Self-triggered control for constrained systems: A contractive set-based approach

Abstract

In this paper, a self-triggered control scheme for constrained discrete-time control systems is presented. The key idea of our approach is to construct a transition system or a graph structure from a collection of polyhedral sets, which are generated based on the notion of set-invariance theory. The interevent time steps are then determined through a standard graph search algorithm to obtain the minimal total cost to a terminal state. The proposed strategy is illustrated through a numerical example.

Synthesizing Communication Plans for Reachability and Safety Specifications

“…In the approach presented in this paper, we deal with nonlinear discrete-time systems and a non-convex safety set and the control objective is to achieve reachability and safety. Thus the proposed approach establishes the novelty with respect to the previous approach in [26]. As we will see later, the key ideas to achieve this novelty is the utilization of several trajectory generation tools, such as RRT [30], RRT* [31], which allows to generate a nominal state trajectory towards a target region in a non-convex safety set (see Section III-A), and the utilization of δ-ISS control Lyapunov functions, which allows to analyze how the actual state trajectory differs from the nominal one according to the occurrence of communication (see Section IV-A).…”

“…While many control strategies to achieve reachability and safety have been proposed as illustrated above, only a few works have been provided to accommodate communication strategies, aiming at reducing the communication load for NCSs, see e.g., [7], [26]. For example, in [7] an aperiodic control scheme was proposed by using the notion of control invariant set, which guarantees the existence of a controller such that the state remains inside the safety set for all time.…”

“…The proposed approach builds upon our previous work [26]. In [26], we construct a collection of polyhedral contractive sets with different inter-event times and control updates.…”

“…The proposed approach builds upon our previous work [26]. In [26], we construct a collection of polyhedral contractive sets with different inter-event times and control updates. Then, these sets are translated into the corresponding symbolic system, and the communication scheduling is generated by graph search algorithms.…”

Self‐triggered robust model predictive control for nonlinear systems with bounded disturbances

“…Hashimoto et al . [9] proposed a self‐triggered strategy by constructing a contractive set to stabilise the constrained discrete‐time systems.…”