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

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 subop-timal 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 inequal-ity 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. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a robust suboptimal feedback control problem is investigated for a nonlinear time-delayed switched system in a 1,3-propanediol microbial fed-batch process. The feedback control strategy based on radial basis function is designed to balance system performance and sensitivity. The problem is transformed into one subject only to box constraints using an exact penalty method and a novel time scaling transformation approach, and solved by a hybrid optimization algorithm. Numerical results demonstrate the effectiveness of the developed algorithm.