Model-based experimental design for nonlinear dynamical systems with unknown state delay and continuous state inequalities

Abstract

This paper studied the model-based design of experiment (MBDoE) for nonlinear dynamical systems with unknown state delay and continuous state inequalities (SDCSI). The design problem is formulated as a time-delay optimal control problem of a dynamic system governed by augmented sensitivity-state equations (ASSE). Consider the co-existence of control delay and multiple state delays in the ASSE, each continuous state inequality constraint is approximated by an integral constraint using a constraint-handling technique based on local smoothing approximation and constraint transcription, which guaranteed the satisfaction of state inequality constraints during the experiment. In addition, an efficient numerical procedure is derived to determine the gradients of the objective function and constraints, which involved integrating an auxiliary impulsive time-delay system backward in time. The procedure is combined with standard gradient-based optimization methods to solve the MBDoE-SDCSI problem. The performance of the proposed scheme is illustrated through the experimental design of a fed-batch biomass fermentation process.