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

Abstract

We solve an adaptive control problem for n + 1 hyperbolic systems using collocated sensing and control, extending recent results for adaptive control of 2×2 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 L2-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 L2-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.