Kurzfassung: Model Predictive Control (MPC) is the prototype of an optimisation-based predictive control scheme: Based on the most recent information, an optimal control w.r.t. a finite-time horizon is determined using knowledge on the system dynamics, e.g., encoded by some differential equation. Then, the first portion of the control function is implemented before the optimisation window is shifted forward in time and the procedure is repeated ad infinitum. While the simplicity of the underlying idea is one of the reasons for the widespread use of MPC in applications, the mathematical analysis requires some care to ensure key properties like asymptotic stability and recursive feasibility of the resulting dynamical (closed-loop) system on the infinite horizon.
In this talk, we provide some insight on the design of nonlinear MPC schemes based on structural properties of the system in consideration. In particular, we emphasise consistency between the different ingredients of the repeatedly solved optimal control problem, i.e., the system dynamics, constraints, and control objective. To motivate and illustrate our findings we consider the example of a mobile robot.