Numerical Schemes for Optimal Control Problems and Differential Games

Efficient approximation schemes for high­ dimensional optimal control problems and games via Dynamic Programming schemes. Approximation of optimal feedbacks and optimal trajectories for free and constrained problems. Patchy domain decomposition. Pursuit­-evasion games, surveillance games. Approximation of Nash equilibria. Extensions to optimal control problems and differential games for hybrid systems via quasi-variational inequalities. Approximation of PDE systems for single and multi-population Mean Field Games (MFGs) on Eulidean spaces and networks via Semi-Lagrangian schemes, Newton, Gauss-Newton and Policy Iteration methods. Applications of MFGs to Cluster Analysis in Machine Learning (K-means, Expectation-Maximization).

Tentacle-like soft-manipulators modeled by systems of controlled PDAEs (Partial Differential Algebraic Equations). Approximation of optimality systems via numerical methods for constrained optimization (Newton-like, augmented Lagrangian, ADMM) and optimal control of PDEs (adjoint-based projected gradient descent). Applications to reachability, obstacle-avoidance and force-closure grasp problems in soft-robotics. 

Components: Alessandro Alla, Simone Cacace and Elisabetta Carlini