Computation of robust control invariant sets with predefined complexity for uncertain systems

Ankit Gupta; Hakan Köroğlu; Paolo Falcone

doi:10.1002/rnc.5378

Computation of robust control invariant sets with predefined complexity for uncertain systems

Ankit Gupta^*, Hakan Köroğlu, Paolo Falcone

^*Corresponding author for this work

Applied Mechanics

Research output: Contribution to journal › Article › Academic › peer-review

2 Downloads (Pure)

Abstract

This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations.

Original language	English
Pages (from-to)	1674-1688
Number of pages	15
Journal	International journal of robust and nonlinear control
Volume	31
Issue number	5
DOIs	https://doi.org/10.1002/rnc.5378
Publication status	Published - 25 Mar 2021

Keywords

invariant set
linear fractional transformation
linear matrix inequalities
linear systems
semi-definite program

Access to Document

10.1002/rnc.5378Licence: CC BY-NC-ND

rnc.5378Final published version, 711 KBLicence: CC BY-NC-ND

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Computation of robust control invariant sets with predefined complexity for uncertain systems'. Together they form a unique fingerprint.

Cite this

@article{4f88e37ef187486eaf328ad6c3ec2c52,

title = "Computation of robust control invariant sets with predefined complexity for uncertain systems",

abstract = "This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations.",

keywords = "invariant set, linear fractional transformation, linear matrix inequalities, linear systems, semi-definite program",

author = "Ankit Gupta and Hakan K{\"o}roğlu and Paolo Falcone",

year = "2021",

month = mar,

day = "25",

doi = "10.1002/rnc.5378",

language = "English",

volume = "31",

pages = "1674--1688",

journal = "International journal of robust and nonlinear control",

issn = "1049-8923",

publisher = "Wiley",

number = "5",

}

TY - JOUR

T1 - Computation of robust control invariant sets with predefined complexity for uncertain systems

AU - Gupta, Ankit

AU - Köroğlu, Hakan

AU - Falcone, Paolo

PY - 2021/3/25

Y1 - 2021/3/25

N2 - This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations.

AB - This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations.

KW - invariant set

KW - linear fractional transformation

KW - linear matrix inequalities

KW - linear systems

KW - semi-definite program

UR - http://www.scopus.com/inward/record.url?scp=85098410883&partnerID=8YFLogxK

U2 - 10.1002/rnc.5378

DO - 10.1002/rnc.5378

M3 - Article

AN - SCOPUS:85098410883

VL - 31

SP - 1674

EP - 1688

JO - International journal of robust and nonlinear control

JF - International journal of robust and nonlinear control

SN - 1049-8923

IS - 5

ER -