Fast Model Predictive Control with Simple Bounds Using Semismooth Newton Method

Abstract

In model predictive control (MPC), an optimal control problem is solved at each time steps to determine control input. To realize on-line control of MPC, reducing computational time is requisite. In this paper, we apply a semismooth Newton method for MPC with simple bounds. The semismooth Newton method is one of iterative methods and is used to solve a complementarity problem and a KKT system of optimization problems. The semismooth Newton method has an advantage over other QP solvers, such as interior point methods and so on, that the initial point can be chosen arbitrarily, and this enables hot start. We show that the proposed method is globally convergent. We also show the condition guaranteeing the nonsingularity of the generalized Jacobian at a solution, which is closely related to the quadratic convergence of the algorithm. This is the first result to clarify the reason why constraints on state variables make MPC computationally expensive from the algorithmic perspective. Some numerical examples show that the proposed method is practically efficient.