Picture of boy being examining by doctor at a tuberculosis sanatorium

Understanding our future through Open Access research about our past...

Strathprints makes available scholarly Open Access content by researchers in the Centre for the Social History of Health & Healthcare (CSHHH), based within the School of Humanities, and considered Scotland's leading centre for the history of health and medicine.

Research at CSHHH explores the modern world since 1800 in locations as diverse as the UK, Asia, Africa, North America, and Europe. Areas of specialism include contraception and sexuality; family health and medical services; occupational health and medicine; disability; the history of psychiatry; conflict and warfare; and, drugs, pharmaceuticals and intoxicants.

Explore the Open Access research of the Centre for the Social History of Health and Healthcare. Or explore all of Strathclyde's Open Access research...

Image: Heart of England NHS Foundation Trust. Wellcome Collection - CC-BY.

Minimum controller substructure for generic arbitrary pole placement : multicommodity flow and TSP based formulations

Kotoky, Atreya and Mahajan, Ashutosh and Arulselvan, Ashwin and Belur, Madhu N. and Kalaimani, Rachel K. (2017) Minimum controller substructure for generic arbitrary pole placement : multicommodity flow and TSP based formulations. In: 2016 European Control Conference (ECC). IEEE, Piscataway, NJ, pp. 849-854. ISBN 9781509025916

Full text not available in this repository. Request a copy from the Strathclyde author


This paper deals with finding a 'least interaction' controller that generically achieves pole placement, given a actuator-sensor interaction possibility for the controller. The structure of the plant and the controller are modeled as an undirected and bipartite graph. Assuming that the plant/controller structures are specified, we find a minimum controller substructure within the specified controller structure such that the controller substructure allows generic eigenvalue assignability. The minimum is in the sense that the bipartite graph consisting of the proposed controller has the minimum number of edges. The complexity of a brute-force algorithm to identify a minimum controller substructure would be exponential and hence we propose two formulations for solving this problem, using recent results about equivalence of generic pole-assignability and covering of plant edges using cycles. The first uses multi-commodity flow networks to include all plant edges in some cycle using the least number of controller edges. We show that an integer solution to this formulation gives a minimum controller substructure for arbitrary pole placement problem. Since the problem of finding a feasible integer flow in multicommodity networks is NP-complete, there is ample reason that identifying a minimum controller substructure is NP-hard. The second formulation uses the framework of travelling salesman with profits (TSP with profits) to cover all vertices of the bipartite graph by cycles using the least number of controller edges. The TSP-with-profits problem too belongs to the class of NP-hard problems. We show that our formulation is equivalent to the so-called Generalized Travelling Salesman Problem (GTSP) thus allowing branch-cut algorithms developed for GTSP problems.