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Zhang, W.H. and Chen, B. (2006) State Feedback H_∞ Control for a Class of Nonlinear Stochastic Systems. SIAM Journal on Control and Optimization, 44, 1973-1991.

has been cited by the following article:

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

  AUTHORS: Alexander W. Bae

  KEYWORDS: Gene Regulatory Network, GMA System, Galerkin’s Approximation, Feedback Design of Biomolecular Systems, Hamilton-Jacobi Equation, Nonlinear Control

  JOURNAL NAME: Computational Molecular Bioscience, Vol.12 No.2, June 29, 2022

  ABSTRACT: 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.