H₂ and H∞-Feedback Control Design for Nonlinear Gene Networks via Successive Galerkin’s Approximation

This paper presents a design method of H2 and H∞-feedback control loop for nonlinear smooth gene networks that are in control affine form. Formulaic solution methodology for solving the nonlinear partial differential equations, namely the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations through successive Galerkin’s approximation is implemented and the results are compared. Throughout the implementation, there were several caveats that need to be further resolved for practical applications in general cases. Such issues and the clarification of causes are mathematically established and reviewed.