Survey A survey of computational complexity results in systems and control

  • Authors:

  • Vincent D. Blondel;John N. Tsitsiklis

  • Affiliations:

  • Department of Mathematical Engineering, Center for Systems Engineering and Applied Mechanics (CESAME), University of Louvain, B-1348 Louvain-la-Neuve, Belgium;Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2000

Quantified Score

Hi-index 22.19

Visualization

Abstract

The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial-time algorithms, NP-completeness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, time-varying linear systems, nonlinear and hybrid systems, and stochastic optimal control.