Prescribed-time predictor control of LTI systems with distributed input delay

Salim Zekraoui, Nicolas Espitia, Wilfrid Perruquetti
2021 2021 60th IEEE Conference on Decision and Control (CDC)  
This paper deals with prescribed-time stabilization of controllable linear systems with distributed input delay. We model the input delay as a transport PDE and reformulate the original problem as a cascade PDE-ODE system while accounting for the infinite dimensionality of the actuator. We build on reduction-based and backstepping-forwarding transformations to convert the system into a target system having the prescribed-time stability property. Then, we prove the bounded invertibility of the
more » ... ansformations and hence we show that the prescribed-time stability property is preserved into the original problem. To better illustrate the ideas of this approach, we focus first on the scalar case. Then, we give a sketch of the main lines for the general case. To this end, we choose the ODE dynamics of the target system to be a Linear Time-Varying system so that we can rely on recent developments which include a polynomial-based Vandermonde matrix and the generalized Laguerre polynomials that allow a compact formulation for the stability analysis. A simulation example is presented to illustrate the obtained results.
doi:10.1109/cdc45484.2021.9683034 fatcat:kqfvpzoltfcifcu25uhqe3ouyy