Robust Gain-Scheduling Output Feedback Control With Noisy Scheduling Parameters

2015 ◽  
Author(s):  
Ali Khudhair Al-Jiboory ◽  
Guoming Zhu
Keyword(s):  
Output Feedback ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Gain Scheduling ◽  
Linear Matrix ◽  
Synthesis Methods ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
Comparison Results ◽  
H2 Performance

Robust Gain-Scheduling (RGS) control strategy has been considered in this paper. In contrast to the conventional gain-scheduling synthesis methods, the scheduling parameters are assumed to be inexactly measured. This is a practical assumption since measurement noise is inevitable even with very accurate sensors. Multi-simplex modeling approach was used to model the scheduling parameters and their uncertainties in a convex domain. Sufficient conditions in terms of Parametrized Linear Matrix Inequalities (PLMIs) for synthesizing dynamic output-feedback controllers are derived. The resulting controller not only guarantees robust stability and H2 performance but also ensures robustness against scheduling parameters uncertainties. The effectiveness of the developed conditions is demonstrated through numerical example with simulation and comparisons with existing approaches from literature. The comparison results confirm that the developed approach outperforms the existing ones considerably.

Vibration control of base-isolated structures using mixed H2/H∞ output-feedback control

2009 ◽  
Vol 223 (6) ◽  
pp. 809-820 ◽  
Author(s):  
H R Karimi ◽  
M Zapateiro ◽  
N Luo
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Design Methodology ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Building Structures ◽  
Matrix Inequalities ◽  
Closed Loop System

A mixed H2/ H∞ output-feedback control design methodology for vibration reduction of base-isolated building structures modelled in the form of second-order linear systems is presented. Sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities. A controller that guarantees asymptotic stability and a mixed H2/ H∞ performance for the closed-loop system of the structure is developed, based on a Lyapunov function. The performance of the controller is evaluated by means of simulations in MATLAB/Simulink.

scholarly journals ℒ2Gain Performance for a Class of Lipschitz Uncertain Nonlinear Systems via Variable Gain Robust Output Feedback Controllers

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hidetoshi Oya ◽  
Kojiro Hagino
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Uncertain Nonlinear Systems ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
Variable Gain ◽  
Output Feedback Controller

We consider a design problem of a variable gain robust output feedback controller with guaranteedℒ2gain performance for a class of Lipschitz uncertain nonlinear systems. The proposed variable gain robust output feedback controller achieves not only robust stability but also a specifiedℒ2gain performance. In this paper, we show that sufficient conditions for the existence of the proposed variable gain robust output feedback controller with guaranteedℒ2gain performance are given in terms of linear matrix inequalities (LMIs). Finally, a simple numerical example is included.

An LMI Optimization Approach to the Design of Structured Linear Controllers Using a Linearization Algorithm

2003 ◽  
Author(s):  
Jeongheon Han ◽  
Robert E. Skelton
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Matrix Inequalities ◽  
Lmi Optimization ◽  
Fixed Order ◽  
H2 Performance ◽  
Linear Controllers

This paper presents a new algorithm for the design of linear controllers with special constraints imposed on the control gain matrix. This so called SLC (Structured Linear Control) problem can be formulated with linear matrix inequalities (LMI’s) with a nonconvex equality constraint. This class of prolems includes fixed order output feedback control, multi-objective controller design, decentralized controller design, joint plant and controller design, and other interesting control problems. Our approach includes two main contributions. One is that many design specifications such as H∞ performance, generalized H2 performance including H2 performance, l∞ performance, and upper covariance bounding controllers are described by a similar matrix inequality. A new matrix variable is introduced to give more freedom to design the controller. Indeed this new variable helps to find the optimal fixed-order output feedback controller. The second contribution uses a linearization algorithm to search for a solution to the nonconvex SLC problems. This has the effect of adding a certain potential function to the nonconvex constraints to make them convex. Although the constraints are added to make functions convex, those modified matrix inequalities will not bring significant conservatism because they will ultimately go to zero, guaranteeing the feasibility of the original nonconvex problem. Numerical examples demonstrate the performance of the proposed algorithms and provide a comparison with some of the existing methods.

Static Output Non-Fragile Control of Fuzzy Bilinear System

2012 ◽  
Vol 198-199 ◽  
pp. 1073-1076
Author(s):  
Guo Zhang ◽  
Yan Hua Zhao
Keyword(s):  
Output Feedback ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Bilinear System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Controller Gain ◽  
Static Output Feedback Control ◽  
Compensation Approach ◽  
Static Output

This paper focuses on the problem of non-fragile static output feedback control for discrete-time fuzzy bilinear systems. Based on the parallel distributed compensation approach, the sufficient conditions are derived in the presence of the additive controller gain perturbations. The stabilization conditions are further formulated into linear matrix inequalities (LMI) so that the desired controller can be easily obtained by using the LMI toolbox.

Robust Gain-Scheduling Output Feedback Control of State-Delayed LFT Systems Using Dynamic IQCs

2015 ◽  
Author(s):  
Chengzhi Yuan ◽  
Fen Wu ◽  
Chang Duan
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Gain Scheduling ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
State Delay ◽  
Synthesis Conditions ◽  
Output Behavior ◽  
Gain Scheduled

This paper is concerned with the robust gain-scheduling output feedback control problem for a class of linear parameter-varying systems with time-varying state delay. The controlled plant under consideration is described as a linear fractional transformation (LFT) model of scheduling parameters. Dynamic integral quadratics (IQCs) are employed to characterize the input-output behavior of the state-delay nonlinearity. The robust stability and the L2-gain performance are first analyzed using quadratic Lyapunov function. Then, the design of dynamic output-feedback controllers robust against the plant state-delay nonlinearity and gain-scheduled by parameters is examined. The synthesis conditions of such robust gain-scheduling controllers are formulated in terms of linear matrix inequalities (LMIs) plus a line search, which can be solved effectively using existing algorithms. A numerical example has been used to demonstrate the effectiveness and advantages of the proposed approach.

Delayed Output Feedback Control for Nonlinear Systems With Fuzzy Observers

2012 ◽  
Author(s):  
Mansour Karkoub ◽  
Tzu Sung Wu
Keyword(s):  
Feedback Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Output Feedback ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
External Disturbances ◽  
Control Scheme

In this paper, the design problem of delayed output feedback control scheme using two-layer interval fuzzy observers for a class of nonlinear systems with state and output delays is investigated. The Takagi-Sugeno type fuzzy linear model with an on-line update law is used to approximate the nonlinear system. Based on the fuzzy model, a two-layer interval fuzzy observer is used to reconstruct the system states according to equal interval output time delay slices. Subsequently, a delayed output feedback adaptive fuzzy controller is developed to override the nonlinearities, time delays, and external disturbances such that the H∞ tracking performance is achieved. The linguistic information is developped by setting the membership functions of the fuzzy logic system and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. The filtered tracking error dynamics are designed to satisfy the Strictly Positive Realness (SPR) condition. Based on the Lyapunov stability criterion and linear matrix inequalities (LMIs), some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbances on the tracking error can be attenuated to any prescribed level and consequently an H∞ tracking control is achieved. Finally, a numerical example of a two-link robot manipulator is given to illustrate the effectiveness of the proposed control scheme.

scholarly journals Static Output-Feedback Control for Vehicle Suspensions: A Single-Step Linear Matrix Inequality Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Josep Rubió-Massegú ◽  
Francisco Palacios-Quiñonero ◽  
Josep M. Rossell ◽  
Hamid Reza Karimi
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Vehicle Suspension ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequality ◽  
Feedback Controllers ◽  
Feedback Information ◽  
Static Output

In this paper, a new strategy to design static output-feedback controllers for a class of vehicle suspension systems is presented. A theoretical background on recent advances in output-feedback control is first provided, which makes possible an effective synthesis of static output-feedback controllers by solving a single linear matrix inequality optimization problem. Next, a simplified model of a quarter-car suspension system is proposed, taking the ride comfort, suspension stroke, road holding ability, and control effort as the main performance criteria in the vehicle suspension design. The new approach is then used to design a static output-feedbackH∞controller that only uses the suspension deflection and the sprung mass velocity as feedback information. Numerical simulations indicate that, despite the restricted feedback information, this static output-feedbackH∞controller exhibits an excellent behavior in terms of both frequency and time responses, when compared with the corresponding state-feedbackH∞controller.

scholarly journals Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3285
Author(s):  
Andreas Rauh ◽  
Swantje Romig
Keyword(s):  
Linear Matrix Inequalities ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Iterative Solution ◽  
Simultaneous Optimization ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Optimization Task ◽  
State Observers

Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H∞ measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller—which was jointly optimized with a linear derivative estimator—with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

scholarly journals Output-Feedback Stabilization Control of Systems with Random Switchings and State Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Wei Qian ◽  
Shen Cong ◽  
Zheng Zheng
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Feedback Stabilization ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Output Feedback Stabilization ◽  
Stabilization Control ◽  
Exponentially Stable

The work is concerned with output-feedback stabilization control problem for a class of systems with random switchings and state jumps. The switching signal is supposed to obey Poisson distribution. Firstly, based on the asymptotical property of the distribution of switching points, we derive some sufficient conditions to guarantee the closed-loop system to be almost surely exponentially stable. Then, we pose a parametrization approach to convert the construction conditions of the output-feedback control into a family of matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of our method.

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