  This paper considers a risk-constrained infinite-horizon optimal control
problem and proposes to solve it in an iterative manner. Each iteration of the
algorithm generates a trajectory from the starting point to the target
equilibrium state by implementing a distributionally robust risk-constrained
model predictive control (MPC) scheme. At each iteration, a set of safe states
(that satisfy the risk-constraint with high probability) and a certain number
of independent and identically distributed samples of the uncertainty governing
the risk constraint are available. These states and samples are accumulated in
previous iterations. The safe states are used as terminal constraint in the MPC
scheme and samples are used to construct a set of distributions, termed
ambiguity set, such that it contains the underlying distribution of the
uncertainty with high probability. The risk-constraint in each iteration is
required to hold for all distributions in the ambiguity set. We establish that
the trajectories generated by our iterative procedure are feasible, safe, and
converge asymptotically to the equilibrium. Simulation example illustrates our
results for the case of finding a risk-constrained path for a mobile robot in
the presence of an uncertain obstacle.
