Abstract: Many modern control applications, including teleoperation and control
over networks, create challenges to applying nonlinear controllers
in the presence of long delays in the actuation or sensing path. I will
present techniques for compensating such delays, with an emphasis on
delays that are time-varying and state-dependent. In the presence of
state-dependent delays, the challenge is not only that the overall
state of the system (plant plus actuator dynamics) is
infinite-dimensional and the delay is time-varying, but also that the
horizon for compensating the delay is not known a priori and the delay
rate becomes dependent on the input. I will present solutions to the
problem of stabilization in the presence of state-dependent delays for
general linear and nonlinear systems. For constant delays, I 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.
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