### Abstract

The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the matrix A satisfies a rank condition, this problem has a unique, sparse solution. Here each row of A comprises one experiment consisting of input/output measurements and cannot be freely chosen. We show that if experiments are poorly designed, the rank condition may never be satisfied, resulting in multiple solutions. We discuss strategies for designing experiments such that A has the desired properties and the problem is therefore well posed. This formulation allows prior knowledge to be taken into account in the form of known nonzero entries of x, requiring fewer experiments to be performed. Simulated examples are given to illustrate the approach, which provides a useful strategy commensurate with the type of experiments and measurements available to biologists. We also confirm suggested limitations on the use of convex relaxations for the efficient solution of this problem.

Original language | English (US) |
---|---|

Pages (from-to) | 9-17 |

Number of pages | 9 |

Journal | Automatica |

Volume | 68 |

DOIs | |

State | Published - 2016 |

### Fingerprint

### Keywords

- Closed-loop identification
- Directed graphs
- Identifiability
- Interconnection matrices
- Linear equations

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*Automatica*,

*68*, 9-17. https://doi.org/10.1016/j.automatica.2016.01.008

**Sparse network identifiability via Compressed Sensing.** / Hayden, David; Chang, Young Hwan; Goncalves, Jorge; Tomlin, Claire J.

Research output: Contribution to journal › Article

*Automatica*, vol. 68, pp. 9-17. https://doi.org/10.1016/j.automatica.2016.01.008

}

TY - JOUR

T1 - Sparse network identifiability via Compressed Sensing

AU - Hayden, David

AU - Chang, Young Hwan

AU - Goncalves, Jorge

AU - Tomlin, Claire J.

PY - 2016

Y1 - 2016

N2 - The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the matrix A satisfies a rank condition, this problem has a unique, sparse solution. Here each row of A comprises one experiment consisting of input/output measurements and cannot be freely chosen. We show that if experiments are poorly designed, the rank condition may never be satisfied, resulting in multiple solutions. We discuss strategies for designing experiments such that A has the desired properties and the problem is therefore well posed. This formulation allows prior knowledge to be taken into account in the form of known nonzero entries of x, requiring fewer experiments to be performed. Simulated examples are given to illustrate the approach, which provides a useful strategy commensurate with the type of experiments and measurements available to biologists. We also confirm suggested limitations on the use of convex relaxations for the efficient solution of this problem.

AB - The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the matrix A satisfies a rank condition, this problem has a unique, sparse solution. Here each row of A comprises one experiment consisting of input/output measurements and cannot be freely chosen. We show that if experiments are poorly designed, the rank condition may never be satisfied, resulting in multiple solutions. We discuss strategies for designing experiments such that A has the desired properties and the problem is therefore well posed. This formulation allows prior knowledge to be taken into account in the form of known nonzero entries of x, requiring fewer experiments to be performed. Simulated examples are given to illustrate the approach, which provides a useful strategy commensurate with the type of experiments and measurements available to biologists. We also confirm suggested limitations on the use of convex relaxations for the efficient solution of this problem.

KW - Closed-loop identification

KW - Directed graphs

KW - Identifiability

KW - Interconnection matrices

KW - Linear equations

UR - http://www.scopus.com/inward/record.url?scp=84958764852&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958764852&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2016.01.008

DO - 10.1016/j.automatica.2016.01.008

M3 - Article

AN - SCOPUS:84958764852

VL - 68

SP - 9

EP - 17

JO - Automatica

JF - Automatica

SN - 0005-1098

ER -