Continuous-Time and Sampled-Data Optimal Control of Linear Stochastic Reaction Networks

Stochastic reaction networks form a powerful class of models for the representation of a wide variety of population models including those arising in biochemistry. The control of such networks has important implications for the control of biological systems and has therefore been a subject of recent interest. The optimal control of stochastic reaction networks, however, has been relatively little studied until now. Here, the continuous-time finite-horizon optimal control problem for linear reaction networks is formulated and solved in the Dynamic Programming framework. The results are formulated through the solution of a non-standard Riccati differential equation. The problem of the optimal sampled-data control of such networks is addressed next and solved using Hybrid Dynamic Programming. In this case, however, the solution is expressed in terms of the solution of coupled Lyapunov differential and Riccati difference equations. An example is given for illustration. The shortcomings of the approach are also discussed.