Adaptive Controller Design and Disturbance Attenuation for Sequentially Interconnected SISO Linear Systems under Noisy Output Measurements

In this paper, we present robust adaptive controller design for a special class of linear system, which is composed of two SISO linear subsystems, S₁ and S₂, under noisy output measurements and sequentially interconnected with additional feedback. We formulate the robust adaptive control problem as a nonlinear H^infin-optimal control problem under imperfect state measurements, and then solve it using game-theoretic approach. The cost-to-come function analysis is carried out to derive the estimators and identifiers of S₁ and S₂, and integrator backstepping methodology is applied recursively to obtain the control law, which guarantees the boundedness of closed-loop signals, and achieves asymptotic tracking under some assumptions. Moreover, the closed-loop system admits a guaranteed disturbance attenuation level with respect to the exogenous disturbance inputs, where the ultimate attenuation lower bound for the achievable performance level is equal to the noise intensity in the measurement channel of S₁.