  Stochastic reaction networks is a powerful class of models for the
representation a wide variety of population models including biochemistry. The
control of such networks has been recently considered due to their important
implications for the control of biological systems. Their optimal control,
however, has been relatively few studied until now. The continuous-time
finite-horizon optimal control problem is formulated first and explicitly
solved in the case of unimolecular reaction networks. The problems of the
optimal sampled-data control, the continuous $H_\infty$ control, and the
sampled-data $H_\infty$ control of such networks are addressed next. The
results in the unimolecular case take the form of nonstandard Riccati
differential equations or differential Lyapunov equations coupled with
difference Riccati equations, which can all be solved numerically by
backward-in-time integration.
