Complexity of the minimum input selection problem for structural controllability

Sepehr Assadi, Sanjeev Khanna, Yang Li, Victor M. Preciado

Research output: Contribution to journalConference articlepeer-review

12 Scopus citations

Abstract

We consider the minimum input selection problem for structural controllability (MISSC), stated as follows: Given a linear system x = Ax, where A is a n x n state matrix with m nonzero entries, find the minimum number of states that need to be driven by an external input so that the resulting system is structurally controllable. The fastest algorithm to solve this problem was recently proposed by Olshevsky in (Olshevsky, 2015) and runs in θ (m√n) operations. In this paper, we propose an alternative algorithm to solve MISSC in min{O(m√n), Õ (n2.37), Õ (m10/7)} operations. This running time is obtained by (i) proving that MISSC problem is computationally equivalent to the maximum bipartite matching (MBM) problem and (ii) considering the three fastest algorithms currently available to solve MBM, namely, the Hopcraft-Karp algorithm, the Mucha-Sankowski algorithm, and Madry's algorithm. Furthermore, our algorithm can directly benefit from future improvements in MBM computation. Conversely, we also show that any algorithmic improvement on solving MISSC would result in an improvement in MBM computation, which would be of great interest for theoretical computer scientists.

Original languageEnglish (US)
Pages (from-to)70-75
Number of pages6
JournalIFAC-PapersOnLine
Volume28
Issue number22
DOIs
StatePublished - Oct 1 2015
Externally publishedYes
Event5th IFAC Workshop on Distributed Estimation and Control in Networked Systems, NecSys 2015 - Philadelphia, United States
Duration: Sep 10 2015Sep 11 2015

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Keywords

  • Computational complexity
  • Graph theory
  • Linear systems
  • Structural controllability
  • Structured systems

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