Adaptive Tracking Control of A Class of First-Order Systems With Binary-Valued Observations and Time-Varying Thresholds

This technical note studies the adaptive tracking control for a class of single parameter systems with binary-valued observations and time-varying thresholds. A projection algorithm is proposed for parameter identification, based on which an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectation of the binary-valued observations with respect to the estimates, it is shown that the identification algorithm is both almost surely and mean square convergent, the closed-loop system is stable, and the adaptive tracking control is asymptotically optimal. A numerical example is given to demonstrate the effectiveness of the algorithms and the main results obtained.