Approximate Explicit MPC on Simplicial Partitions with Guaranteed Stability for Constrained Linear Systems

This paper proposes an approximate explicit model predictive control design approach for regulating linear time-invariant systems subject to both state and control constraints. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. First, the regularity of the simplicial partition allows a very efficient implementation of the control law on digital circuits, with computation performed in tens of nanoseconds. Second, the asymptotic stability of the closed-loop system is enforced a priori by design.