From optimal control to feedback: AI-assisted pattern extraction for the regulation of microbial populations M2 internship (5–6 months) – GreenOwl project-team

Context. Nonlinear mechanistic population dynamics models, described by ordinary differential equations (ODEs), lead to optimal control problems driven by biotechnological goals: sustaining species coexistence in a microbial consortium (bioremediation, microbiome engineering), maximizing bioproduction or reaching a target composition in minimum time, by acting on levers such as dilution, nutrient supply or light (optogenetics). The same approach applies to cell populations under therapy. The analysis of optimal solutions, in particular through Pontryagin's Maximum Principle (PMP), can reveal various structures: bang-bang arcs, singular arcs, switching surfaces and turnpike behavior. These solutions are, however, obtained in open loop, and their PMP-based characterization involves adjoint states with no direct physical meaning. Turning them into explicit and robust state-feedback laws therefore remains a challenge. Objectives. The internship aims to develop a methodology in which AI acts as a knowledge generator built on optimal solutions, rather than a replacement for optimal control. The work will include: 1. numerically solving optimal control problems with direct methods (collocation, CasADi/Bocop) across a range of initial conditions and parameters, in order to build a database of optimal trajectories; 2. extracting switching rules and recurrent patterns with interpretable learning tools (shallow oblique decision trees, sparse logistic regression, clustering, sparse symbolic regression of switching surfaces); 3. cross-checking these rules against PMP-based geometric analysis; 4. synthesizing state-feedback laws and assessing their closed-loop robustness under parametric uncertainty; depending on progress, coupling them with state observers. Profile. M2 student in applied mathematics, control engineering or data science. Solid knowledge of ODEs and optimization, together with experience in Python or Julia, is expected. An interest in biology is a plus