A novel optimal trajectory tracking scheme is introduced for nonlinear continuous-time systems in strict feedback form with uncertain dynamics by using neural networks (NNs). The method employs an actor-critic-based NN back-stepping technique for minimizing a discounted value function along with an identifier to approximate unknown system dynamics that are expressed in augmented form. Novel online weight update laws for the actor and critic NNs are derived by using both the NN identifier and Hamilton-Jacobi-Bellman residual error. A new continual lifelong learning technique utilizing the Fisher Information Matrix via Hamilton-Jacobi-Bellman residual error is introduced to obtain the significance of weights in an online mode to overcome the issue of catastrophic forgetting for NNs, and closed-loop stability is analyzed and demonstrated. The effectiveness of the proposed method is shown in simulation by contrasting the proposed with a recent method from the literature on an underactuated unmanned aerial vehicle, covering both its translational and attitude dynamics.


Electrical and Computer Engineering

Second Department

Computer Science

Publication Status

Open Access


Office of Naval Research, Grant N00014-21-1-2232

Keywords and Phrases

Continual lifelong learning; neural networks; optimal control; strict-feedback systems; unmanned aerial vehicles

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2024 The Authors, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Mar 2024