Reach-Avoid Analysis for Sampled-Data Systems with Measurement Uncertainties

Digital control has become increasingly prevalent in modern systems, making continuous-time plants controlled by discrete-time (digital) controllers ubiquitous and crucial across industries, including aerospace, automotive, and manufacturing. This paper focuses on investigating the reach-avoid problem in such systems, where the objective is to reach a goal set while avoiding unsafe states, especially in the presence of state measurement uncertainties. We propose an approach that builds upon the concept of exponential control guidance-barrier functions, originally used for synthesizing continuous-time feedback controllers. We introduce a sufficient condition that, if met by a given continuous-time feedback controller, ensures the safe guidance of the system into the goal set in its sampled-data implementation, despite state measurement uncertainties. The event of reaching the goal set is determined based on state measurements obtained at the sampling time instants. Numerical examples are provided to demonstrate the validity of our theoretical developments, showcasing successful implementation in solving the reach-avoid problem in sampled-data systems with state measurement uncertainties.