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SMT solvers for embedded hybrid MPC



Damian Frick

Many practical problems arising from hybrid model predictive control (MPC) can be written as discrete-time affine systems with some logic coupling. Such systems include systems controlled by inverters such as electric drives or power converters, systems with discrete states such as gear switching in cars or even systems with non-linear dynamics, for example friction models for race cars.

All of these problems have to be controlled in the millisecond to microsecond range with the code running on an embedded platform that is typically much less powerful than a desktop computer. The resulting MPC problems can be written as mixed-integer quadratic programs, which are known to be NP-hard. Therefore solving these MPC problems within a short time poses a significant challenge.

In this project we want to explore an alternative way of solving these problems by using tools from software checking, in particular we want so use satisfiability modulo theories (SMT) solvers. The MPC problem can be viewed as a collection of logical statements involving affine functions. SMT solvers check the correctness of a collection of such statements by providing an example that satisfied them, thus providing a feasible trajectory (including control inputs) which can be used for controlling the system.

This project has a focus on implementation in MATLAB and/or C/C++, the candidates are expected to be strong in math and programming. Courses from model predictive control and mathematical optimization are a plus.

The embedded optimization group at IfA develops methods and tools for numerical optimization on embedded hardware, mostly for use in the model predictive control context.

Weitere Informationen

Manfred Morari

Art der Arbeit: Semester-/Masterthesis
20% Theory
60% Implementation
10% Testing
10% Documentation
Voraussetzungen: MPC or Optimization a plus
Anzahl StudentInnen: 1
Status: taken
Projektstart: 22.02.2016
Semester: Spring 2016