  We address the problem of finite-horizon control of a discrete-time linear
system, where the initial state distribution follows a Gaussian mixture model,
the terminal state must follow a specified Gaussian distribution, and the state
and control inputs must obey chance constraints. We show that, throughout the
time horizon, the state and control distributions are fully characterized by
Gaussian mixtures. We then formulate the cost, distributional terminal
constraint, and affine/2-norm chance constraints on the state and control, as
convex functions of the decision variables. This is leveraged to formulate the
chance-constrained path planning problem as a single semidefinite programming
problem. A numerical example demonstrates the effectiveness of the proposed
method.
