Policy-Iteration-Based Finite-Horizon Approximate Dynamic Programming for Continuous-Time Nonlinear Optimal Control

The Hamilton-Jacobi-Bellman (HJB) equation serves as the necessary and sufficient condition for the optimal solution to the continuous-time (CT) optimal control problem (OCP). Compared with the infinite-horizon HJB equation, the solving of the finite-horizon (FH) HJB equation has been a long-standin...

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Vydáno v:IEEE transaction on neural networks and learning systems Ročník 34; číslo 9; s. 1 - 13
Hlavní autoři: Lin, Ziyu, Duan, Jingliang, Li, Shengbo Eben, Ma, Haitong, Li, Jie, Chen, Jianyu, Cheng, Bo, Ma, Jun
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.09.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Actor critic
Algorithms
approximate dynamic programming (ADP)
Approximation algorithms
Artificial neural networks
Complex systems
Dynamic programming
finite-horizon (FH)
Hamilton–Jacobi–Bellman (HJB) equation
Heuristic algorithms
Horizon
Linear quadratic regulator
Mathematical models
Multilayers
Neural networks
Nonlinear control
Nonlinear dynamical systems
Optimal control
Optimization
policy iteration (PI)
System effectiveness
Tracking problem
ISSN:2162-237X, 2162-2388, 2162-2388
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Popis
Shrnutí:The Hamilton-Jacobi-Bellman (HJB) equation serves as the necessary and sufficient condition for the optimal solution to the continuous-time (CT) optimal control problem (OCP). Compared with the infinite-horizon HJB equation, the solving of the finite-horizon (FH) HJB equation has been a long-standing challenge, because the partial time derivative of the value function is involved as an additional unknown term. To address this problem, this study first-time bridges the link between the partial time derivative and the terminal-time utility function, and thus it facilitates the use of the policy iteration (PI) technique to solve the CT FH OCPs. Based on this key finding, the FH approximate dynamic programming (ADP) algorithm is proposed leveraging an actor-critic framework. It is shown that the algorithm exhibits important properties in terms of convergence and optimality. Rather importantly, with the use of multilayer neural networks (NNs) in the actor-critic architecture, the algorithm is suitable for CT FH OCPs toward more general nonlinear and complex systems. Finally, the effectiveness of the proposed algorithm is demonstrated by conducting a series of simulations on both a linear quadratic regulator (LQR) problem and a nonlinear vehicle tracking problem.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2022.3225090