TY - GEN

T1 - Left-invertibility under sparse assumption

T2 - 2021 European Control Conference, ECC 2021

AU - Barbot, J. P.

AU - Busawon, K.

AU - Edwards, C.

PY - 2021/6/29

Y1 - 2021/6/29

N2 - This paper deals with the issue of dynamical left-invertibility for linear continuous-time dynamical systems. More precisely, we provide sufficient conditions in order to estimate unknown inputs, using known outputs, under sparse input assumptions for linear continuous-time dynamical systems that are not necessarily square. In fact, there exists an algorithm in the literature that allows verification of left-invertibility for linear square systems; that is, systems with p known outputs and p unknown inputs. However, a similar algorithm does not exist for the rectangular case, where the number of inputs is much larger than the number of outputs. In this paper, we first use the square case algorithm as a stepping stone in order to propose a new algorithm for the rectangular case. However, it shown that even if the proposed algorithm converges successfully, it is not sufficient to estimate the unknown inputs. Consequently, it has been deemed necessary to include a sparse input assumption and to verify the well-known Restrictive Isometric Property (RIP) conditions of a specific matrix. Finally, an academic example is given in order to highlight the feasibility of the proposed approach.

AB - This paper deals with the issue of dynamical left-invertibility for linear continuous-time dynamical systems. More precisely, we provide sufficient conditions in order to estimate unknown inputs, using known outputs, under sparse input assumptions for linear continuous-time dynamical systems that are not necessarily square. In fact, there exists an algorithm in the literature that allows verification of left-invertibility for linear square systems; that is, systems with p known outputs and p unknown inputs. However, a similar algorithm does not exist for the rectangular case, where the number of inputs is much larger than the number of outputs. In this paper, we first use the square case algorithm as a stepping stone in order to propose a new algorithm for the rectangular case. However, it shown that even if the proposed algorithm converges successfully, it is not sufficient to estimate the unknown inputs. Consequently, it has been deemed necessary to include a sparse input assumption and to verify the well-known Restrictive Isometric Property (RIP) conditions of a specific matrix. Finally, an academic example is given in order to highlight the feasibility of the proposed approach.

UR - http://www.scopus.com/inward/record.url?scp=85124886573&partnerID=8YFLogxK

U2 - 10.23919/ECC54610.2021.9655127

DO - 10.23919/ECC54610.2021.9655127

M3 - Conference contribution

AN - SCOPUS:85124886573

SN - 9781665479455

T3 - 2021 European Control Conference, ECC 2021

SP - 548

EP - 554

BT - 2021 European Control Conference, ECC 2021

PB - Institute of Electrical and Electronics Engineers Inc.

CY - Piscataway, US

Y2 - 29 June 2021 through 2 July 2021

ER -