Semi-Explicit Linear MPC Using a Warm-Started Active-Set QP Algorithm with Exact Complexity Guarantees

We propose a semi-explicit approach for linear MPC in which a dual active-set quadratic programming algorithm is initialized through a pre-computed warm start. By using a recently developed complexity certification method for active-set algorithms for quadratic programming, we show how the computational complexity of the dual active-set algorithm can be determined offline for a given warm start. We also show how these complexity certificates can be used as quality measures when constructing warm starts, enabling the online complexity to be reduced further by iteratively refining the warm start. In addition to showing how the computational complexity of any pre-computed warm start can be determined, we also propose a novel technique for generating warm starts with low overhead, both in terms of computations and memory.