Adaptive controller design and disturbance attenuation for sequentially interconnected SISO linear systems under noisy output measurements with partly measured disturbances

In this paper, we present robust adaptive controller design for a special class of linear system, which is composed of two sequentially interconnected SISO linear subsystems, S-1 and S-2, under noisy output measurements and with partly measured disturbances. Based on worst-case analysis approach, we formulate the robust adaptive control problem as a nonlinear H-infinity-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 S-1 and S-2, and integrator backstepping methodology is applied recursively to obtain the control law. The design paradigm is the same as [1] with the only difference being the treatment of the measured disturbance. The same result of [1] is achieved. In addition, the designed controller achieves the disturbance attenuation level zero or arbitrary positive disturbance attenuation level with respect to the measured disturbances. Moreover, for the measured disturbances that the controller can achieve disturbance attenuation level zero with respect to, the asymptotic tracking objective is achieved even if they are only uniformly bounded without being of finite energy.