2025/03/06 by Ahan Basu, Basu, Ahan, Bhabani Shankar Dey +3
Computer Science · Engineering · Physics and Astronomy · #Adaptive Control of Nonlinear Systems #Adaptive Dynamic Programming Control #FOS: Electrical engineering #Model Reduction and Neural Networks #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2503.04129
openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work aims to synthesize a controller that ensures that an unknown discrete-time system is incrementally input-to-state stable (δ-ISS). In this work, we introduce the notion of δ-ISS control Lyapunov function (δ-ISS-CLF), which, in conjunction with the controller, ensures that the closed-loop system is incrementally ISS. To address the unknown dynamics of the system, we parameterize the controller as well as the δ-ISS-CLF as neural networks and learn them by utilizing the sampled data from the state space of the unknown system. To formally verify the obtained δ-ISS-CLF, we develop a validity condition and incorporate the condition into the training framework to ensure a provable correctness guarantee at the end of the training process. Finally, the usefulness of the proposed approach is proved using multiple case studies - the first one is a scalar system with a non-affine non-polynomial structure, the second example is a one-link manipulator system, the third system is a nonlinear Moore-Grietzer model of the jet engine and the final one is a rotating rigid spacecraft model.