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Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound
Fei-Yue Wang1, Ning Jin, Derong Liu
1Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China. feiyue.wang@ia.ac.cn
IEEE Transactions on Neural Networks
|September 30, 2010
Summary
This study introduces an adaptive dynamic programming (ADP) method for discrete-time nonlinear systems. The approach finds optimal control laws and steps, ensuring performance within an error bound using neural networks.
Area of Science:
- Control Theory
- Artificial Intelligence
- Nonlinear Systems
Background:
- Optimal control problems are crucial for discrete-time nonlinear systems.
- Existing methods may face challenges in complex system dynamics and performance optimization.
- Adaptive Dynamic Programming (ADP) offers a promising framework for solving these problems.
Purpose of the Study:
- To develop and analyze iterative adaptive dynamic programming algorithms for finite-horizon optimal control of discrete-time nonlinear systems.
- To achieve an optimal control law that minimizes the performance index within a specified error bound (ε).
- To determine the optimal number of control steps using the proposed ADP algorithms.
Main Methods:
- Iterative adaptive dynamic programming (ADP) algorithms are employed.
- Neural networks are utilized for function approximation (performance index), control policy computation, and system modeling.
- Convergence analysis is performed for the performance index function and control policy.
Main Results:
- The proposed ADP algorithms successfully derive optimal control laws for discrete-time nonlinear systems.
- The method achieves performance indices close to the greatest lower bound within an ε-error.
- The optimal number of control steps can be determined.
- Simulation examples validate the effectiveness and applicability of the approach.
Conclusions:
- The presented iterative ADP approach, enhanced by neural networks, provides an effective solution for finite-horizon optimal control of discrete-time nonlinear systems.
- The method demonstrates convergence and achieves near-optimal performance with a quantifiable error bound.
- The use of neural networks facilitates practical implementation and broadens the applicability of ADP in complex control scenarios.
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