Safety constrained digital control of nonlinear systems with state delays

In this paper, the digital event-based stabilization problem under safety constraints is studied for nonlinear systems with state delays. In particular, a methodology for the design of quantized sampled-data event-triggered safe stabilizers is provided for nonlinear systems affected by state delays. The proposed design procedure relies on the notion of Safe Steepest Descent Feedback (SSDF) which is based on the combination of Steepest Descent Feedbacks and Barrier functions. The stabilization in the sample-and-hold sense theory is used as a tool to show the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the digital implementation of SSDFs, updated through a proposed event-triggered mechanism, ensures the semi-global practical safe stability property of the related closed-loop system with arbitrarily small final target ball of the origin. A first order spline approximation is used to cope with the possible unavailability in the buffer of required past values of the state measurements. In the theory here developed, time-varying sampling periods and the non-uniform quantization of both input/output channels are allowed. The proposed theoretical results are validated through an application concerning the plasma glucose regulation problem in Type-2 diabetic patients via artificial pancreas.