Physics-Informed Extreme Learning Machine Lyapunov Functions

We demonstrate that a convex optimization formulation of physics-informed neural networks for solving partial differential equations can address a variety of computationally challenging tasks in nonlinear system analysis and control. This includes computing Lyapunov functions, region-of-attraction estimates, and optimal controllers. Through numerical examples, we illustrate that the formulation is effective in solving both low- and high-dimensional analysis and control problems. We compare it with alternative approaches, including semidefinite programming and nonconvex neural network optimization, to demonstrate its potential advantages.