Disturbance attenuating adaptive controllers for parametric strict feedback nonlinear systems with output measurements

We present a systematic procedure for H infinity-optimal adaptive controlle rs for a class of single-input single-output parametric strict-feedback non linear systems that are in the output-feedback form. The uncertain nonlinea r system is minimum phase with a known relative degree and known sign of th e high-frequency gain. We use soft projection on the parameter estimates to keep them bounded in the absence of persistent excitations. The objective is to obtain disturbance attenuating output-feedback controllers which will track a smooth bounded trajectory and keep all closed-loop signals bounded in the presence of exogenous disturbances. Two recent papers (Pan and Basa r, 1996a; Marino and Tomei, 1950 addressed a similar problem with full stat e information, using two different approaches, and obtained asymptotically tracking and disturbance-attenuating adaptive controllers. Here, we extend these results to the output measurement case of a class of minimum phase no nlinear systems where the nonlinearities depend only on the measured output . It is shown that arbitrarily small disturbance attenuation levels can be obtained at the expense of increased control effort. The backstepping metho dology, cost-to-come function based H-infinity-filtering and singular pertu rbations analysis constitute the framework of our robust adaptive control d esign scheme.