Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces e...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2017-03, Vol.28 (3), p.714-725
Main Authors: Zhu, Yuanheng, Zhao, Dongbin, Li, Xiangjun
Format: Article
Language:English
Subjects:
<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H ∞ control
Adaptive algorithms
Adaptive control
Adaptive dynamic programming (ADP)
Algorithm design and analysis
Approximation algorithms
Artificial neural networks
Attenuation
Computer & video games
Computer simulation
Control systems
Control systems design
Disturbance
Dynamic programming
Feasibility studies
Game theory
Games
Gauss-Newton method
H-infinity control
Heuristic algorithms
Internet
Iterative methods
Least squares method
Mathematical model
Neural networks
Newton methods
Optimization
policy iteration (PI)
Theoretical analysis
Zero sum games
zero-sum game (ZSG)
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Summary:H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2016.2561300