Recent studies showed that certain drugs can change regulatory reaction parameters in gene regulatory networks (GRNs) and therefore restore pathological cells to a normal state. A state control framework for regulating biological networks has been built based on attractors and bifurcation theory to analyze this phenomenon. However, the control signal is self-developed in this framework, of which the parameter perturbation method can only calculate the state transition time of cells with single control variable. Therefore, an optimal control method based on the dynamic optimization algorithms is proposed for complex biological networks modeled by nonlinear ordinary differential equations (ODEs). In this approach, dynamic optimization problems are constructed based on basic characteristics of the biological networks. Furthermore, using an example of a simple low-dimensional three-node GRN and a complex high-dimensional cancer GRN, MATLAB is utilized to calculate optimal control strategies with either single or multiple control variables. This method aims to achieve accurate and rapid state regulation for biological networks, which can provide a reference for experimental researches and medical treatment.
