A Fully Automated Framework for Control of Linear Systems from LTL Specifications

  • Marius Kloetzer
  • Calin Belta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)


We consider the following problem: given a linear system and an LTL  − − X formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included.


Transition System Temporal Logic Feedback Controller Linear Temporal Logic Atomic Proposition 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marius Kloetzer
    • 1
  • Calin Belta
    • 1
  1. 1.Center for Information and Systems EngineeringBoston UniversityBostonUSA

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