On Tuesday, March 10, 2018 Kai König (Ruhr-Universität Bochum, Germany) gave a lecture on "Speeding Up Regional Predictive Control - An Optimal and Suboptimal Approach".
Speaker: Kai König, Automatic Control and Systems Theory, Ruhr-Universität Bochum, Germany
Title: Speeding up regional predictive control - An optimal and suboptimal approach
Date, time, and place: April 10, 2018, 10:00am, room no. 641
Model predictive control (MPC) is based on periodically solving optimal control problems. Usually these problems must be solved numerically resulting in a control law that is defined only implicitly, or point-by-point. The solution to the linear quadratic MPC problem at a point, however, actually provides an optimal affine control law and a polytopic region of validity. These affine pieces can be used to create a simple regional MPC approach: Instead of solving an optimization problem in every time step, the control law obtained from the pointwise solution is applied to the system as long as it remains in the current polytope, and an optimal control problem is only solved if the system leaves the current polytope.
We propose two approaches for reducing the number of optimal control problems further. The first approach is based on updating the optimal control law by analyzing the crossed facets of neighboring polytopes. The second approach uses a known affine law even if it becomes suboptimal.