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

Adaptive control of feedforward nonlinear systems with uncertain time‐varying parameters and an unknown time‐varying delay in the input

“…Note that the predictor control methods of Reference 1,4,6 are not directly applicable to our considered system () because there is no information on the upper bound and time‐varying rate of the delay. The unknown input‐delay actually exists due to the processing and transport of information, computation, physical limitations of sensors, etc 1,2,22 When c is known in Assumption 3, the condition () reduces to the same linear growth condition as in References 14,15.…”

“…Our problem is to regulate the considered system by using memoryless controller which avoids issues with reduction or predictor type controllers in References 1,2,4‐6. Although in Reference 22, the authors propose a memoryless controller to regulate nonlinear systems with an unknown time‐varying delay in the input, their result cannot treat nonlinear systems with uncertain time‐varying parameters. Specifically, our considered problems have the following generalized features: (i) the delay is time‐varying and unknown where there is no information on the upper bound of delay over; 1,4,6 (ii) there exists uncertain time‐varying parameters associated with main diagonal states and input where these uncertain parameters are not necessarily small over 3,12,14,20 ; (iii) there is no restriction on the time‐varying rates of delay and parameters over; 14,17‐21 (iv) nonlinearities are extended by containing unknown growth rate over 5‐7,14 .…”

“…Specifically, our considered problems have the following generalized features: (i) the delay is time‐varying and unknown where there is no information on the upper bound of delay over; 1,4,6 (ii) there exists uncertain time‐varying parameters associated with main diagonal states and input where these uncertain parameters are not necessarily small over 3,12,14,20 ; (iii) there is no restriction on the time‐varying rates of delay and parameters over; 14,17‐21 (iv) nonlinearities are extended by containing unknown growth rate over 5‐7,14 . Overall, all the aforementioned existing results 1‐7,12,14,17‐22 are not applicable to our considered system.…”

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

“…[7][8][9][10][11][12][13] In many cases, the actuator of the control system is subject to not only saturation but also time delay, which bring a tremendous challenge to the analysis and design of control systems, and a few results are available in the literature. [14][15][16][17] Feedforward nonlinear systems described by equations with an upper triangular structure are an important kind of nonlinear systems 18,19 because many practical models can be described in that form, such as the planar vertical takeoff and landing aircraft, 20 inertia wheel pendulum, 21 and low-bias active magnetic bearing. 22 The study on the global stabilization of feedforward systems can be traced to the pioneer work of Teel,23 in which a nonlinear controller was established for a chain of integrators by using bounded feedback.…”

Output feedback regulation of upper triangular nonlinear systems with uncertain time‐varying delays in states and input

“…In practice, time‐delays exist and can be obstacles for system regulation or stabilization, and many related studies have been performed before . Time‐delay problems are significant because time‐delays often cause the system instability.…”