Abstract---We present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic c1osed-loop stability. The scheme can be applied to both stable and unstable systems with input constraints. The objective functional to be minimized consists of an integral square error (ISE) part over a finite time horizon plus a quadratic terminal cost. The terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate Lyapunov equation. Furthermore, the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region. If the Jacobian linearization of the nonlinear system to be controlled is stabilizable, we prove that feasibility of the open-loop optimal control problem at time t = 0 implies asymptotic stability of the closed-loop system. The size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense. ~)

The development of control methods based on data has seen a surge of interest in recent years. When applying data-driven controllers in real-world applications, providing theoretical guarantees for the closedloop system is of crucial importance to ensure reliable operation. In this review, we provide an overview of data-driven model predictive control (MPC) methods for controlling unknown systems with guarantees on systems-theoretic properties such as stability, robustness, and constraint satisfaction. The considered approaches rely on the Fundamental Lemma from behavioral theory in order to predict input-output trajectories directly from data. We cover various setups, ranging from linear systems and noise-free data to more realistic formulations with noise and nonlinearities, and we provide an overview of different techniques to ensure guarantees for the closed-loop system. Moreover, we discuss avenues for future research that may further improve the theoretical understanding and practical applicability of data-driven MPC.

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We consider the problem of designing robust statefeedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single openloop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closedloop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the H∞-control problem as a special case. Further, we show how the proposed framework can be extended to take partial model knowledge into account. The validity of the proposed approach is illustrated via a numerical example.