We show how an important class of nonlinearfeedback controllers can be designed using idealized abstractchemical reactions that can be implemented via DNA strand dis-placement (DSD) reactions. Exploitingchemical reaction networks(CRNs) as a programming language for the design of complexcircuits and networks, we show how a set of unimolecularand bimolecular reactions can be used to realize ultrasensitiveinput-output dynamics that produce a nonlinearquasi slidingmode(QSM) feedback controller. The kinetics of the requiredchemical reactions can then be implemented as enzyme-free,entropy-driven DNA reactions using DNA strand displacementvia Watson-Crick base pairing and branch migration. We demon-strate that the closed loop response of the nonlinear QSM con-troller outperforms a traditional linear controller by facilitatingmuch faster tracking response dynamics without introducingovershoots in the transient response. The resulting controller ishighly modular and is less affected by retroactivity effects thanstandard linear designs.
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