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| Received:August 16, 2010Revised:March 21, 2011 |
| 基金项目:This work was supported by the National Aeronautics and Space Administration (NASA) (No.ARMD NRA NNH07ZEA001N-IRAC1), and the National Science Foundation (NSF). |
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| Approximate dynamic programming solutions with a single network adaptive critic for a class of nonlinear systems |
| Jie DING,S. N. BALAKRISHNAN |
| (Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology) |
| Abstract: |
| Approximate dynamic programming (ADP) formulation implemented with an adaptive critic (AC)-based neural network (NN) structure has evolved as a powerful technique for solving the Hamilton-Jacobi-Bellman (HJB) equations. As interest in ADP and the AC solutions are escalating with time, there is a dire need to consider possible enabling
factors for their implementations. A typical AC structure consists of two interacting NNs, which is computationally expensive. In this paper, a new architecture, called the ‘cost-function-based single network adaptive critic (J-SNAC)’ is presented, which eliminates one of the networks in a typical AC structure. This approach is applicable to a wide class of nonlinear systems in engineering. In order to demonstrate the benefits and the control synthesis with the J-SNAC, two problems have been solved with the AC and the J-SNAC approaches. Results are presented, which show savings of about 50% of the computational costs by J-SNAC while having the same accuracy levels of the dual network structure in solving for optimal control. Furthermore, convergence of the J-SNAC iterations, which reduces to a least-squares problem, is discussed; for linear systems, the iterative process is shown to reduce to solving the familiar algebraic Ricatti equation. |
| Key words: Approximate dynamic programming Optimal control Nonlinear control Adaptive critic Cost-functionbased single network adaptive critic J-SNAC architecture |
