Abstract
We develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for nonlinear systems in parametric-strict-feedback form and subject to additional exogenous disturbance inputs. Our approach is performance based, where the objective is to find not only an adaptive controller, but also an appropriate cost functional, compatible with desired asymptotic tracking and disturbance attenuation specifications, with respect to which the adaptive controller is "worst-case optimal." Using the backstepping methodology, worst-case identification schemes, and singular perturbations analysis, we obtain closed-form expressions for the solutions of associated Hamilton-Jacobi-Isaacs equations or inequalities, thereby guaranteeing satisfaction of dissipation inequalities for the adaptive controllers.
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