Complete stability analysis of a heuristic ADP control design
This provides incremental stability guarantees for ADHDP control in deep learning applications, benefiting researchers and practitioners in autonomous systems and control theory.
The paper tackles the stability analysis of Action-Dependent Heuristic Dynamic Programming (ADHDP) control for multi-layer neural networks, showing that the approach achieves uniform ultimate boundedness under specific learning rate conditions without constraints on the temporal discount factor. The results demonstrate significantly improved learning and control performance compared to state-of-the-art methods in linear and nonlinear systems, including the cart-pole balancing problem.
This paper provides new stability results for Action-Dependent Heuristic Dynamic Programming (ADHDP), using a control algorithm that iteratively improves an internal model of the external world in the autonomous system based on its continuous interaction with the environment. We extend previous results by ADHDP control to the case of general multi-layer neural networks with deep learning across all layers. In particular, we show that the introduced control approach is uniformly ultimately bounded (UUB) under specific conditions on the learning rates, without explicit constraints on the temporal discount factor. We demonstrate the benefit of our results to the control of linear and nonlinear systems, including the cart-pole balancing problem. Our results show significantly improved learning and control performance as compared to the state-of-art.