Adaptive bounded bilinear control of coupled first-order 1-D hyperbolic PDEs and infinite ODEs with unknown time-varying source term

In this paper, we investigate the problem of bounded adaptive bilinear control of a system of coupled first-order 1-D hyperbolic PDE and infinite-dimensional ODE, with an unknown time-varying source term. Only boundary measurements are available, and the manipulated variable is the transport velocity. Moreover, input constraints have to be satisfied. Using boundary injection and an energy-like principle, a bounded adaptive output feedback controller is designed in the Lyapunov approach. This controller ensures the ultimate boundedness of the tracking, the state, and the parameter estimation errors while it respects the input constraints. A direct application of this study is the one-loop solar collector parabolic trough, where the solar irradiance is the unknown time-varying parameter and the flow rate is the manipulated variable. The measurements are provided by two sensors placed at the tube's inlet and outlet. Simulation results are provided to illustrate the performance of the theoretical findings.