Model Predictive Control for Nonlinear Continuous-Time Systems with and without Time-Delays

Model predictive control (MPC) is a modern control method based on the repeated online solution of a finite horizon optimal control problem. It is particularly attractive due to its ability to take hard constraints and performance criteria directly into account. The objective of this thesis is the development of novel MPC schemes for nonlinear continuoustime systems with and without time-delays in the states which guarantee asymptotic stability of the closed-loop. The most well-studied MPC approaches with guaranteed stability use a control Lyapunov function as terminal cost. Since the actual calculation of such a function can be difficult, it is desirable to replace this assumption by a less restrictive controllability assumption. For discrete-time systems, the latter assumption has been used in the literature for the stability analysis of so-called unconstrained MPC, i.e., MPC without terminal cost and terminal constraints. The contributions of this thesis are twofold. In the first part, we propose novel MPC schemes with guaranteed stability based on a controllability assumption, whereas we extend different MPC schemes with guaranteed stability to nonlinear time-delay systems in the second part. In the first part of this thesis, we derive for the first time explicit stability conditions on the prediction horizon as well as performance guarantees for unconstrained MPC for continuous-time systems. Starting from this result, we propose novel alternative MPC formulations based on combinations of the controllability assumption with terminal cost and terminal constraints. Thereby, we show connections of our results to previous MPC schemes and highlight advantages. One of the main contributions is the development of a unifying MPC framework which allows to consider both MPC schemes with terminal cost and terminal constraints as well as unconstrained MPC as limit cases of our framework. In the second part of this thesis, we show that several MPC schemes with and without terminal constraints can be extended to nonlinear time-delay systems. Due to the infinite-dimensional nature of these systems, the problem is more involved and additional assumptions are required in the controller design. For MPC schemes with terminal constraints, we prove that stability conditions similar to the delay-free case are sufficient for closed-loop stability. However, the calculation of suitable terminal cost functionals and terminal regions based on the Jacobi linearization about the origin is more difficult. We propose and investigate different procedures to overcome these difficulties. For MPC schemes without terminal constraints, we discuss MPC schemes with and without terminal cost functionals. If the terminal region is defined as a sublevel set of the terminal cost, we show that the terminal constraint can be omitted from the optimal control problem while maintaining asymptotic stability. Similar to the results in the first part of the thesis, explicit stability conditions on the prediction horizon are derived based on a modified controllability assumption suitable for time-delay systems.