  This article introduces a numerical algorithm that serves as a preliminary
step toward solving continuous-time model predictive control (MPC) problems
directly without explicit time-discretization. The chief ingredients of the
underlying optimal control problem (OCP) are a linear time-invariant system,
quadratic instantaneous and terminal cost functions, and convex path
constraints. The thrust of the method involves finitely parameterizing the
admissible space of control trajectories and solving the OCP satisfying the
given constraints at every time instant in a tractable manner without explicit
time-discretization. The ensuing OCP turns out to be a convex semi-infinite
program (SIP), and some recently developed results are employed to obtain an
optimal solution to this convex SIP. Numerical illustrations on some benchmark
models are included to show the efficacy of the algorithm.
