Parallel MPC for Linear Systems With Input Constraints

This article is about a real-time model predictive control algorithm for large-scale, structured linear systems with polytopic control constraints. The proposed controller receives the current state measurement as an input, and computes a suboptimal control reaction by evaluating a finite number of piecewise affine functions that correspond to the explicit solution maps of small-scale parametric quadratic programming (QP) problems. We provide asymptotic stability guarantees, which can be verified offline. The feedback controller is computing approximations of the optimal input, because we are enforcing real-time requirements assuming that it is not possible to solve the given large-scale QP in the given amount of time. Here, a key contribution of this article is that we provide a bound on the suboptimality of the controller. The approach is illustrated by benchmark case studies.