Reducing the Number of Optimization Problems in Trajectory Tracking Model Predictive Control

Abstract

This paper presents a model predictive control (MPC) approach for tracking reference trajectories for constrained linear-time invariant systems. The approach is special in that it exploits the piecewise-affine structure of the underlying feedback law and solves MPC optimization problems on demand only. We include the predefined reference trajectory in the optimization problem and use a modified state-space vector that contains future target points of the considered reference trajectory. As the state-space vector grows with the number of considered target points, the computational effort to solve the underlying quadratic program increases. This additional computational load can be a bottleneck on embedded hardware. To overcome this limitation and to maintain the performance of the presented trajectory tracking MPC approach, a particular variant of event-triggered controller is used that solves MPC problems only when the current optimal affine piece of the underlying optimal feedback law is no longer optimal. This leads to a reduction in the number of solved quadratic programs. Our approach is particularly useful for systems in a network. The computational load on the embedded system can be reduced by solving all optimization problems on a central server node in this case. The embedded system then only needs to evaluate affine optimal feedback laws that it receives from the central server node. We apply this method to a real differential drive mobile robot.