Region-Based Self-Triggered Control for Perturbed and Uncertain Nonlinear Systems

Abstract

In this work, we derive a region-based selftriggered control (STC) scheme for nonlinear systems with bounded disturbances and model uncertainties. The proposed STC scheme is able to guarantee different performance specifications (e.g., stability, boundedness, etc.), depending on the event-triggered control (ETC) triggering function that is chosen to be emulated. To deal with disturbances and uncertainties, we employ differential inclusions (DIs). By introducing ETC/STC notions in the context of DIs, we extend well-known results on ETC/STC to perturbed uncertain systems. Given these results, and adapting tools from our previous work, we derive inner approximations of isochronous manifolds of perturbed uncertain ETC systems. These approximations dictate a partition of the state space into regions, each of which is associated with a uniform intersampling time. At each sampling time instant, the controller checks which region the measured state belongs to and correspondingly decides the next sampling instant.

Self-Triggered Stabilization of Discrete-Time Linear Systems With Quantized State Measurements

“…△ Remark 4.3 (Use of other norms). The inequalities (11) and (12) are satisfied also for diagonally-weighted p-norms, where 1 ≤ p ≤ ∞. However, Lemma 4.2 holds only for diagonally-weighted ∞-norms in general.…”

“…For self-triggered control of nonlinear systems, various techniques have been introduced, e.g., approximation of isochronous manifolds [4,11,12], polynomial approximation of Lyapunov functions [5], and reduction of conservativeness through disturbance observers [43]. Approaches based on the small gain theorem [29,44] and control Lyapunov functions [35] have been also discussed.…”

Self-triggered output feedback control for nonlinear networked control systems based on hybrid Lyapunov functions

“…Small gain techniques are used in Tolic et al (2012); Liu and Jiang (2015). In Anta and Tabuada (2010); Delimpaltadakis and Mazo (2020Mazo ( , 2021, isochroneity properties ⋆ © 2023 the authors. This work has been accepted to IFAC for publication under a Creative Commons Licence CC-BY-NC-ND.…”

Model Predictive Control for Nonlinear Systems Under Sample‐and‐Hold Control Structure: An Integral‐Type Double Self‐Triggering Method

“…Researchers of event-triggering mechanism control have proposed two main schemes: event-triggered (ET) control [3][4][5][6] and ST control. [7][8][9][10] MPC is widely used in control processes because of its superiority in improving system control performance and its ability to handle optimization problems with constraints. Combining the DOI: 10.1002/adts.202300324 event-mechanism control scheme with MPC can further improve the control quality of the system.…”

“…Researchers of event‐triggering mechanism control have proposed two main schemes: event‐triggered (ET) control [ 3–6 ] and ST control. [ 7–10 ]…”