Event-triggered Stabilization for Nonlinear Systems with Center Manifolds

Saradagi, A and Mahindrakar, AD and Tallapragada, P (2020) Event-triggered Stabilization for Nonlinear Systems with Center Manifolds. In: 59th IEEE Conference on Decision and Control, CDC 2020, 14-18 Dec 2020, Virtual, Jeju Island; South Korea, pp. 751-756.

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Abstract

In this work, we consider event-based implementation of control laws designed for local stabilization of nonlinear systems with center-manifolds. The systems being considered possess linearised models with uncontrollable modes on the imaginary axis. The controller chosen decides both the structure of the center-manifold and its stability. Although the control of systems with center-manifolds is well studied, event-based control of such systems is yet to be probed. This involves the exploration of input-to-state stability (ISS) properties of such systems, with respect to measurement errors. Considering the most general structure for the controller, we prove that a controller that locally asymptotically stabilizes the dynamics on the center-manifold, also renders the overall system locally input-to-state stable (LISS) and find the comparison functions involved in the Lyapunov characterization of ISS. This general characterization required a nonlinear change of variables, involving the center-manifold, which can only be approximately determined in most cases. Because of this, it is found to be unsuitable for designing event-triggered controllers. We then explore an approach that does not resort to this change of variables and present our findings. We discuss the possibility of a simpler relative thresholding mechanism and present simulation results for an illustrative example. © 2020 IEEE.

Item Type:	Conference Paper
Publication:	Proceedings of the IEEE Conference on Decision and Control
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright of this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Functions; Nonlinear systems; Stabilization, Change of variables; Comparison functions; Event-based control; General structures; Input to state stable; Input-to-state stability; Local stabilizations; Nonlinear changes, Controllers
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	04 Mar 2021 09:58
Last Modified:	04 Mar 2021 09:58
URI:	http://eprints.iisc.ac.in/id/eprint/67973

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