A Sampling Control Framework and Applications to Robust and Adaptive Control

TL;DR

This paper introduces a new sampling control framework that enhances robust and adaptive control by managing sampling errors and uncertainties, enabling stabilization even with partial state feedback and unknown bounds.

Contribution

The paper presents a novel sampling control framework that handles partial feedback, uncertainties, and non-ISS systems, extending adaptive control methods without requiring Lipschitz conditions.

Findings

Bounded-error sampling control achieves stabilization.

Adaptive control without Lipschitz conditions.

Event-triggered gain control for unknown bounds.

Abstract

In this paper, we propose a novel sampling control framework based on the emulation technique where the sampling error is regarded as an auxiliary input to the emulated system. Utilizing the supremum norm of sampling error, the design of periodic sampling and event-triggered control law renders the error dynamics bounded-input-bounded-state (BIBS), and when coupled with system dynamics, achieves global or semi-global stabilization. The proposed framework is then extended to tackle the event-triggered and periodic sampling stabilization for a system where only partial state is available for feedback and the system is subject to parameter uncertainties. The proposed framework is further extended to solve two classes of event-triggered adaptive control problems where the emulated closed-loop system does not admit an input-to-state stability (ISS) Lyapunov function. For the first class of systems with linear parameterized uncertainties, even-triggered global adaptive stabilization is achieved without the global Lipschitz condition on nonlinearities as often required in the literature. For the second class of systems with uncertainties whose bound is unknown, the event-triggered adaptive (dynamic) gain controller is designed for the first time. Finally, theoretical results are verified by two numerical examples.