Adaptive controller design and disturbance attenuation for a general class of sequentially interconnected SISO linear systems with noisy output measurements and partly measured disturbances

We study the adaptive controller design for a special class of MIMO system, which is composed of arbitrary but a finite number of SISO linear subsystems under noisy output measurements and partly measured disturbances sequentially interconnected with additional feedbacks. We first formulate the robust adaptive control problem as a nonlinear H^∞ control problem under imperfect state measurement, derive the estimators and identifiers of subsystems using cost-to-come analysis, and then apply integrator backstepping methodology to obtain the control law. The obtained adaptive controller guarantees the boundedness of closed-loop signals with bounded exogenous disturbances, and achieves asymptotic tracking if exogenous disturbances are bounded and of finite energy. Moreover, the closed-loop system admits a guaranteed disturbance attenuation level with respect to the unmeasured 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, and arbitrary positive disturbance attenuation level with respect to the measured disturbance inputs. In addition, the proposed controller achieves zero or arbitrary small disturbance attenuation level with respect to the measured disturbances.