Titre : $H_\infty$ event triggering with performance guarantees: what can we prove and what cannot (yet)
– Résumé : Time-triggered (TT) sampled-data control assumes that sampling instances are generated in a process-independent fashion, normally via an external clock. Event-triggered (ET) control, in which sampling instances may be generated on the basis of the actual evolution of control and controlled variables, has a potential to outperform TT controllers, namely to guarantee the same performance under slower sampling. This property, first proved in the seminal 1999 paper by Åström and Bernhardsson, is extensively exploited in the context of stochastic, LQG-like, optimal control. However, most results studying ET control in the $H_\infty$, i.e. worst-case deterministic, context lack performance guarantees. On contrary, many $H_\infty$ ET results are inferior to the optimal TT solutions.
In this talk I’ll present an approach to ET $H_\infty$ control, which guarantees that each sampling interval does not exceed the sampling period $h$ of the optimal TT solution (periodic sampling for this problem) under the same performance level. Moreover, the class of disturbances, dubbed \emph{spoilers}, for which the proposed ET mechanism cannot guarantee sampling intervals strictly larger than $h$ is limited to a finite-dimensional subspace of $L_2[0,h]$, so is not quite plausible. Still, because one step of the solution is based on only a sufficient condition, it is not clear whether or not there is a different ET law that can guarantee the same for all disturbances. I’ll discuss perspectives of answering this question and technical difficulties associated with that.
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