# Michal Kvasnica (Slovak Uni. of Tech. in Bratislava): Novel Results in Complexity Reduction of Explicit Model Predictive Control

A last-minute announcement of a seminar on Tuesday, October 9, given by Doc. Ing. Michal Kvasnica, Ph.D. from Slovak University of Technology in Bratislava , who is a visiting rearcher at Department of Control Engineering at FEE CTU in Prague during October through December 2012. The seminar will take place in the room K14 at the building E at the FEE CTU campus at Karlovo namesti 13. The seminar will start at 16.15 and will end by 17:00.

Abstrakt: Model Predictive Control (MPC) is popular both in theory and in practice due to its ability to operate the controlled process in an optimal fashion while explicitly taking process constraints into account. Closed-loop implementation of MPC, however, is cumbersome since an optimization problem needs to be solved at each sampling instant. Implementing MPC on simple, cheap embedded platforms is therefore challenging, to say the least. The implementation effort can be reduced, to some extent, by pre-computing, off-line, the optimal solution for all possible initial conditions. For a rich class of MPC problems the pre-computed explicit solution can be shown to take a form of a Piecewise Affine (PWA) function which maps measured states to optimal control inputs. Such an explicit representation of the MPC feedback law, however, is often prohibitively large for typical embedded control hardware. Therefore in this talk we discuss three novel approaches which allow to substantially reduce complexity of explicit MPC controllers. The first two methods provide an "equivalent" simplification. Here, a given (complex) optimal explicit MPC controller is simplified in a way such that no amount of optimality is lost. In the third method we then show that, by giving up some amount of performance, even much simpler controllers can be obtained. To construct the simple controllers we use basic mathematical tools and approaches, including linear programming and global positivity of polynomials.