Adaptive output regulator for wave PDEs with unknown harmonic disturbance Abstract   This paper focuses on developing boundary controller for a wave PDE with two disturbances;     (  i  )     spatially varying and timeinvariant indomain disturbance,     (  i  i  )     timevarying sinusoidal boundary disturbance. We consider the case that the sensor is collocated with the actuator and harmonic disturbance is anticollocated with the sensoractuator. We aim to regulate the rate of change of the opposite boundary, relative to the actuator, around a given constant reference. Towards that aim, we reformulate the opposite boundary equation as a linear system with known parameters, the sinusoidal disturbances and simultaneous inputoutput delays. In this way, the control input and sensor become collocated with the disturbance. Then, we parametrize the disturbance and represent the delays as a transport PDE. We develop an observerbased adaptive boundary controller for the ODExe2x80x93PDE cascade system. We prove that all signals are bounded and the rate of change of the opposite boundary tracks a given constant reference. The performance of the controller is demonstrated in a numerical simulation.

Adaptive boundary observer design for linear hyperbolic systems; Application to estimation in heat exchangers Abstract   In this work, we consider the estimation of temperature along the pipes of concentric heat exchanger tubes in which CO2 is the working fluid. The transport phenomenon is modeled using (2x2) linear hyperbolic partial differential equations, with one rightward equation for the hot flow and one leftward equation for the cold flow. Both flows exchange energy through the wall interface, which physically induces a coupling between the two dynamics. Our objective is to estimate the temperature distribution along the flows from measurements at the tubes boundaries only. In this framework, we propose an adaptive boundary observer that can estimate not only the full state of the system, but also unknown indomain parameters. The design is based on transforming the error system via a finitedimensional backsteppinglike transformation into a desired filterbased system, for which standard backstepping observer techniques and adaptation laws can be used. The theoretical results are evaluated against the temperature measurements taken from a CO2 refrigeration apparatus built at CERN, Switzerland.