A Model Predictive Control Framework for Hybrid Dynamical Systems

A Model Predictive Control Framework for Asymptotic Stabilization of Discretized Hybrid Dynamical Systems

“…For a visual demonstration of prediction scenarios associated with (7), we refer the readers to Figure 1 of [2], which illustrates the same idea in the case of nondiscretized hybrid systems.…”

“…The use of optimizationbased techniques for the control of such systems has promise. Recently, a framework for model predictive control (MPC) for hybrid dynamical systems was introduced in [2], [3]. In these articles, hybrid dynamical systems are given as in [4], specifically, in terms of differential equations and difference equations with constraints.…”

“…Such a framework captures a wide variety of hybrid models, including switched systems and hybrid automata. The work in [2] and [3] pertains to what could be considered to be "pure" nondiscretized hybrid dynamical systems, which is the cornerstone of a general theory of computational MPC for hybrid systems.…”

“…In this paper, we make a first step towards that general theory by formulating a framework for MPC for discretized hybrid dynamical systems. For this purpose, given a hybrid dynamical system as in [4], [2], [3], we discretize it following the ideas in [5]. For these discretized models, we first formulate a set-based prediction horizon and a corresponding optimal control problem.…”

“…On the other hand, many systems labeled as "hybrid" in the broader control literature do not possess such a partition, and have continuously evolving states that exhibit jumps, due to events. Aside from the recent framework introduced in [2], [3], MPC strategies for these systems are not available in the literature, with the most relevant work being the impulsive and measure-driven frameworks in [9] and [10]; see [6] for a recent survey. Following the formulation in [2], [3], the MPC framework introduced in this paper makes no distinction between continous-and discrete-valued states and/or inputs, and identifies the underlying dynamical model by a combination of two constrained difference equations, one of which corresponds to the discretization of the continuous-time dynamics.…”