Title: Complexity, sensitivity and robustness in explicit model predictive control

Project code: APVV SK-FR-2013-0026

Partners:

• Slovak University of Technology in Bratislava (M. Kvasnica, J. Drgoňa, J. Holaza, B. Takács)
• Ecole Superieur d'Electricite (SUPELEC) (P. Rodriguez-Ayerbe, S. Olaru, C. Vlad, A. Nguyen, T.M. Nguyen)

Duration: 2014-2015

Abstract:

The proposed project is dedicated to the topic of model predictive control with a specific emphasis in their explicit solutions. The main goal is to develop new techniques for designing such control law with low complexity in view of deployment for fast real-time applications. In this project the scientific objective is to address complexity reduction in the explicit control laws, to analyse sensitivity of the optimal solutions and their implications to the robustness/fragility, and to apply developed algorithms in applications (power converters, or other appropriate benchmarks).

Project description:

In Model Predictive Control (MPC), control actions are computed by solving a suitable optimal control problem. This allows to take constraints into account and to optimize for performance. Feedback implementation of MPC requires the optimal control problem to be solved at each sampling step taking updated initial conditions into account. Therefore the success of real-time implementation of MPC requires that the optimization has to terminate within of one sampling instance. Violation of this requirement can, in a better case, lead to a deteriorated performance or, in the worst case, even to constraint violation or loss of stability.

Therefore the research in the area of MPC in the last decade was largely invested in development of novel ways of reducing the computational burden involved in implementing MPC solutions in real time. One of the attractive directions achieving such a goal is the technique of explicit MPC. Here, the aim is to “pre- compute” the solution to the given optimization problem for all possible values of the initial conditions, hence obtaining an analytic solution to MPC. Such an analytic form thus allows to reduce the task of MPC implementation to a mere function evaluation, which can be performed much faster. This allows MPC to be applied to process with fast sampling times (mili- and micro-seconds).

This project aims to address two main challenges of explicit MPC. The first challenge is to reduce size of analytic solutions, which often exceeds practical limits. The second challenge is to synthesize robust explicit MPC regulators which can adapt on-the-fly to varying parameters of the controlled process. Solution to these two challenges is divided into three main parts:

1. Reduction of complexity of explicit regulators such that the required storage space and computational resources are minimized.
2. Synthesis of robust explicit MPC regulators for systems with parametric uncertainties.
3. Development of software tools which will implement novel algorithms developed during the project.

In the first part we will use rich experience of both groups in the area of complexity reduction. In particular, we will exploit geometric properties of explicit solutions as to minimize the number of regions over which the explicit feedback law is defined. This will be achieved by utilizing tools and techniques from the field of computational geometry and convex sets. The emphasis will be put mainly on numerical reliability and runtime performance such that even very complex controllers could be reduced. Secondly, we will employ techniques of data compression to further decrease the required memory storage.

The second stage of the project will employ techniques of robust control and sensitivity analysis as to obtain controllers that can adapt, on-the-fly, to varying parameters of controlled systems. Since such parameters enter the problem formulation in a nonlinear fashion, we will employ equality-based substitutions and PWA approximation techniques to remove such nonlinearities.

The third stage is important mainly from the point of view of dissemination. In particular, we aim at providing freely-available implementation of all developed algoritms which could be used by academicians and practicians alike. The main goal of this stage is to facilitate a faster application of developed algoritms in practical conditions.