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

Abstract

We present robust adaptive controller design for SISO linear systems with noisy output measurements and partly measured disturbances. Using the worst-case analysis approach, we formulate the robust adaptive control problem as a nonlinear H/sup /spl infin//-optimal control problem under imperfect state measurements, and solve it using game theory. The design paradigm is the same as that in (Z. Pan et al., July 2000) with the only difference being the treatment of the measured disturbances. The same results as those in (Z. Pan et al., July 200) are achieved. In addition, when the relative degrees from the measured disturbances to the output are no less than that from the control input, the controllers designed achieve the zero disturbance attenuation level with respect to the measured disturbance inputs. The asymptotic tracking objective is achieved even if the measured disturbance is only uniformly bounded, without requiring it to be of finite energy. This strong robustness property is then illustrated by a numerical example.