State-Dependent Delays and Nonlinear Control Over Networks

Control over networks creates a need for feedback strategies that compensate significant delays in actuation and sensing. In the presence of state-dependent delays, the challenge is not only that the state is infinite-dimensional and the delay is timevarying, but also that the horizon for compensating the delay is not known a priori and the delay rate becomes dependent on the input. The speaker will present solutions to the problem of stabilization in the presence of state-dependent delays for general linear and nonlinear systems. For constant delays, the presenter will introduce sampled-data nonlinear controllers that compensate delays of arbitrary length, under arbitrarily sparse sampling. Illustration will be provided through several examples, including stabilization of the nonholonomic unicycle.