Dimension reduction based adaptive dynamic programming for optimal control of discrete-time nonlinear control-affine systems

Dynamic programming based methods have been widely used in solving discrete-time nonlinear constrained optimal control problems. However, applying these methods in real-time is challenging because a large amount of memory is needed and the associated computational cost is high. Here, a search space...

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Bibliographic Details
Published in:International journal of control Vol. 96; no. 11; pp. 2799 - 2811
Main Authors: Li, Qiang, Xu, Yunjun
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.11.2023
Taylor & Francis Ltd
Subjects:
Adaptive control
adaptive dynamic programming
Algorithms
Closed loops
Computational efficiency
Computing costs
Control theory
control-affine system
Discrete time systems
Dynamic programming
Feedback control
Inverse dynamics
Iterative methods
Nonlinear constrained optimal control
Nonlinear control
Nonlinear systems
Optimal control
Optimization
real-time control
uncertainty
ISSN:0020-7179, 1366-5820
Online Access:Get full text
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Summary:Dynamic programming based methods have been widely used in solving discrete-time nonlinear constrained optimal control problems. However, applying these methods in real-time is challenging because a large amount of memory is needed and the associated computational cost is high. Here, a search space dimension reduction strategy is proposed for a class of nonlinear discrete-time systems that are control-affine and invertible. Specifically, a bio-inspired motion rule is combined with inverse dynamics to reduce the value iteration search space to one dimension. The corresponding suboptimal control algorithm is developed and its optimality is analysed. An adaptation rule is developed to estimate uncertainties and improve the base policy. The closed-loop system is proven to be asymptotically stable. The advantages of the algorithm including much smaller computational cost and significantly reduced memory usage are demonstrated with two simulation examples.
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2022.2113438