  Model predictive control (MPC) has become a hot cake technology for various
applications due to its ability to handle multi-input multi-output systems with
physical constraints. The optimization solvers require considerable time,
limiting their embedded implementation for real-time control. To overcome the
bottleneck of traditional quadratic programming (QP) solvers, this paper
proposes a robust penalty method (RPM) to solve an optimization problem in a
linear MPC. The main idea of RPM is to solve an unconstrained QP problem using
Broyden Fletcher Goldfarb Shannon (BFGS) algorithm. The beauty of this method
is that it can find optimal solutions even if initial conditions are in an
infeasible region, which makes it robust. Moreover, the RPM is computationally
inexpensive as compared to the traditional QP solvers. The proposed RPM is
implemented on resource-limited embedded hardware (STM32 microcontroller), and
its performance is validated with a case study of a citation aircraft control
problem. We show the hardware-in-the-loop co-simulation results of the proposed
RPM and compared them with the active set method (ASM) and interior point
method (IPM) QP solvers. The performance of MPC with the aforementioned solvers
is compared by considering the optimality, time complexity, and ease of
hardware implementation. Presented results show that the proposed RPM gives the
same optimality as ASM and IPM, and outperforms them in terms of speed.
