2021/11/29 by Briat, Corentin, Khammash, Mustafa
#FOS: Biological sciences #FOS: Electrical engineering #FOS: Mathematics #Molecular Networks (q-bio.MN) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2111.14754
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_∞ control, and the sampled-data H_∞ 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.