A Computational Governor for Maintaining Feasibility and Low Computational Cost in Model Predictive Control

This article introduces an approach for reducing the computational cost of implementing linear quadratic model predictive control (MPC) for set-point tracking subject to pointwise-in-time state and control constraints. The approach consists of the following three key components: First, a log-domain interior-point method used to solve the receding horizon optimal control problems; second, a method of warm-starting this optimizer by using the MPC solution from the previous timestep; and third, a computational governor that maintains feasibility and bounds the suboptimality of the warm-start by altering the reference command provided to the MPC problem. Theoretical guarantees regarding the recursive feasibility of the MPC problem, asymptotic stability of the target equilibrium, and finite-time convergence of the reference signal are provided for the resulting closed-loop system. In a numerical experiment on a lateral vehicle dynamics model, the worst-case execution time of a standard MPC implementation is reduced by over a factor of 10 when the computational governor is added to the closed-loop system.