We demonstrate that a convex optimization formulation of physics-informed neural networks
for solving partial differential equations can address a variety of computationally challenging …

This paper proposes a fully data-driven approach for optimal control of nonlinear control-
affine systems represented by a stochastic diffusion. The focus is on the scenario where both …

Control Lyapunov functions are a central tool in the design and analysis of stabilizing
controllers for nonlinear systems. Constructing such functions, however, remains a …

Designing control policies for stabilization tasks with provable guarantees is a long-standing
problem in nonlinear control. A crucial performance metric is the size of the resulting region …

Homogeneous vector fields play an important role in approximating general nonlinear
systems. We propose a neural network approach for finding global Lyapunov functions for …

Nonlinear optimal control is vital for numerous applications but remains challenging for
unknown systems due to the difficulties in accurately modelling dynamics and handling …

In this paper, we present a novel method to drive a nonlinear system to a desired state, with
limited a priori knowledge of its dynamic model: local dynamics at a single point and the …

Optimal control for high-dimensional nonlinear systems remains a fundamental challenge.
One bottleneck is that classical approaches for solving the Hamilton-Jacobi-Bellman (HJB) …