Maximal controllability of input constrained unstable systems by the addition of implicit constraints

  • Authors:

  • Adrian Medioli;Maria Seron;Richard Middleton

  • Affiliations:

  • The ARC Centre for Complex Dynamic Systems & Control, The University of Newcastle, Australia;The ARC Centre for Complex Dynamic Systems & Control, The University of Newcastle, Australia;The Hamilton Institute, NUI Maynooth, Co Kildare, Ireland

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

The null controllable set of a system is the largest set of states that can be controlled to the origin. Control systems that have a region of attraction equal to the null controllable set are said to be maximally controllable closed-loop systems. In the case of open-loop unstable plants with amplitude constrained control it is well known that the null controllable set does not cover the entire state-space. Further the combination of input constraints and unstable system dynamics results in a set of state constraints which we call implicit constraints. It is shown that the simple inclusion of implicit constraints in a controller formulation results in a controller that achieves maximal controllability for a class of open-loop unstable systems.