Improved multiobjective switching gain‐scheduled controller synthesis exploiting inexact scheduling parameters

Abstract

In this article, the design problem of switching gain-scheduled output-feedback (SGSOF) controller with mixed  2 ∕ ∞ performance exploiting inexact scheduling parameters for continuous-time linear parameter-varying (LPV) systems is tackled. The absolute and proportional uncertainties on the scheduling parameters are considered. All the system matrices of the LPV plant are supposed to have polynomial dependency of arbitrary degree on the scheduling parameters. By exploiting hysteresis switching law and utilizing two independent families of parameter-dependent Lyapunov matrices and a family of slack variables, introducing additional degrees of freedom, performance improvement is achieved. A design approach, involving a two-step algorithm, is proposed in terms of solutions to a set of parameter-dependent linear matrix inequalities (LMIs) including parameter searches for two scalar values. The merit of the proposed method lies in its less conservativeness in comparison with the available approaches in the literature. Numerical studies are carried out to demonstrate the effectiveness of the presented method.

Robust gain-scheduled output feedback H2 controller synthesis with reduced conservativeness: An application to EMS system

“…In the sequel, for the reason that will be mentioned later, V and Y are considered as parameter-independent matrices in expense of some conservatism (Yavari et al, 2020, 2021). Therefore, one can obtain…”

“…Roughly speaking, for systems with time-varying parameters, gain-scheduled controllers may lead to better performance than the robust ones when the scheduling parameters can be measured or estimated in real time. In this context, gain-scheduled output feedback (GSOF) control design for the continuous-time LPV systems has received considerable attention in the literature and references therein (Agulhari et al, 2013; Al-Jiboory and Zhu, 2018; Apkarian and Adams, 1998; Apkarian et al, 1995; Apkarian and Gahinet, 1995; Daafouz et al, 2008; Peixoto et al, 2021; Sadeghzadeh, 2018a; Sato, 2011c, 2011d; Sato and Peaucelle, 2013; Scherer, 1996; Sereni et al, 2020; Xie, 2013; Yavari et al, 2020, 2021; Zhang et al, 2019).…”

Simultaneous design of robust gain‐scheduled static output‐feedback controller and scaling matrices for linear parameter varying systems with inexact scheduling parameters

“…One way to cope with the inexact measurement scheduling parameters is to model the admissible region of the real scheduling parameters and measured ones as a convex polytope 9‐12 . For different kinds of measurement errors, such as bias 9 or proportional 10 or mixed measurement errors, 11,12 the convex polytope has corresponding different vertices.…”

“…If the parameter‐dependent controller synthesis conditions are ensured to hold at any point in this convex polytope, the closed‐loop system would be robust against inexact scheduling parameters. In the literature, this process has been applied in the design of gain‐scheduled control strategy, including dynamic output‐feedback controllers, 11 static output‐feedback controllers, 13 state‐feedback controllers, 14 and switching controllers 9,10 . Among them, the controller synthesis conditions are expressed as a set of matrix inequalities that are multi‐affine 11 or polynomial 10,13 depending on scheduling parameters.…”

“…In the literature, this process has been applied in the design of gain‐scheduled control strategy, including dynamic output‐feedback controllers, 11 static output‐feedback controllers, 13 state‐feedback controllers, 14 and switching controllers 9,10 . Among them, the controller synthesis conditions are expressed as a set of matrix inequalities that are multi‐affine 11 or polynomial 10,13 depending on scheduling parameters. For solving polynomially parameter‐dependent matrix inequalities, it is possible to use sum‐of‐square relaxations or other relaxation methods from a theoretical perspective 15 .…”