Optimal Control with Low Sensitivity to Sampling Period Uncertainty

In this research, the optimal control design of a sampled-data system with sampling period uncertainty is considered. Digital discrete-time systems use analog-to-digital converters to convert the analog sensor signals to a digital signal. These converters use a sample and hold process for conversion with a prespecified sampling period. Although it is set in advance, the sampling period may be subject to small variations during the operation of the system. These small variations can negatively impact the system performance. To reduce the impact of potential uncertainty in the sampling period, a sensitivity function is defined to represent its effect on the system performance. A quadratic performance index is considered and minimized for optimal control design. Such a performance index is augmented to include the sensitivity function. Minimization of the augmented performance index ensures reduction of performance sensitivity.