Some problems of modeling and parameter estimation in continous-time for control and communication

Abstract: Stochastic system identification is of great interest in the areas of control and communication. In stochastic system identification, a model of a dynamic system is determined based on given inputs and received outputs from the system, where stochastic uncertainties are also involved. The scope of the report is to consider continuous-time models used within control and communication and to estimate the model parameters from sampled data with high accuracy in a computational efficient way. Continuous-time models of systems controlled in a networked environment, stochastic closed-loop systems, and wireless channels are considered. The parameters of a transfer function based model for the process in a networked control system are first estimated by a covariance function based approach, relying upon the second order statistical properties of the output signal. Some other approaches for estimating the parameters of continuous-time models for processes in networked environments are also considered. Further, the parameters of continuous-time autoregressive exogenous models are estimated from closed-loop filtered data, where the controllers in the closed-loop are of proportional and proportional integral type, and where the closed-loop also contains a time-delay. Moreover, a stochastic differential equation is derived for Jakes's wireless channel model, describing the dynamics of a scattered electric field with the moving receiver incorporating a Doppler shift.