Measurement Unknown Delay Estimation in Cyber-Physical Systems: a PDE approach

Delays in distributed large-scale systems are sources of uncertainties and instabilities, making control of these systems challenging. The control issue becomes critical when the controller depends on measurements that are subjected to unknown delays. Cyber-Physical Systems (CPS) are subjected to delays due to both physical and cyber components delay. To improve the performance of these systems, delay estimation and mitigation is of the utmost importance. This paper considers an unknown delay in a distributed cyber-physical system due to the communication and sensor measurement delays. This paper aims to provide an observer-based algorithm to estimate the unknown delay and the states of the system despite the effects of delay. The proposed algorithm consists of a Partial Differential Equation (PDE) observer designed based on a transport PDE delay model. The stability analysis of the proposed method is developed using the Lyapunov methods. A numerical example and simulation results are provided to illustrate the effectiveness of the suggested method.