scholarly journals A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

Processes ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 814 ◽  
Author(s):  
Francisco-Ronay López-Estrada ◽  
Damiano Rotondo ◽  
Guillermo Valencia-Palomo
Keyword(s):  
Linear Models ◽  
Fault Tolerant ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
Complex Nonlinear Systems ◽  
Takagi Sugeno ◽  
Feedback Tracking ◽  
Equivalent Description

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).

Fault-tolerant control design using the linear parameter varying approach

2014 ◽  
Vol 24 (14) ◽  
pp. 1969-1988 ◽  
Author(s):  
Saúl Montes de Oca ◽  
Sebastian Tornil-Sin ◽  
Vicenç Puig ◽  
Didier Theilliol
Keyword(s):  
Fault Tolerant ◽  
Control Design ◽  
Fault Tolerant Control ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying

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.

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 Output feedback controller design for polynomial linear parameter varying system via parameter-dependent Lyapunov functions

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769032 ◽  
Author(s):  
Xiaobao Han ◽  
Zhenbao Liu ◽  
Huacong Li ◽  
Xianwei Liu
Keyword(s):  
Output Feedback ◽  
Optimization Problem ◽  
Controller Design ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Output Feedback Controller ◽  
Parameter Varying ◽  
Parameter Dependent

This article presents a new output feedback controller design method for polynomial linear parameter varying model with bounded parameter variation rate. Based on parameter-dependent Lyapunov function, the polynomial linear parameter varying system controller design is formulated into an optimization problem constrained by parameterized linear matrix inequalities. To solve this problem, first, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameter-dependent Lyapunov function, controller, and object coefficient matrices. Then, the control solving problem was reduced to a normal convex optimization problem with linear matrix inequalities constraint on a newly constructed convex polyhedron. Moreover, a parameter scheduling output feedback controller was achieved on the operating condition, which satisfies robust performance and dynamic performances. Finally, the feasibility and validity of the controller analysis and synthesis method are verified by the numerical simulation.

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