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

摘要

We present a systematic procedure for designing H/sup /spl infin//-optimal adaptive controllers for a class of single-input single-output parametric strict-feedback nonlinear systems that are in the output-feedback form. The uncertain nonlinear system is minimum phase with known sign of the high-frequency gain. We use soft projection on the parameter estimates to keep them bounded in the absence of persistent excitations. The control objective is to achieve tracking of a smooth bounded reference trajectory, and at the same time keep all closed-loop signals bounded. Pan and Basar (1996) and Marino and Tomei (1995) addressed a similar problem with full state information, using two different approaches. Here, we extend these results to the output measurement case for a class of minimum phase nonlinear 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. We investigate two different measurement schemes, one involving the derivative of the system output. The backstepping methodology, cost-to-come function based H/sup /spl infin//-filtering and singular perturbations analysis constitute the framework of our robust adaptive control design scheme.