Simultaneous Online System Identification and Control using Composite Adaptive Lyapunov-Based Deep Neural Networks

ICLR 2025 Conference Submission12570 Authors

Keywords: Adaptive control, Online Learning, Control Theory, Robotics

TL;DR: A composite adaptive deep neural network controller is developed with adaptation law comprising of the tracking error and prediction error to update the weights of all layers of the DNN.

Abstract: Although deep neural network (DNN)-based controllers are popularly used to control uncertain nonlinear dynamic systems, most results use DNNs that are pretrained offline and the corresponding controller is implemented post-training. Recent advancements in adaptive control have developed controllers with Lyapunov-based update laws (i.e., control and update laws derived from a Lyapunov-based stability analysis) for updating the DNN weights online to ensure the system states track a desired trajectory. However, the update laws are based on the tracking error, and offer guarantees on only the tracking error convergence, without providing any guarantees on system identification. This paper provides the first result on simultaneous online system identification and trajectory tracking control of nonlinear systems using adaptive updates for all layers of the DNN. A combined Lyapunov-based stability analysis is provided, which guarantees that the tracking error, state-derivative estimation error, and DNN weight estimation errors are uniformly ultimately bounded. Under the persistence of excitation (PE) condition, the tracking and weight estimation errors are shown to exponentially converge to a neighborhood of the origin, where the rate of convergence and the size of this neighborhood depends on the gains and a factor quantifying PE, thus achieving system identification and enhanced trajectory tracking performance. As an outcome of the system identification, the DNN model can be propagated forward to predict and compensate for the uncertainty in dynamics under intermittent loss of state feedback. Comparative simulation results are provided on a two-link manipulator system and an unmanned underwater vehicle system with intermittent loss of state feedback, where the developed method yields significant performance improvement compared to baseline methods.

Primary Area: applications to robotics, autonomy, planning

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Submission Number: 12570