Fast control parameterization optimal control with improved Polak–Ribière–Polyak conjugate gradient implementation for industrial dynamic processes

This paper proposes a fast control parameterization optimal control algorithm for industrial dynamic process with constraints. Derived from the frame of control variable parameterization (CVP) technique, the proposed method combines an efficient gradient computation strategy with an improved nonline...

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Bibliographic Details
Published in:ISA transactions Vol. 123; pp. 188 - 199
Main Authors: Liu, Ping, Hu, Qingquan, Li, Lei, Liu, Mingjie, Chen, Xiaolei, Piao, Changhao, Liu, Xinggao
Format: Journal Article
Language:English
Published: United States Elsevier Ltd 01.04.2022
Subjects:
Control parameterization
Dynamic processes
Fast computation
Optimal control
PRP conjugate gradient method
Fast computation
PRP conjugate gradient method
Dynamic processes
Control parameterization
Optimal control
ISSN:0019-0578, 1879-2022, 1879-2022
Online Access:Get full text
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Summary:This paper proposes a fast control parameterization optimal control algorithm for industrial dynamic process with constraints. Derived from the frame of control variable parameterization (CVP) technique, the proposed method combines an efficient gradient computation strategy with an improved nonlinear optimization computation approach to overcome the challenge of computation efficiency caused by gradients and bounds in optimal control problems. Firstly, a fast gradient computation method based on the costate system of Hamiltonian function is developed to decrease the computational expense of gradients by employing approximate treatments and numerical integration strategy. Then, a trigonometric function transformation scheme is presented to tackle the boundary constraints so that the original optimal control problem is further converted into an unconstrained one. On this basis, an improved restricted Polak–Ribière–Polyak (PRP) conjugate gradient approach is introduced to solve the nonlinear optimization problem by using conjugate gradient iterations and strong Wolfe line search. Meanwhile, to enhance the convergence, a restricting condition is imposed in strong Wolfe line search to create iteration step-length. Finally, the proposed algorithm is implemented on three dynamic processes. The detailed comparison among the classical CVP method, literature results and the proposed method are carried out. Simulation studies show that the proposed fast approach averagely saves more than 90% computation time in contrast to the classical CVP method, demonstrating the effectiveness of the proposed fast optimal control approach. •A fast CVP method for industrial dynamic process with constraints is proposed.•An improved restricted PRP approach is proposed for unconstrained NLP problem.•Test results reveal that the proposed method saves more than 90% CPU time.
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ISSN:0019-0578
1879-2022
1879-2022
DOI:10.1016/j.isatra.2021.05.020