Robust suboptimal feedback control for a fed-batch nonlinear time-delayed switched system

• Published in: Journal of the Franklin Institute Vol. 360; no. 3; pp. 1835 - 1869
• Main Authors: Yuan, Jinlong, Wu, Changzhi, Liu, Chongyang, Teo, Kok Lay, Xie, Jun
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2023
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2022.12.027

•We propose a robust suboptimal feedback control problem designed based on the radial basis function.•This problem is approximated as a sequence of nonlinear programming subproblems by some techniques.•A hybrid algorithm is proposed to escape local optimal solutions. 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.