switching Rule Design for Boost Converters with Uncertain Parameters and Disturbances

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yang Yang ◽  
Hamid Reza Karimi ◽  
Zhengrong Xiang
Keyword(s):  
Lyapunov Function ◽  
Linear System ◽  
Design Problem ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Common Lyapunov Function ◽  
Reference Tracking ◽  
Boost Converters ◽  
Switching Rule

This paper is concerned with the design problem of robust switching rule for Boost converters with uncertain parameters and disturbances. Firstly, the Boost converter is modeled as a switched affine linear system with uncertain parameters and disturbances. Then, using common Lyapunov function approach and linear matrix inequality (LMI) technique, a novel switching rule is proposed such that the model reference tracking performance is satisfied. Finally, a simulation result is provided to show the validity of the proposed method.

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

scholarly journals Nonfragile Integral-Based Event-Triggered Control of Uncertain Cyber-Physical Systems under Cyber‐Attacks

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Shen Yan ◽  
Sing Kiong Nguang ◽  
Liruo Zhang
Keyword(s):  
Sufficient Conditions ◽  
Cyber Physical Systems ◽  
Cyber Attacks ◽  
Linear Matrix ◽  
Time Interval ◽  
System State ◽  
Network Resources ◽  
Physical Systems ◽  
Mean Square Stability ◽  
Event Triggered

This article studies the problem of nonfragile integral-based event-triggered control for uncertain cyber-physical systems under cyber-attacks. An integral-based event-triggered scheme is proposed to reduce the data transmissions and save the limited network resources. The triggering condition is related to the mean of system state over a finite time interval instead of instant system state. Random cyber-attacks in a communication channel are taken into account and described by a stochastic variable subject to Bernoulli distribution. A novel Lyapunov–Krasovskii functional based on Legendre polynomials is constructed, and the Bessel–Legendre inequality technique is employed to handle the integral term induced by the integral-based event-triggered scheme. Resorting to these treatments, sufficient conditions are established via a set of linear matrix inequalities to guarantee the asymptotic mean-square stability of the closed-loop system. Finally, a numerical example shows that the presented method is effective.

Robust Reliable Sliding Mode H∞ Control for Uncertain Stochastic Nonlinear Jump Systems with Actuator Failures

2011 ◽  
Vol 480-481 ◽  
pp. 1475-1479
Author(s):  
Zhong Yi Tang ◽  
Sang Chen Ni ◽  
Wei Ping Duan
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Sliding Mode ◽  
Uncertain System ◽  
The State ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Sliding Surface ◽  
State Matrix ◽  
Actuator Failures

The problems of stochastic stability and robust reliable sliding mode H∞ control for a class of nonlinear matched and mismatched uncertain systems with stochastic jumps are considered in this paper. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix. The transition of the jumping parameters in the systems is governed by a finite-state markov process. A sufficient condition is given for the existence of integral sliding surface in terms of linear matrix inequalities (LMIs). Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in finite time. Moreover, a state feedback controller is also constructed by using the solution of LMIS. Finally, we give a design example in order to show the effectiveness of our method.

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