Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems

In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize...

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Vydané v:IEEE transactions on cybernetics Ročník 46; číslo 3; s. 840 - 853
Hlavní autori: Wei, Qinglai, Liu, Derong, Lin, Hanquan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States IEEE 01.03.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Adaptive control systems
Adaptive critic designs
adaptive dynamic programming (ADP)
Algorithms
approximate dynamic programming
Computer simulation
Convergence
Dynamic programming
Dynamical systems
Heuristic algorithms
Iterative algorithms
Iterative methods
Mathematical analysis
Mathematical models
neural networks
neuro-dynamic programming
Nonlinear dynamics
Nonlinear systems
Optimal control
Performance analysis
reinforcement learning
value iteration
approximate dynamic programming
neural networks
optimal control
neuro-dynamic programming
Adaptive critic designs
adaptive dynamic programming (ADP)
reinforcement learning
value iteration
ISSN:2168-2267, 2168-2275, 2168-2275
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Shrnutí:In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.
Bibliografia:ObjectType-Article-1
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2015.2492242