A Sampling Control Framework and Its Applications to Robust and Adaptive Control

• Published in: IEEE transactions on automatic control Vol. 68; no. 12; pp. 1 - 14
• Main Authors: Zhu, Lijun, Chen, Zhiyong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Closed loop systems; Closed loops; Control systems design; Control theory; Emulation; Errors; Feedback control; Liapunov functions; Lipschitz condition; Lyapunov methods; Nonlinear dynamical systems; Parameter uncertainty; Power system dynamics; Robust control; Sampling; Sampling error; Stabilization; System dynamics; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3259525

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 it is coupled with system dynamics, achieves global or semi-global stabilization. The proposed framework is then extended to tackle the stabilization problem for a system where the state of dynamic uncertainty is not available for feedback and the dynamics 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 three numerical examples.