A Hybrid PID Design for Asymptotic Stabilization with Intermittent Measurements

In this paper, we propose a modeling and design technique for a proportional-integral-derivative (PID) controller in the presence of aperiodic intermittent sensor measurements. Using classical control design methods, PID controllers can be designed when measurements are available periodically, at discrete time instances, or continuously. Unfortunately, such design do not apply when measurements are available intermittently. Using the hybrid inclusions framework, we model the continuous-time plant to control, the mechanism triggering intermittent measurements, and a hybrid PID control law defining a hybrid closed-loop system. We provide sufficient conditions for uniform global asymptotic stability using Lyapunov set stability methods. These sufficient conditions are used for the design of the gains of the hybrid PID controller. Also, we propose relaxed sufficient conditions to provide a computationally tractable design method leveraging a polytopic embedding approach. The results are illustrated via numerical examples.