Adaptive set-point regulation of linear n+1 hyperbolic systems with uncertain affine boundary condition using collocated sensing and control

摘要

We solve an adaptive control problem for n + 1 hyperbolic systems using collocated sensing and control, extending recent results for adaptive control of 2 x 2 systems and systems with non-collocated sensing and control. The boundary condition has an affine form with both unknown reflective and additive parameters and can be used to model well-reservoir interactions in oil and gas drilling where properties of the reservoir are unknown. Boundedness of the system states in the L-2-norm, and convergence to a steady state profile satisfying a control objective relevant to the drilling application, are proved. The state estimation error is shown to converge to zero in the L-2-norm and one of the boundary parameter estimates (modelling the reservoir pressure in the drilling application) is shown to converge to the true parameter value. The design is illustrated in a simulation example. (C) 2020 The Author(s). Published by Elsevier B.V.