Input‐output triggered control using
‐stability over finite horizons |
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| Authors: | Domagoj Tolić Ricardo G. Sanfelice Rafael Fierro |
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| Affiliation: | 1. Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, 10000, Croatia;2. Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, AZ 85721, USA;3. Electrical and Computer Engineering Department, University of New Mexico, Albuquerque, NM 87131, USA |
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| Abstract: | 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 In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided.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  ‐stable (with bias) closed‐loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on  ‐stability are presented. The prediction of a triggering event is achieved by employing  ‐gains over a finite horizon. By resorting to convex programming, a method to compute  ‐gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking problem for unicycles. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | intermittent information self‐triggering small gain theorem
‐stability hybrid systems |
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