Direct time injection in the loop: A new adaptive control point of view

In this paper, we show that adaptive control can be traded off against time-varying static state feedback (TVSSF) for a certain class of uncertain nonlinear systems. More precisely, we propose a systematic design procedure leading to TVSSF guaranteeing asymptotic (exponential) stability. Our approach, coined Direct time injection in the loop (DTIL), allows to remove the need for the integral action which is known to be instrumental in classical adaptive control design. The time-varying functions involved in the control law, allow an explicit selection of the convergence rates. Hence, exponential stability can be achieved without any requirement such as the persistency of excitation (PE). Interestingly, under certain conditions, the unknown parameters can be identified through a static function of the states and time.