  In this paper we study how to shape temporal pulses to switch a bistable
system between its stable steady states. Our motivation for pulse-based control
comes from applications in synthetic biology, where it is generally difficult
to implement real-time feedback control systems due to technical limitations in
sensors and actuators. We show that for monotone bistable systems, the
estimation of the set of all pulses that switch the system reduces to the
computation of one non-increasing curve. We provide an efficient algorithm to
compute this curve and illustrate the results with a genetic bistable system
commonly used in synthetic biology. We also extend these results to models with
parametric uncertainty and provide a number of examples and counterexamples
that demonstrate the power and limitations of the current theory. In order to
show the full potential of the framework, we consider the problem of inducing
oscillations in a monotone biochemical system using a combination of temporal
pulses and event-based control. Our results provide an insight into the
dynamics of bistable systems under external inputs and open up numerous
directions for future investigation.
