 
Summary: A Probabilistic Approach for Control of a Stochastic System from LTL
Specifications
M. Lahijanian, S. B. Andersson, and C. Belta
Mechanical Engineering, Boston University, Boston, MA 02215
{morteza,sanderss,cbelta}@bu.edu
Abstract We consider the problem of controlling a
continuoustime linear stochastic system from a specification
given as a Linear Temporal Logic (LTL) formula over a set of
linear predicates in the state of the system. We propose a three
step symbolic approach. First, we define a polyhedral partition
of the state space and a finite set of feedback controllers driving
the system among the regions of the partitions and use them to
construct a Markov Decision Process (MDP). Second, by using
an algorithm resembling LTL model checking, we determine
a run satisfying the formula in the corresponding Kripke
structure. Third, we determine a sequence of control symbols
that maximizes the probability of following the satisfying run
in the MDP. We present illustrative simulation results.
I. INTRODUCTION
In control problems, "complex" models, such as sys
