Adaptive Control of a Class of Time-Delay Systems

The control of physical systems in the presence of time-delays becomes particularly challenging when parametric uncertainties are present. To cope with these ubiquitous uncertainties, we propose an adaptive controller in this paper that can accommodate both a time-delay and parametric uncertainties. The controller includes a) a control architecture that is based on the plant relative degree rather than the plant order, b) an integral implementation of the well known Posicast Controller so as to accommodate unstable plants, c) high-order tuners for parameter adaptation, and d) a Lyapunov-Krasvoskii functional that allows adaptive stabilization. The controller is shown to be semi-global in the time-delay τ and to result in asymptotic tracking. The implications of the adaptive controller are explored in the context of combustion control through simulation studies. Robustness properties of the controller are briefly discussed.