Constrained-Cost Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems

For discrete-time nonlinear systems, this research is concerned with optimal control problems (OCPs) with constrained cost, and a novel value iteration with constrained cost (VICC) method is developed to solve the optimal control law with the constrained cost functions. The VICC method is initialize...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 35; no. 3; pp. 1 - 14
Main Authors: Wei, Qinglai, Li, Tao
Format: Journal Article
Language:English
Published: United States IEEE 01.03.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive control
Adaptive dynamic programming (ADP)
approximate dynamic programming
constrained cost
Control theory
Convergence
Cost function
Costs
Discrete time systems
Dynamic programming
Feasibility
Neural networks
Nonlinear control
Nonlinear systems
Optimal control
Performance analysis
reinforcement learning
value iteration (VI)
ISSN:2162-237X, 2162-2388, 2162-2388
Online Access:Get full text
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Summary:For discrete-time nonlinear systems, this research is concerned with optimal control problems (OCPs) with constrained cost, and a novel value iteration with constrained cost (VICC) method is developed to solve the optimal control law with the constrained cost functions. The VICC method is initialized through a value function constructed by a feasible control law. It is proven that the iterative value function is nonincreasing and converges to the solution of the Bellman equation with constrained cost. The feasibility of the iterative control law is proven. The method to find the initial feasible control law is given. Implementation using neural networks (NNs) is introduced, and the convergence is proven by considering the approximation error. Finally, the property of the present VICC method is shown by two simulation examples.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2023.3237586