Bounded iteration for multiple box constraints on linear complementarity model predictive control and its application to vehicle steering control

This paper presents linear model predictive control (MPC) for multiple kinds of constraint based on the linear complementarity problem (LCP) that gives the explicit upper bound of computational complexity. MPC generally solves constrained optimization problems. Its computational time should be strictly bounded for real-time applications. In a previous study, we proposed MPC based on the LCP for which a modified n-step vector successfully limits the number of iterations for the combinatorial problem. However, its class of applications is limited due to the existence of the modified n-step vector. In addition, MPC with a time-varying system is not included in this class since the modified n-step vector must be found for each problem at the corresponding time instance. This paper introduces a perturbation on constraints and applies a sequential LCP algorithm that gives a priori knowledge of the explicit upper bound of computational complexity and the accuracy of the solution. The iteration bounds are evaluated using the steering control of an autonomous driving vehicle for an obstacle avoidance manoeuvre.