Asian Engineering Review

In nonlinear biochemical systems, complex dynamic behaviors, such as multistability and oscillations, are often induced by internal feedback mechanisms. These behaviors pose significant challenges for optimal control problems, as traditional optimization approaches that focus solely on performance criteria can lead to instability or oscillations. In this work, a novel stability-constrained optimal control approach is developed for a high-dimensional artificial cell system, leveraging bifurcation analysis, machine learning, and dynamic optimization. The mechanistic model accounts for the coupled dynamics of gene expression, metabolic reactions, energy balance, and cell growth. As a result, the mechanistic model is a nonlinear dynamic system with rich dynamics. Bifurcation analysis is used to identify regions of stability loss, including Hopf bifurcation points. A dataset is constructed from the states of the dynamic system and the corresponding dominant eigenvalue information. A neural network surrogate approximates the stability behavior based on the dynamic system's states. The neural network is integrated into a dynamic optimization problem using the Pyomo optimization library. As a result, stability information is included in the objective function of the optimization problem. A smooth penalty approach is used to define the objective function based on the dominant eigenvalue information. The smooth penalty approach is used to avoid non-differentiability in the objective function. The optimization problem is solved using a direct transcription approach with collocation. The results clearly indicate that the proposed framework can identify control trajectories that maximize product formation while maintaining system stability. In contrast, optimization problems that are not constrained for stability considerations lead to degenerate or physically unrealistic solutions. In addition, this study clearly indicates that proper model formulation, including consideration of metabolite decay, is important for achieving robust solutions.