Adaptive controller design and disturbance attenuation for SISO linear systems with noisy output measurements

We address the worst-case adaptive controller design problem for uncertain single-input single-output linear systems with noisy output measurements, under the assumption that the (parametrically) unknown system is minimum phase with a known relative degree and unknown high-frequency gain of known sign. We first formulate this adaptive control problem as a nonlinear H^∞ control problem with imperfect state measurements, which then directly addresses transient performance and robustness of adaptive control systems. Then, by utilizing cost-to-come function analysis and integrator backstepping methodology, we derive explicit expressions for the worst-case adaptive controllers. Using a soft projection technique, we guarantee the bounded-input bounded-output property of the closed-loop system with respect to exogenous disturbance inputs without any assumption of persistency of excitation of the reference signal.