DNN-Based AI-Driven H2/H∞ Filter Design of Nonlinear Stochastic Systems via Two-Coupled HJIEs-Supervised Adam Learning Algorithm
Bor‐Sen Chen, Jin Ma, Ruei-Syuan Wu · Artificial Intelligence Advances · 2024
This study introduces a new approach using supervised learning deep neural networks (DNNs) to develop an AI-driven filter for nonlinear stochastic signal systems with external disturbance and measurement noise. The filter aims to achieve a balanced design between and norm of the state estimation error to achieve both optimal and robust filtering design of nonlinear signal system simultaneously while considering environmental disturbance and measurement noise. Traditionally, this nonlinear filter design involves solving complex two-coupled Hamilton-Jacobi-Issac Equations (HJIEs). To simplify this complicated design process, a novel two-coupled HJIEs-supervised Adam learning algorithm is proposed for DNN-based AI-driven filter. This algorithm trains a DNN-based AI-driven filter offline using worst-case scenarios of environmental disturbance and measurement noise. This training phase generates state estimation errors that teach the DNN-based AI-driven filter how to coordinate nonlinear system model with worst-case external disturbance and measurement noise, Luenberger-type filter, estimation error dynamic model and two-coupled HJIEs-supervised deep Adam learning algorithm to achieve the mixed filtering strategy effectively. The study demonstrates theoretically that this approach will achieve the desired mixed filtering strategy once the Adam learning algorithm converges. Finally, the effectiveness of the proposed DNN-based AI-driven filter design method is validated through simulations, specifically involving trajectory estimation and prediction of an incoming ballistic missile detected by a radar system.