Online Switching Control of LFT Parameter-Dependent Systems

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Ke Dong ◽  
Fen Wu
Keyword(s):  
Switching Control ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Control Approach ◽  
Control Scheme ◽  
Gain Scheduling Control ◽  
Gain Scheduled Controller ◽  
Parameter Dependent ◽  
Gain Scheduled

To improve controlled performance and expand gain-scheduling control capability, we propose a switching control approach of linear fractional transformation parameter-dependent systems using multiple Lyapunov functions combined with online control techniques. At each switching instant, a gain-scheduled controller working for the next switching interval will be designed online. The switching control synthesis condition is formulated as linear matrix inequalities and can be solved efficiently, upon which the controller will be constructed. The online switching control scheme is demonstrated using an uninhabited combat aerospace vehicle problem.

A Nonlinear Gain-Scheduling Compensation Approach Using Parameter-Dependent Lyapunov Functions

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Fen Wu ◽  
Xun Song ◽  
Zhang Ren
Keyword(s):  
Lyapunov Functions ◽  
Gain Scheduling ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Nonlinear Gain ◽  
Control Approach ◽  
Lpv Control ◽  
Gain Scheduling Control ◽  
Output Information ◽  
Parameter Dependent

This paper addresses the gain-scheduling control design for nonlinear systems to achieve output regulation. For gain-scheduling control, the linear parameter-varying (LPV) model is obtained by linearizing the plant about zero-error trajectories upon which an LPV controller is based. A key in this process is to find a nonlinear output feedback compensator such that its linearization matches with the designed LPV controller. Then, the stability and performance properties of LPV control about the zero-error trajectories can be inherited when the nonlinear compensator is implemented. By incorporating the exosystem, nominal input, and measured output information into the LPV model, the LPV control synthesis problem is formulated as linear matrix inequalities (LMIs) using parameter-dependent Lyapunov functions (PDLFs). Moreover, explicit formulae for the construction of the nonlinear gain-scheduled compensator have been derived to meet the linearization requirement. Finally, the validity of the proposed nonlinear gain-scheduling control approach is demonstrated through a ball and beam example.

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

Gain Scheduled Control of Gas Turbine Engines: Stability and Verification

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Mehrdad Pakmehr ◽  
Nathan Fitzgerald ◽  
Eric M. Feron ◽  
Jeff S. Shamma ◽  
Alireza Behbahani
Keyword(s):  
Convex Optimization ◽  
Gas Turbine ◽  
Closed Loop ◽  
Gas Turbine Engine ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Turbine Engine ◽  
Gain Scheduled Controller ◽  
Gain Scheduled

A stable gain scheduled controller for a gas turbine engine that drives a variable pitch propeller is developed and described. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and nonequilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. To verify the stability of the closed-loop system on-line, an optimization problem is proposed, which is solvable using convex optimization tools. Simulation results show that the developed gain scheduled controller is capable to regulate a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

LPV Modeling of Buck Converter and Gain Scheduling Control

2011 ◽  
Vol 317-319 ◽  
pp. 1390-1393
Author(s):  
Guo Xian Lin ◽  
Wei Xie
Keyword(s):  
State Feedback ◽  
Specific Area ◽  
Gain Scheduling ◽  
Buck Converter ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Signal Model ◽  
Line Voltage ◽  
Gain Scheduling Control ◽  
Gain Scheduled

A kind of gain scheduling control is designed for Buck converter. The small signal model of the Buck converter is translated into the Linear Parameter-Varying (LPV) dynamic equation with the load and the line voltage as the scheduled parameters. Based on it, the closed-loop system poles assignment is taken to the specific area with gain scheduled state feedback via linear matrix inequalities (LMIs) technique, the gain scheduled state feedback is designed to regulate the duty cycle of the switch conduction. Compared with robust state feedback control, it has better disturbance rejection performance.

Reduction in the Number of Gain-Scheduling Parameters Using Dimensional Transformation

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Haftay Hailu ◽  
Sean Brennan
Keyword(s):  
Linear Time ◽  
Gain Scheduling ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lti System ◽  
Gain Scheduled Controller ◽  
Parameter Dependent ◽  
Time Invariant ◽  
Linear Parameter Varying System ◽  
Gain Scheduled

A method is presented that can often reduce the number of scheduling parameters for gain-scheduled controller implementation by transformation of the system representation using parameter-dependent dimensional transformations. In some cases, the reduction in parameter dependence is so significant that a linear parameter-varying system can be transformed to an equivalent linear time invariant (LTI) system, and a simple example of this is given. A general analysis of the parameter-dependent dimensional transformation using a matrix-based approach is then presented. It is shown that, while some transformations simplify gain scheduling, others may increase the number of scheduling parameters. This work explores the mathematical conditions causing an increase or decrease in varying parameters resulting from a given transformation, thereby allowing one to seek transformations that most reduce the number of gain-scheduled parameters in the controller synthesis step.

scholarly journals A Parameter-Dependent Approach to Observer-BasedH∞Control for Networked Control LPV Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Yanhui Li ◽  
Xiujie Zhou ◽  
Chang Zhang ◽  
Hamid Reza Karimi
Keyword(s):  
Collaborative Design ◽  
Controller Design ◽  
Lyapunov Stability Theory ◽  
Networked Control ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Time Varying ◽  
Infinite Dimensional ◽  
Lpv Systems ◽  
Parameter Dependent

We address the observer-basedH∞controller design problem for networked control LPV (NC LPV) systems, which are network-based systems that depend on unknown but measurable time-varying parameters. According to the analysis of the special issues brought by introducing network into LPV systems and the state reconstruction based on the observer, a new augmented model is established with two independent time-varying delays, which can carry out the controller and observer collaborative design effectively. Based on the parameter-dependent Lyapunov stability theory, a sufficient condition is proposed to ensure that the closed-loop system is asymptotically stable with a guaranteedH∞performance levelγ, in which the coupling between Lyapunov function matrices and the system matrices existed. By using the Projection Lemma and introducing a slack matrix, the decoupling is achieved successfully, which refers to reducing conservatism. In the present study, the condition for stability analysis and control synthesis is formulated in terms of the parameterized linear matrix inequality (PLMI), which is infinite-dimensional and can be transformed into finite by using the basis function method and gridding technique. A numerical example is given to demonstrate the high validity and merit of the proposed approach.

Advanced gain scheduledH∞controller for robotic manipulators

Robotica ◽  
2002 ◽  
Vol 20 (5) ◽  
pp. 537-544
Author(s):  
Zhongwei Yu ◽  
Huitang Chen ◽  
Peng-Yung Woo
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Robotic Manipulators ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Vertex Set ◽  
Parameter Dependent ◽  
Gain Scheduled ◽  
Upper Boundary

SummaryA conservatism-reduced design of a gain scheduled output feedbackH∞controller for ann-joint rigid robotic manipulator, which integrates the varying-parameter rate without their feedback, is proposed. The robotic system is reduced to a 1inear parameter varying (LPV) form, which depends on the varying-parameter. By using a parameter-dependent Lyapunov function, the design of a controller, which satisfies the closed-loopH∞performance, is reduced to a solution of the parameterized linear matrix inequalities (LMIs) of parameter matrices. With a use of the concept of “multi-convexity”, the solution of the infinite LMIs in the varying-parameter and its rate space is reduced to a solution of the finite LMIs for the vertex set. The proposed controller eliminates the feedback of the varying-parameter rate and fixes its upper boundary so that the conservatism of the controller design is reduced. Experimental results verify the effectiveness of the proposed design.

scholarly journals Event-triggered Synchronization of Uncertain Delayed Generalized RDNNs

2021 ◽  
Author(s):  
Weiyuan Zhang ◽  
Junmin Li ◽  
Keyi Xing ◽  
Rui Zhang ◽  
Xinyu Zhang
Keyword(s):  
Reaction Diffusion ◽  
Delay System ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Control Scheme ◽  
Halanay’S Inequality ◽  
Network Transmission ◽  
Inequality Techniques ◽  
And Control ◽  
Event Triggered

Abstract This paper investigates the exponential synchronization analysis of master–slave chaotic uncertain delayed generalized reaction-diffusion neural networks (GRDNNs) with event-triggered control scheme. A delay GRDNNs system model for the analysis is constructed by investigating the effect of the network transmission delay. By constructing a novel Lyapunov–Krasovskii functional and using a delay system approach for designing event-triggered controllers and some inequality techniques like Jensen’s inequality, Wirtinger’s inequality and Halanay’s inequality, the criteria are obtained for the event-triggered synchronization analysis and control synthesis of delayed GRDNNs. The synchronization criteria are formulated in terms of linear matrix inequalities. Finally, we conclude that the slave systems synchronize with the master systems. Two examples show the proposed theoretical results are feasible and effective.

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