IEEE Transactions on Automatic Control, Vol.65, No.4, 1484-1498, 2020
Output Feedback Energy Control of the Sine-Gordon PDE Model Using Collocated Spatially Sampled Sensing and Actuation
The present investigation focuses on the output energy control of the nonlinear sine-Gordon model in a practical situation where only spatially sampled sensing and actuation are available. The speed-gradient method that has corroborated its utility for the sine-Gordon model, controlled through the manipulable parameters of the external field and boundary actuation, is now generalized to the spatially sampled sensing and actuation, aiming to pump/dissipate the energy of the model to a desired level. Luenberger-type observers are additionally developed in the present nonlinear PDE setting to be involved into the output feedback synthesis over collocated state (position and/or velocity) measurements. Capabilities of the proposed synthesis are illustrated in numerical simulations.
Keywords:Sensors;Actuators;Observers;Boundary conditions;Output feedback;Velocity measurement;Oscillators;Energy control;sine-Gordon equation;speed gradient