An explicit optimal input design for first order systems identification

This paper focuses on the problem of closed loop online identification of the time constant in the single input single output (SISO) first order linear model. A new explicit approach for the simultaneous online optimal experiment design (OED) and model parameter identification is presented. Based on the observation theory and a model based predictive control (MPC) algorithm, this approach aims to solve an optimal control problem where input and output constraints may be specified. This constrained control objective aims to maximize the sensitivity of the model output with respect to the unknown model parameter (the time constant). The control law is derived explicitly offline and simple to be implemented: the input may be computed fast online while the unknown model time constant is estimated at the same time.