An Optimization Approach to State-Delay Identification

We consider a nonlinear delay-differential system with unknown state-delays. Our goal is to identify these state-delays using experimental data. To this end, we formulate a dynamic optimization problem in which the state-delays are decision variables and the cost function measures the discrepancy between predicted and observed system output. We then show that the gradient of this problem´s cost function can be computed by solving an auxiliary delay-differential system. By exploiting this result, the state-delay identification problem can be solved efficiently using a gradient-based optimization method.