Robust optimal control problem with multiple characteristic time points in the objective for a batch nonlinear time-varying process using parallel global optimization

In this paper, we consider a nonlinear time-varying dynamical (NTVD) system with uncertain system parameters assigned to their nominal values in batch culture of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumoniae. Some important properties of the NTVD system are discussed. Our goal is to choose a time-varying function for the NTVD system. Thus, an optimal control problem (OCP) governed by the NTVD system and subject to continuous state inequality constraints arising from engineering specifications is proposed, where the time-varying function is the control function to be chosen such that system cost (the relative error between experimental data and the simulated output of the system) and system robustness (robustness of the system with respect to uncertain system parameters) is optimized. Based on the actual fermentation process, the time-varying function is specified by a four-piecewise linear function with unknown kinetic parameters and switching instants. The resulting OCP is approximated as a sequence of nonlinear mathematical programming subproblems by the time-scaling transformation, the constraint transcription and the locally smoothing approximation techniques. A parallel global optimization algorithm, based on a novel combination of limited information particle swarm optimization and local search strategy, is then developed to solve these subproblems. Numerical results show the effectiveness and applicability of our proposed algorithm.