  We establish a linear programming formulation for the solution of joint
chance constrained optimal control problems over finite time horizons. The
joint chance constraint may represent an invariance, reachability or
reach-avoid specification that the trajectory must satisfy with a predefined
probability. For finite state and action spaces, the solution is exact and our
method computationally superior to approaches in the literature. For continuous
state or action spaces, our linear programming formulation enables basis
function approximations.
