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Explore data-driven algorithms for online identification and control of partial differential equations (PDEs) with unknown parameters in this 56-minute conference talk from the DDPS seminar series. Learn about two distinct scenarios for addressing key challenges in controlling complex dynamical systems. Discover the first approach where PDEs are observable given control input and initial conditions, utilizing State-Dependent Riccati Equation (SDRE) for control computation and Bayesian Linear Regression for iterative parameter updates. Examine the second scenario addressing incomplete information challenges including unknown initial conditions, sparse boundary data, and unknown PDE coefficients through Physics-Informed Neural Networks (PINNs) for open-loop optimal control problems. Understand how neural networks predict state, adjoint, and control variables while identifying parameters online from sparse uncontrolled problem data. Review numerical examples demonstrating method effectiveness in highly challenging scenarios with significant uncertainty and incomplete information. Gain insights from collaborative research spanning multiple Italian universities focusing on optimal control for PDEs, model order reduction, and data-driven modeling applications.
