An Adaptive Dynamic Programming Scheme for Nonlinear Optimal Control With Unknown Dynamics and Its Application to Turbofan Engines

In this article, a novel adaptive dynamic programming (ADP) approach is proposed for the optimal control problem of nonlinear continuous control systems with unknown dynamics. First, an alternating iteration algorithm based on Hamilton-Jacobi-Bellman equation is proposed for the optimal control of k...

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Bibliographic Details
Published in:IEEE transactions on industrial informatics Vol. 17; no. 1; pp. 367 - 376
Main Authors: Sun, Tao, Sun, Xi-Ming
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.01.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive control
Adaptive dynamic programming (ADP)
Algorithms
Approximation
Approximation algorithms
Basis functions
Convergence
convergence analysis
Dynamic models
Dynamic programming
Dynamical systems
Feedback control
Fuel control
global asymptotic stability
Hamilton–Jacobi–Bellman (HJB) equation
Heuristic algorithms
Iterative algorithms
Iterative methods
Mathematical model
Nonlinear control
Nonlinear dynamical systems
Nonlinear dynamics
nonlinear optimal control
Nonlinear systems
Optimal control
Tracking control
Turbofan engines
ISSN:1551-3203, 1941-0050
Online Access:Get full text
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Summary:In this article, a novel adaptive dynamic programming (ADP) approach is proposed for the optimal control problem of nonlinear continuous control systems with unknown dynamics. First, an alternating iteration algorithm based on Hamilton-Jacobi-Bellman equation is proposed for the optimal control of known nonlinear control systems. Then, the convergence results of the alternating iteration algorithm are obtained by using mathematical induction and monotone bounded convergence theorem. Moreover, the global asymptotic stability of the nonlinear closed-loop system is proved. Second, based on the scheme of alternating iteration algorithm, an ADP algorithm for the optimal control problem with unknown nonlinear dynamic model is developed by using the basis function approximation method and Newton-Leibniz formula, which can update the control strategy online by utilizing input and output information of the system. In addition, the convergence analysis of the proposed ADP algorithm is derived. Finally, the feasibility of the established results is verified by two examples, and the ADP method is applied to the optimal tracking fuel control problem of turbofan engines.
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ISSN:1551-3203
1941-0050
DOI:10.1109/TII.2020.2979779