Dissipativity-based model predictive controller for a family of parameterized systems

Abstract

We present stability results for dissipative interconnected parameterized systems controlled by model predictive controller (MPC). According to the extensive literature, numerous results have been already developed to stabilize dissipative systems. However, they are still not explored enough in the context of MPC. Therefore, it naturally arises the need to investigate stability properties of dissipative dynamics for this particular class of controllers. In order to construct the efficient algorithm it is a fundamental requirement to get the full information about the plant dynamics. In general, this is very hard to obtain or, even not possible at all. Hence, we aim to stabilise the approximate dynamics containing a set of unknown parameters. Typically, for this type of problems the controller relies on a properly defined adaptation rule which forces the unknown parameter to converge inside a specified closed, convex set. Eventually, the controller drives the state solution to the optimal set-point. Asymptotic stability properties are analysed with respect to the specific quadratic supply rate and linear protocol. We assume that the output is available for a feedback all the time.