Optimal and $H_\infty$ Control of Stochastic Reaction Networks

TL;DR

This paper develops optimal and $H_ abla$ control strategies for stochastic reaction networks, especially unimolecular types, using Riccati equations, with implications for biological system regulation.

Contribution

It provides explicit solutions for optimal control and extends to $H_ abla$ control problems, including sampled-data and continuous cases, for stochastic reaction networks.

Findings

Explicit solutions for unimolecular networks using Riccati equations.

Extension of control methods to sampled-data and $H_ abla$ control.

Numerical methods for solving the control equations via backward integration.

Abstract

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.