State-delay estimation for nonlinear systems using inexact output data

This paper considers the problem of using inexact output data to estimate the values of unknown state-delays in a general nonlinear time-delay system. We formulate the problem as a nonlinear optimization problem in which the state-delays are decision parameters and the cost function penalizes a weighted sum of the mean and variance of the least-squares error between actual and predicted system output. Our main result shows that the gradient of the least-squares cost function can be computed by solving an auxiliary time-advance system backward in time. On this basis, the state-delay estimation problem can be solved efficiently using standard gradient-based optimization algorithms such as sequential quadratic programming. We conclude the paper by testing this approach on a dynamic model of a continuously-stirred tank reactor with recycle loop.