Non-predictor controller for feedforward and non-feedforward nonlinear systems with an unknown time-varying delay in the input

We consider a global regulation problem of a class of nonlinear systems that have uncertain high-order feedforward and non-feedforward nonlinear terms. There also exists an unknown time-varying delay in the main control input. While many existing results have employed predictor methods to deal with the input delay, we propose a non-predictor controller with a dynamic gain such that it does not require any memories of past input values nor any information on the time-varying delay. Moreover, we introduce new high-order conditions on feedforward and non-feedforward terms along with unknown time-varying input delay. A class of extended nonlinear systems which are applicable by our controller are identified. Via numerical and application examples, we demonstrate that the nonlinear time-delay systems which cannot be dealt by the existing methods are successfully regulated by our non-predictor state feedback controller.