Biochemical implementation of acceleration sensing and PIDA control (Extended Version)

Designing dependable, self-regulated biochemical systems has long posed a challenge in the field of Synthetic Biology. Here, we propose a realization of a Proportional-Integral-Derivative-Acceleration (PIDA) control scheme as a Chemical Reaction Network (CRN) governed by mass action kinetics. A constituent element of this architecture is a speed and acceleration biosensing mechanism we introduce and, subsequently, place within a feedback configuration. Our control scheme provides enhanced dynamic performance and robust steady-state tracking. In addition to our theoretical analysis, this is practically highlighted in both the deterministic and stochastic settings by regulating a specific biochemical process in-silico and drawing comparisons with a simpler PID controller.