Robust suboptimal feedback control for a fed-batch nonlinear time-delayed switched system |
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| Institution: | 1. Department of Applied Mathematics, School of Science, Dalian Maritime University, Dalian 116026, PR China;2. College of Transportation Engineering, Dalian Maritime University, Dalian, Liaoning 116026, PR China;3. School of Management, Guangzhou University, Guangzhou, 510006, PR China;4. School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, PR China;5. School of Mathematical Sciences, Sunway University, Bandar Sunway, Selangor Darul Ehsan 47500, Malaysia;6. Teaching and Research Office of Mathematics, Department of Basics, PLA Dalian Naval Academy, Dalian, Liaoning 116018, PR China |
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| Abstract: | The optimal control strategy constructed in the form of a state feedback is effective for small state perturbations caused by changes in modeling uncertainty. In this paper, we investigate a robust suboptimal feedback control (RSPFC) problem governed by a nonlinear time-delayed switched system with uncertain time delay arising in a 1,3-propanediol (1,3-PD) microbial fed-batch process. The feedback control strategy is designed based on the radial basis function to balance the two (possibly competing) objectives: (i) the system performance (concentration of 1,3-PD at the terminal time of the fermentation) is to be optimal; and (ii) the system sensitivity (the system performance with respect to the uncertainty of the time-delay) is to be minimized. The RSPFC problem is subject to the continuous state inequality constraints. An exact penalty method and a novel time scaling transformation approach are used to transform the RSPFC problem into the one subject only to box constraints. The resulting problem is solved by a hybrid optimization algorithm based on a filled function method and a gradient-based algorithm. Numerical results are given to verify the effectiveness of the developed hybrid optimization algorithm. |
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