Direct Parallel Computations of Second-Order Search Directions for Model Predictive Control

Abstract

Model predictive control ( MPC ) is one of the most widely spread advanced control schemes in industry today. In MPC , a constrained finite-time optimal control ( CFTOC ) problem is solved at each iteration in the control loop. The CFTOC problem can be solved using, for example, second-order methods, such as interior-point or active-set methods, where the computationally most demanding part often consists of computing the sequence of second-order search directions. Each search direction can be computed by solving a set of linear equations that corresponds to solving an unconstrained finite-time optimal control ( UFTOC ) problem. In this paper, different direct (noniterative) parallel algorithms for solving UFTOC problems are presented. The parallel algorithms are all based on a recursive variable elimination and solution propagation technique. Numerical evaluations of one of the parallel algorithms indicate that a significant boost in performance can be obtained, which can facilitate high-performance second-order MPC solvers.