Control of LPV systems subject to state constraints and input saturation

2018 ◽  
Vol 40 (14) ◽  
pp. 3985-3993 ◽  
Author(s):  
Yanmei Hu ◽  
Guangren Duan ◽  
Feng Tan
Keyword(s):  
Linear Matrix Inequalities ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Parameter Uncertainties ◽  
Linear Parameter Varying ◽  
Linear Parameter Varying Systems ◽  
Parameter Varying

This paper deals with the stabilization of state-constrained linear parameter-varying systems subject to parameter uncertainties and input saturation. Based on a class of parameter-dependent Lyapunov functions, and the set invariance, sufficient conditions for the stabilization problem of the linear parameter-varying systems are established in terms of parameterized linear matrix inequalities. Further, these conditions are converted into linear matrix inequalities by using a parameter relaxation technique. Finally, detailed simulation results are presented to illustrate the effectiveness of the proposed methodology.

scholarly journals Finite-time non-fragile controller design for a class of switching linear parameter varying systems based on linear matrix inequalities

2018 ◽  
Vol 233 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Chengcheng Ren ◽  
Longfang Li ◽  
Shuping He
Keyword(s):  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
Linear Parameter Varying System

The finite-time non-fragile controller design problem is studied for a class of switching linear parameter varying system in this article. We aim to design a suitable finite-time non-fragile controller such that the closed-loop switching linear parameter varying system is finite-time bounded. Based on the linear matrix inequalities and multiple Lyapunov functions methods, sufficient conditions on the existence of the finite-time non-fragile controller are proposed and proved. Considering the parameters dependence, we change the infinite linear matrix inequalities into finite linear matrix inequalities by using approximate basis functions and gridding techniques. Finally, a simulation example is given to illustrate the effectiveness of the design methods.

State estimation for a class of Linear Parameter-Varying systems with parametric uncertainties

2020 ◽  
Vol 42 (15) ◽  
pp. 3035-3042
Author(s):  
Zhongwei He ◽  
Wei Xie
Keyword(s):  
State Estimation ◽  
Sufficient Conditions ◽  
Estimation Methods ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Observation Error ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Linear Parameter Varying Systems ◽  
Parameter Varying

This paper is concerned with interval state estimation for a class of Linear Parameter-Varying systems with parametric uncertainties. Firstly, sufficient conditions to guarantee both the cooperativity and stability of observation error dynamics are presented in terms of parameterized matrix inequality formulations. Secondly, a novel method for scheduled controller law design is proposed in the framework of interval observer design. Under the assumptions that scheduled parameters have a polytopic structure property, the problems of the existence conditions of observers and scheduled controller design are transformed into finite linear matrix inequalities ones, which can be solved by convex optimization algorithms. The validity of the proposed state estimation methods is illustrated through a simple example.

An observer-based H∞ linear parameter varying controller for time delayed linear parameter varying systems using dilated linear matrix inequalities and Wirtinger inequality

2021 ◽  
pp. 014233122098362
Author(s):  
Mohamed Hechmi Bouazizi
Keyword(s):  
Linear Matrix Inequalities ◽  
State Feedback ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Synthesis Conditions ◽  
Time Varying Delay ◽  
Parameter Varying

In this study, we give a method for the design of linear parameter varying (LPV) observers in order to perform an LPV time delayed state feedback control for LPV systems with time varying delay. We derive some tractable analysis and synthesis conditions expressed in terms of linear matrix inequalities (LMIs). We show how it is possible to reduce significantly the conservatism of the quadratic approach by using parameter dependent Lyapunov-Krasovskii functional and LMI dilation techniques jointed to the Wirtinger integral inequality. We also present a method that makes it possible to do without the separation principle when determining the observer and the state feedback parameters. The synthesis problem is formulated without this principle. A numerical example is provided to illustrate the effectiveness of our approach that leads to a better H∞ level compared with other results, from literature, for the same example.

Robust linear parameter varying attitude control of a quadrotor unmanned aerial vehicle with state constraints and input saturation subject to wind disturbance

2019 ◽  
Vol 42 (6) ◽  
pp. 1083-1096 ◽  
Author(s):  
Mohammad Reza Soltanpour ◽  
Farshad Hasanvand ◽  
Reza Hooshmand
Keyword(s):  
Unmanned Aerial Vehicle ◽  
Attitude Control ◽  
Input Saturation ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Aerial Vehicle ◽  
Parameter Varying ◽  
Parameter Dependent

In this paper, a gain scheduled [Formula: see text] state-feedback controller has been designed to control the attitude of a linear parameter varying (LPV) model of a quadrotor unmanned aerial vehicle (UAV). The scheduling parameters vector, which consists of some states and the control inputs, must vary in a specified polyhedron so that the affine LPV model would be analyzable; therefore, some pre-assumed constraints on states and input saturation have been taken into account in design process. The stabilization and disturbance attenuation conditions are obtained via elementary manipulations on the notion of [Formula: see text] control design. The resulting parameter dependent linear matrix inequalities are solved through a Robust LMI Parser (Rolmip) – which works jointly with YALMIP (A toolbox for modeling and optimization in MATLAB)– by transforming polynomial parameter dependent matrices into multi-simplex domain, to best deal with nonconvex problems. In the end, simulation results have been presented and compared with existing literature to examine the capability of such method in the presence and absence of wind disturbances.

scholarly journals Sliding Mode Observers Based-Simultaneous Actuator and Sensor Faults Estimation for Linear Parameter Varying Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Ali Ben Brahim ◽  
Slim Dhahri ◽  
Fayçal Ben Hmida ◽  
Anis Sallami
Keyword(s):  
Sliding Mode ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
System States ◽  
Sliding Mode Observers

This paper proposes a scheme to estimate actuator and sensor faults simultaneously for a class of linear parameter varying system expressed in polytopic structure where its parameters evolve in the hypercube domain. Transformed coordinate system design is adopted to decouple faults in actuators and sensors during the course of the system’s operation coincidentally, and then two polytopic subsystems are constructed. The first subsystem includes the effect of actuator faults but is free from sensor faults and the second one is affected only by sensor faults. The main contribution is to conceive two polytopic sliding mode observers in order to estimate the system states and actuator and sensor faults at the same time. Meanwhile, in linear matrix inequality optimization formalism, sufficient conditions are derived withH∞performances to guarantee the stability of estimation error and to minimize the effect of disturbances. Therefore, all parameters of observers can be designed by solving these conditions. Finally, simulation results are given to illustrate the effectiveness of the proposed simultaneous actuator and sensor faults estimation.

Interval observer-based methodology for passive fault tolerant control of linear parameter-varying systems

2021 ◽  
pp. 014233122110403
Author(s):  
Rihab Lamouchi ◽  
Tarek Raissi ◽  
Messaoud Amairi ◽  
Mohamed Aoun
Keyword(s):  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Fault Tolerant Control ◽  
System Stability ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Linear Parameter Varying Systems ◽  
Parameter Varying ◽  
Interval Observer ◽  
Component Faults

The paper deals with passive fault tolerant control for linear parameter varying systems subject to component faults. Under the assumption that the faults magnitudes are considered unknown but bounded, a novel methodology is proposed using interval observer with an [Formula: see text] formalism to attenuate the effects of the uncertainties and to improve the accuracy of the proposed observer. The necessary and sufficient conditions of the control system stability are developed in terms of matrix inequalities constraints using Lyapunov stability theory. Based on a linear state feedback, a fault tolerant control strategy is designed to handle component faults effect as well as external disturbances and preserve the system closed-loop stability for both fault-free and component faulty cases. Two simulation examples are presented to demonstrate the effectiveness of the proposed method.

scholarly journals Asynchronous finite-time control for networked switched linear parameter-varying systems via an event-triggered communication scheme

2018 ◽  
Vol 233 (1) ◽  
pp. 44-57
Author(s):  
Hangli Ren ◽  
Guangdeng Zong
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Parameter ◽  
Input Output ◽  
Linear Parameter Varying ◽  
Linear Parameter Varying Systems ◽  
Time Control ◽  
Communication Scheme ◽  
Parameter Varying ◽  
Event Triggered

This article addresses the finite-time control problem for a class of switched linear parameter-varying systems via an event-triggered communication scheme. Different from the existing finite-time problems, not only the problem of finite-time boundedness but also the problem of input-output finite-time stability is considered in this article. Using an asynchronous switching scheme, sufficient conditions are established to guarantee the event-based closed-loop systems are both finite-time bounded and input-output finite-time stable. Then, a parameter-dependent asynchronous controller is designed by solving a set of linear matrix inequalities. Finally, a numerical example is presented to show the effectiveness of the result.

Generalized dynamic observer design for quasi-LPV systems

2018 ◽  
Vol 66 (3) ◽  
pp. 225-233 ◽  
Author(s):  
A.-J. Pérez-Estrada ◽  
G.-L. Osorio-Gordillo ◽  
M. Darouach ◽  
V.-H. Olivares-Peregrino
Keyword(s):  
Linear Matrix Inequalities ◽  
Estimation Error ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Lpv Systems ◽  
Algebraic Constraints ◽  
Dynamic Observer

Abstract This paper presents a new generalized dynamic observer (GDO) for quasi-linear parameter varying (LPV) systems. It generalises the structures of the proportional observer (PO) and proportional integral observer (PIO). The design of the GDO is derived from the solution of linear matrix inequalities (LMIs) and the solution of the algebraic constraints obtained from the estimation error analysis. The efficiency of the proposed approach is illustrated by a numerical example.

scholarly journals Passive gain-scheduling filtering for jumping linear parameter varying systems with fading channels based on the hidden Markov model

2018 ◽  
Vol 233 (1) ◽  
pp. 67-79 ◽  
Author(s):  
Liang Shen ◽  
Xiaofei Yang ◽  
Jing Wang ◽  
Jianwei Xia
Keyword(s):  
Fading Channels ◽  
Information Exchange ◽  
Hidden Markov ◽  
Sufficient Conditions ◽  
Gain Scheduling ◽  
Linear Parameter ◽  
Markov Jump ◽  
Linear Parameter Varying ◽  
Linear Parameter Varying Systems ◽  
Parameter Varying

This work is aimed to address the passive gain-scheduling filtering problem for Markov jump linear parameter varying systems with fading channels. A hidden Markov process is employed to describe mode information exchange between the system and the presented filter. By the aid of stochastic analysis theory, some sufficient conditions for guaranteeing the existence of an available passive gain-scheduling filter are established. On the basis of the designed filter, the passivity of the filtering error system is ensured in the presence of randomly occurring fading channels. Finally, an explained example is put forward to verify the effectiveness of the filter.

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