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Abstract
This paper deals with finding a 'least interaction' controller that generically achieves pole placement, given a actuatorsensor 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 bruteforce 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 poleassignability and covering of plant edges using cycles. The first uses multicommodity 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 NPcomplete, there is ample reason that identifying a minimum controller substructure is NPhard. 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 TSPwithprofits problem too belongs to the class of NPhard problems. We show that our formulation is equivalent to the socalled Generalized Travelling Salesman Problem (GTSP) thus allowing branchcut algorithms developed for GTSP problems.
Original language  English 

Title of host publication  2016 European Control Conference (ECC) 
Place of Publication  Piscataway, NJ 
Publisher  IEEE 
Pages  849854 
Number of pages  6 
ISBN (Electronic)  9781509025916 
DOIs  
Publication status  Published  9 Jan 2017 
Event  2016 European Control Conference  Aalborg, Denmark Duration: 29 Jun 2016 → 1 Jul 2017 
Conference
Conference  2016 European Control Conference 

Abbreviated title  ECC16 
Country/Territory  Denmark 
City  Aalborg 
Period  29/06/16 → 1/07/17 
Keywords
 bipartite graph
 mathematical model
 electronic mail
 differential equations
 NPhard problem
 sensors
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 1 Visiting an external academic institution

Indian Institute of Technology
Ashwin Arulselvan (Visiting lecturer)
1 Feb 2015 → 28 Feb 2015Activity: Visiting an external institution types › Visiting an external academic institution