Optimal control of hybrid manufacturing systems by log-exponential smoothing aggregation

Kobamelo Mashaba; Jianxing Li; Honglei Xu; Xinhua Jiang

doi:10.3934/dcdss.2020100

Article Contents

2020, Volume 13, Issue 6: 1711-1719. Doi: 10.3934/dcdss.2020100

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Optimal control of hybrid manufacturing systems by log-exponential smoothing aggregation

1.
School of Electrical Engineering, Computing, Mathematical Sciences, Curtin Univerity, Perth, 6845 WA, Australia
2.
School of Information Science and Engineering, Fujian University of Technology, Fuzhou, Fujian 350118, China

^* Corresponding author: Jianxing Li and Honglei Xu
^* Corresponding author: Jianxing Li and Honglei Xu

Received: February 28, 2018

Revised: August 31, 2018

Published: April 2020

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Abstract

This paper studies new optimal control policies for solving complex decision-making problems encountered in industrial hybrid systems in a manufacturing setting where critical jobs exist in a busy structure. In such setting, different dynamical systems interlink each other and share common functions for smooth task execution. Entities arriving at shared resources compete for service. The interactions of industrial hybrid systems become more and more complex and need a suitable controller to achieve the best performance and to obtain the best possible service for each of the entities arriving at the system. To solve these challenges, we propose an optimal control policy to minimize the operational cost for the manufacturing system. Furthermore, we develop a hybrid model and a new smoothing algorithm for the cost balancing between the quality and the job tardiness by finding optimal service time of each job in the system.

Keywords:

Mathematics Subject Classification: Primary: 37C75, 93C10; Secondary: 34D20.

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Table 1. Job arrival $ 0.4\le r_i \le 1.5 $

$ F_1 \, \| \, \text{no-wait, seq-dependent}\, \| \, x_{\max} $				$ F_1 \, \| \, \text{wait, seq-dependent}\, \| \, x_{\max} $
Job Arrival time	Control input	Completion time	Processing cost	Control input	Completion time	Processing cost
0.4	0.3162	0.5000	2.4500	0.4404	0.5940	1.4872
0.5	0.4472	0.7000	1.5900	0.4404	0.7950	1.7664
0.7	0.4472	0.9000	1.9100	0.4404	0.9959	2.1262
0.9	0.5300	1.1809	2.1777	0.5132	1.2593	2.4211
1.3	0.4472	1.5000	3.3500	0.447214	1.5000	3.3500
1.5	0.4423	1.6956	3.9998	0.4423	1.6956	3.9998
Total cost: 15.4775				Total cost: 15.1507

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Table 2. Job arrival $ 1.1\le r_i \le 2.3 $

$ F_1 \, \| \, \text{no-wait, seq-dependent}\, \| \, x_{\max} $				$ F_1 \, \| \, \text{wait, seq-dependent}\, \| \, x_{\max} $
Job Arrival time	Control input	Completion time	Processing cost	Control input	Completion time	Processing cost
1.1	0.4963	1.3463	2.7057	0.4963	1.3463	2.7057
1.4	0.4472	1.6000	3.6600	0.4472	1.6000	3.6600
1.6	0.3162	1.7000	5.0900	0.4310	1.7857	4.3733
1.7	0.4204	1.8767	4.7668	0.4121	1.9530	5.1098
2.2	0.3162	2.3000	7.4900	0.3652	2.3393	7.2480
2.3	0.3690	2.4361	7.5503	0.3633	2.4713	7.9814
Total cost: 31.2628				Total cost: 31.0782

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