A Min-Max Approach to Event- and Self-Triggered Sampling and Regulation of Linear Systems


This paper presents both an event- and a self-triggered sampling and regulation scheme for continuous time linear dynamic systems by using zero-sum game formulation. A novel performance index is defined wherein the control policy is treated as the first player and the threshold for control input error due to aperiodic dynamic feedback is treated as the second player. The optimal control policy and sampling intervals are generated using the saddle point or Nash equilibrium solution, which is obtained from the corresponding game algebraic Riccati equation. To determine the optimal event-based sampling scheme, an event-triggering condition is derived by utilizing the worst case control input error as the threshold. To avoid the additional hardware for the event-triggering mechanism, a near optimal self-triggering condition is derived to determine the future sampling instants given the current state vector. To guarantee Zeno free behavior in both the event and self-triggered closed-loop system, the minimum inter-sample times are shown to be lower bounded by a nonzero positive number. Asymptotic stability of the closed-loop system is ensured using Lyapunov stability analysis. Finally, simulation examples are provided to substantiate the analytical claims.


Electrical and Computer Engineering


This work is supported in part by the intelligent systems center, Rolla, MO, USA, NSF Department of ECCS under Grant #1406533 and CMMI under Grant #1547042, and start-up fund Oklahoma State University, Stillwater, OK, USA.

Keywords and Phrases

Asymptotic stability; Closed loop systems; Computer hardware; Continuous time systems; Game theory; Hardware; Linear control systems; Linear systems; Riccati equations; Event-triggered controls; Games; Optimal controls; Performance analysis; Self-triggered controls; Zero-sum game; Closed loop control systems; Self-triggered control

International Standard Serial Number (ISSN)

0278-0046; 1557-9948

Document Type

Article - Journal

Document Version


File Type





© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jul 2019