We propose a continuous-time model predictive control (MPC) strategy in the presence of intermittent sampling due to limited computational power. Using hybrid systems tools, the proposed scheme explicitly models the (not necessarily periodic) computation events associated with prediction and optimization. When the terminal cost is a control Lyapunov function and the implicit MPC control law in the proposed setting is continuous, the closed-loop system can tolerate disturbances, unmodeled dynamics, and measurement noise, as well as errors due to asynchronous actuation and sporadic data losses. These findings apply to a wide range of linear systems, and are particularly important for the target application area of cyber-physical systems, where real-time safety constraints require robustness in the presence of computational limitations.

We show that pre-asymptotic stability of a compact set for a hybrid system is semiglobally and practically robust in the presence of delayed jumps under mild conditions on the data. More precisely, when the delay-free system has a pre-asymptotically stable compact set, it is shown that for small enough delays, solutions of the delayed system converge to a neighborhood of a set of interest related to the aforementioned compact set. Unlike prior work, this notion of practical stability also holds for time-varying delays in the presence of Zeno solutions. Simulation results of a state estimator with intermittent and delayed information validate the findings.

This paper presents a model predictive control (MPC) algorithm that asymptotically stabilizes a compact set of interest for a given hybrid dynamical system. The considered class of systems are described by a general model, which identifies the dynamics by the combination of constrained differential and difference equations. The model allows for trajectories that exhibit multiple jumps at the same time instant, or portray Zeno behavior. At every optimization time, the proposed algorithm minimizes a cost functional weighting the state and the input during both the continuous and discrete phases, and at the terminal time via a terminal cost, without discretizing the continuous dynamics. To account for the structure of time domains defining solution pairs, the minimization is performed in a manner akin to free end-time optimal control. When the terminal cost is a control Lyapunov function on the terminal constraint set, recursive feasibility and asymptotic stability of the proposed algorithm can be guaranteed. A sample-and-hold control system and a bouncing ball model are two examples reported to demonstrate the applicability and effectiveness of the proposed approach.

We present a model predictive control (MPC) algorithm for the appropriate discretizations of (nondiscretized) hybrid dynamical systems. The optimization problem associated with the MPC algorithm is formulated with a set-based prediction horizon and the discretized hybrid dynamics as part of its constraints. Sufficient conditions guaranteeing structural properties of the problem and asymptotic stability of a closed set are revealed. These conditions include the existence of a control Lyapunov function assuring an invariance property on the terminal constraint set. In addition, we formulate a method to obtain numerical solutions to the hybrid optimal control problem, amenable to off-the-shelf optimization solvers, and demonstrate this method on the discretization of a prototypical hybrid system.