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In this paper, we further develop a recently proposed control method toswitch a bistable system between its steady states using temporal pulses. Themotivation for using pulses comes from biomedical and biological applications(e.g. synthetic biology), where it is generally difficult to build feedbackcontrol systems due to technical limitations in sensing and actuation. Theoriginal framework was derived for monotone systems and all the extensionsrelied on monotone systems theory. In contrast, we introduce the concept ofswitching function which is related to eigenfunctions of the so-called Koopmanoperator subject to a fixed control pulse. Using the level sets of theswitching function we can (i) compute the set of all pulses that drive thesystem toward the steady state in a synchronous way and (ii) estimate the timeneeded by the flow to reach an epsilon neighborhood of the target steady state.Additionally, we show that for monotone systems the switching function is alsomonotone in some sense, a property that can yield efficient algorithms tocompute it. This observation recovers and further extends the results of theoriginal framework, which we illustrate on numerical examples inspired bybiological applications.

Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator