Artificial intelligence–based avoidance of hopf bifurcations in dynamic optimal control of fermentation systems

Abstract

In biochemical systems, nonlinear processes are often associated with the Hopf bifurcation, which can result in oscillations, instability, and reduced product concentration. While bifurcation analysis tools such as MATCONT, implemented in MATLAB, can efficiently determine Hopf bifurcation points and associated stability boundaries, the direct incorporation of these results into dynamic optimal control problems remains an area of research. This paper presents an artificial intelligence-based approach for the optimal control of nonlinear biochemical processes. The proposed approach first determines the Hopf bifurcation points using the bifurcation analysis tool MATCONT. A neural network is then developed to determine the dominant eigenvalue or its proximity as an artificial intelligence-based surrogate model. This surrogate model is then incorporated into the optimal control framework based on the Pyomo model. The results demonstrate the efficiency of the proposed approach in maximizing product concentration while ensuring process stability. The proposed approach achieves near-optimal product concentrations, with only a small reduction compared to the unconstrained case, while effectively avoiding Hopf bifurcation-induced oscillations. In addition, the resulting control profiles remain smooth and practically implementable, highlighting the robustness of the proposed framework.