MPC on chip was tried a decade ago [1]. It was based on the idea of parametric programming, where solutions of an optimization problem (a quadratic program, QP) were pre-computed and the control law essentially only involved doing lookups. Lookups were fast and avoided the computational cost of solving an optimization problem on-line.

However, as you can imagine, pre-computing optimal solutions is of exponential complexity so scaling up this technique was difficult at the time. (I'm not sure what the state of the art is).

Computation however has come a long way since, so today it might be possible to actually solve a decent sized quadratic program (QP) on chip at very frequencies in real-time.

[1] https://www.sciencedirect.com/science/article/abs/pii/S00981...