Linear quadratic control of LPV systems using static and shifting specifications

Rotondo, Damiano; Puig, Vicenç; Nejjari, Fatiha

doi:10.1109/ecc.2015.7331007

Cited by 13 publications

(4 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is worth noting that what has been discussed in this section about the control of convex systems does not apply only to the problem of controller design for quadratic stabilization but also to the case of other specifications, such as D-stabilization [108], H ∞ control [109], control with guaranteed cost [110] and many more. The described methods can be adapted to deal with convex systems with piecewise constant parameters, which provide a unifying concept lying in between the robust and the gain-scheduled perspectives, including both as extremal cases [111].…”

Section: Final Comments On Control Of Convex Systemsmentioning

confidence: 99%

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

2019

Self Cite

View full text Add to dashboard Cite

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).

show abstract

Section: Final Comments On Control Of Convex Systemsmentioning

confidence: 99%

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

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…De forma parecida, se puede realizar el control H ∞ cuadrático utilizando (29), en la cual el término superior izquierdo A(θ) T P + PA(θ) es reemplazado por el término a mano izquierda en (41). Finalmente, de acuerdo con (Rotondo et al, 2015b), el control con coste garantizado puede diseñarse modificando el criterio cuadrático (30) en:…”

Section: Control Por Realimentación Del Estadounclassified

Análisis y diseño de sistemas lineales con parámetros variamtes utilizando LMIs

Rotondo

Sánchez

Nejjari

et al. 2018

Rev. iberoam. autom. inform. ind.

Self Cite

View full text Add to dashboard Cite

<p>En este artículo se presenta un tutorial sobre análisis y diseño de sistemas lineales con parámetros variantes (LPV) utilizando las desigualdades lineales matriciales (LMIs). Varias especificaciones, tales como la D-estabilidad, el desempeño H<sub>∞</sub> garantizado y el coste cuadrático garantizado, así como también diferentes estructuras de control, tales como el control por realimentación de estado, el control por realimentación de salida y el control basado en observador, han sido consideradas. Para ilustrar de forma didáctica el desarrollo completo del diseño mediante LMIs, se utilizan un ejemplo numérico y un modelo simplificado de un helicóptero de dos grados de libertad (TRMS).</p>

show abstract

“…First, the proposed work extends the historical evolution of optimal control theory to LPV systems purely analytically. Second, parametric variations and corresponding controllers are not constrained to be polytopic in nature as is usually the case with LMIbased approaches [7,8]. Third, the computational complexity of solving an LMI is greater than that of solving an ARE.…”

Section: Introductionmentioning

confidence: 99%

“…A SISO linear system affected by parametric variations can be defined in the LPV framework [7] as given below:…”

Section: Problem Statementmentioning

confidence: 99%

Robust optimal stabilization of balance systems with parametric variations

Zaffar¹,

Memon²

2017

Turk J Elec Eng & Comp Sci

View full text Add to dashboard Cite

This paper proposes a method of robust optimal stabilization for balance systems such as rocket and missile systems, Segway human transportation systems, and inverted pendulum systems. Constant-gain controllers such as linear-quadratic regulators may not guarantee stability let alone optimality for balance systems affected by parametric variations. The robust stability and robust performance achieved through the proposed variable-gain controller are better than those of the linear-quadratic regulator. The proposed controller consists of two components, one of which is designed offline for nominal values of parametric variations and one of which is updated online for off-nominal values of parametric variations. A salient feature of the proposed method is a linear transformation that converts the vector control input of balance systems into scalar control input for application of the proposed method. A fourth-order linearized model of an inverted pendulum system is simulated to show the efficacy of the proposed method.

show abstract

Linear quadratic control of LPV systems using static and shifting specifications

Cited by 13 publications

References 28 publications

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

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

Análisis y diseño de sistemas lineales con parámetros variamtes utilizando LMIs

Robust optimal stabilization of balance systems with parametric variations

Contact Info

Product

Resources

About