Adaptive Control of Hyperbolic PDEs Coupled With a Disturbed and Highly Uncertain ODE

In this article, we address adaptive output-feedback boundary control of coupled hyperbolic partial differential equations (PDEs) with spatially varying coefficients and on a time-varying domain, whose uncontrolled boundary is coupled with a disturbed ordinary differential equation (ODE), where multiple parameters in the state matrix and the amplitudes of the harmonic disturbance are unknown. The asymptotic convergence to zero of the ODE state and the boundedness of the PDE states are ensured. This article is motivated by lateral vibration suppression of a mining cable elevator, where the interaction dynamics between the cage and the flexible guide is approximated as a viscoelastic system, including spring and damping, with unknown stiffness and damping coefficients. The performance of the proposed controller is tested in the application of the mining cable elevator by numerical simulation.