Michal Kvasnica

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The Multiparametric toolbox is a collection of algorithms for modeling, control, analysis, and deployment of constrained optimal controllers developed under Matlab. It features a powerful geometric library that extends the application of the toolbox beyond optimal control to various problems arising in computational geometry. The new version 3.0 is a(More)
Piecewise affine systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. This paper illustrates how reachability analysis based on(More)
We show that explicit MPC solutions admit a closed-form solution which does not require the storage of critical regions. Therefore significant amount of memory can be saved. In fact, not even the construction of such regions is required. Instead, all possible optimal active sets are first extensively enumerated. Then, for each optimal, only the analytical(More)
Amount of memory needed to describe explicit model predictive control (MPC) solutions is an often neglected, but a very important factor which decides whether it will be possible to implement such a control strategy on a selected control platform. We show how to exploit geometric properties of explicit MPC controllers to obtain their memory-efficient(More)
A given explicit piecewise affine representation of an MPC feedback law is approximated by a single polynomial, computed using linear programming. This polynomial state feedback control law guarantees closed-loop stability and constraint satisfaction. The polynomial feedback can be implemented in real time even on very simple devices with severe limitations(More)
This paper addresses the issue of the practical implementation of Model Predictive Controllers (MPC) to processes with short sampling times. Given an explicit solution to an MPC problem, the main idea is to approximate the optimal control law defined over state space regions by a single polynomial of pre-specified degree which, when applied as a(More)