Adaptive output feedback control of nonlinear time-varying systems

Single-input single-output nonlinear systems with unknown smooth, uniformly bounded, arbitrarily time-varying parameters and output dependent nonlinearities are considered: they include as a special case linear time-varying systems. The output, which is the only measured variable, is required to track a given smooth bounded reference trajectory. The system is supposed to be minimum-phase and to have known and constant relative degree, known sign of the high frequency gain and known upper bound on the system order. An output feedback control algorithm is designed which guarantees: i) boundedness of all closed loop signals; ii) arbitrarily improved transient performance of the tracking error, with respect to parameter estimation errors and parameter time derivatives; iii) asymptotically vanishing tracking errors when the parameters belong to a compact set pre-determined by the controller and their time derivatives are bounded L₁ signals.