Journal
AUTOMATICA
Volume 59, Issue -, Pages 9-18Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2015.06.001
Keywords
Adaptive dynamic programming; Action-Dependent Heuristic Dynamic Programming; Adaptive control; Adaptive critic; Neural network; Gradient descent; Lyapunov function
Funding
- National Science Foundation (NSF) [DMS-13-11165]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1311165] Funding Source: National Science Foundation
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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 for 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-the-art. (C) 2015 Elsevier Ltd. All rights reserved.
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