  Nonlinear model predictive control has been widely adopted to manipulate
bilinear systems with dynamics that include products of the inputs and the
states. These systems are ubiquitous in chemical processes, mechanical systems,
and quantum physics, to name a few. Running a bilinear MPC controller in real
time requires solving a non-convex optimization problem within a limited
sampling time. This paper proposes a novel parallel proximal-point Lagrangian
based bilinear MPC solver via an interlacing horizon-splitting scheme. The
resulting algorithm converts the non-convex MPC control problem into a set of
parallelizable small-scale multi-parametric quadratic programs (mpQPs) and an
equality-constrained linear-quadratic regulator problem. As a result, the
solutions of mpQPs can be pre-computed offline to enable efficient online
computation. The proposed algorithm is validated on a simulation of an HVAC
system control. It is deployed on a TI LaunchPad XL F28379D microcontroller to
execute speed control on a field-controlled DC motor, where the MPC updates at
10 ms and solves the problem in 1.764 ms on average and at most 2.088 ms.
