Unsupervised Physics-Informed Neural Network-based Nonlinear Observer design for autonomous systems using contraction analysis

TL;DR

This paper introduces an innovative neural network-based method for designing nonlinear observers in autonomous systems, leveraging contraction analysis and physics-informed neural networks to address longstanding analytical and numerical challenges.

Contribution

It presents a novel unsupervised PINN approach that enforces contraction inequalities directly in the training process for observer design.

Findings

Successful numerical simulation validation

Robustness to measurement noise demonstrated

Effective handling of complex nonlinear systems

Abstract

Contraction analysis offers, through elegant mathematical developments, a unified way of designing observers for a general class of nonlinear systems, where the observer correction term is obtained by solving an infinite dimensional inequality that guarantees global exponential convergence. However, solving the matrix partial differential inequality involved in contraction analysis design is both analytically and numerically challenging and represents a long-lasting challenge that prevented its wide use. Therefore, the present paper proposes a novel approach that relies on an unsupervised Physics Informed Neural Network (PINN) to design the observer's correction term by enforcing the partial differential inequality in the loss function. The performance of the proposed PINN-based nonlinear observer is assessed in numerical simulation as well as its robustness to measurement noise and neural network approximation error.