Input-output triggered control using [Formulaomitted]-stability over finite horizons

• Published in: International journal of robust and nonlinear control 2015-09, Vol.25 (14), p.2299-2327
• Main Authors: Tolic, Domagoj, Sanfelice, Ricardo G, Fierro, Rafael
• Format: Article
• Language: English
• Subjects: Algorithms; Asymptotic properties; Construction; Control systems; Horizon; Mathematical analysis; Mathematical models; Nonlinearity
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.3203

This paper investigates stability of nonlinear control systems under intermittent information. Following recent results in the literature, we replace the traditional periodic paradigm, where the up-to-date information is transmitted and control laws are executed in a periodic fashion, with the event-triggered paradigm. Building on the small gain theorem, we develop input-output triggered control algorithms yielding stable closed-loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise in the environment, the developed algorithm yields stable, asymptotically stable, and [Formulaomitted]-stable (with bias) closed-loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on [Formulaomitted]-stability are presented. The prediction of a triggering event is achieved by employing [Formulaomitted]-gains over a finite horizon. By resorting to convex programming, a method to compute [Formulaomitted]-gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking problem for unicycles.