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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| Published in: | ISA transactions Vol. 123; pp. 188 - 199 |
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| Main Authors: | , , , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Ltd
01.04.2022
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| ISSN: | 0019-0578, 1879-2022, 1879-2022 |
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| Abstract | 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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| AbstractList | 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.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. 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. 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. |
| Author | Piao, Changhao Liu, Mingjie Chen, Xiaolei Liu, Xinggao Liu, Ping Li, Lei Hu, Qingquan |
| Author_xml | – sequence: 1 givenname: Ping surname: Liu fullname: Liu, Ping email: liuping_cqupt@cqupt.edu.cn organization: College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China – sequence: 2 givenname: Qingquan surname: Hu fullname: Hu, Qingquan organization: College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China – sequence: 3 givenname: Lei surname: Li fullname: Li, Lei organization: College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China – sequence: 4 givenname: Mingjie surname: Liu fullname: Liu, Mingjie organization: College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China – sequence: 5 givenname: Xiaolei surname: Chen fullname: Chen, Xiaolei organization: College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China – sequence: 6 givenname: Changhao surname: Piao fullname: Piao, Changhao email: piaoch@cqupt.edu.cn organization: College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China – sequence: 7 givenname: Xinggao surname: Liu fullname: Liu, Xinggao organization: State Key Laboratory of Industry Control Technology, College of Control Science & Engineering, Zhejiang University, Hangzhou 310027, China |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/34020789$$D View this record in MEDLINE/PubMed |
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| Keywords | Fast computation PRP conjugate gradient method Dynamic processes Control parameterization Optimal control |
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| Title | Fast control parameterization optimal control with improved Polak–Ribière–Polyak conjugate gradient implementation for industrial dynamic processes |
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