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Lyapunov-based dropout deep neural network (Lb-DDNN) adaptive controller
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DOI：10.1016/j.automatica.2026.113037.png)
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Abstract
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Deep neural networks (DNNs) are well-established tools for function approximation. However, DNNs are known to suffer from issues such as overfitting and co-adaptation, which affect the generalization and overall performance of the DNN. One powerful regularization technique to mitigate the overfitting and co-adaptation issues is dropout. In the dropout technique, randomly selected neurons are ignored or “dropped out”, meaning that their contributions to the downstream neurons are temporarily removed, which helps mitigate overfitting and co-adaptation of those neurons. In this paper, a Lyapunov-based dropout DNN (Lb-DDNN) regularization method is developed to deactivate the weights associated with stochastically selected neurons at each layer of the DNN. The Lb-DDNN is modeled using a switched mechanism involving an ensemble of DNN-based controllers that each approximate the unknown nonlinear dynamics individually. Switching between each individual DNN is conducted through a general state- and time-dependent switching signal. Simultaneously, an analytical Lyapunov stability-driven weight adaptation law is developed that adapts the weights of the DDNN online. Asymptotic convergence of the tracking error is ensured through a Lyapunov-based switched stability analysis. An extensive ablation study is provided based on simulations of a five-dimensional nonlinear system to investigate the effects of the various dropout training parameters on the performance of the Lb-DDNN controller. Simulation results indicate a 34.56% improvement in the tracking error, a 43.69% improvement in the function approximation error, and 33.88% lower control effort when compared to a baseline Lyapunov-based DNN (Lb-DNN) adaptive controller without dropout regularization.
Keywords:
Dropout
Deep Neural Networks
Lyapunov Stability
Adaptive Control
Switched Systems
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5.9
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