Convexity Properties of the Model Predictive Control Problem for Subclasses of Multilinear Time-Invariant Systems*

There are many efficient algorithms to compute linear model predictive control (MPC) optimization problems. The description of system dynamics using linear models often fails if nonlinear effects are essential. Multilinear Time Invariant systems (MTI systems) can be a suitable approximation for such systems. This paper focuses on the convexity proof of the optimization problem for model predictive control by using MTI systems. The convexity properties are shown for different prediction horizons and classes of MTI systems. The advantage for engineering applications is shown for a heating system example by solving such an optimization problem effciently.