Dynamic Mode Decomposition for Control Systems with Input Delays

Dynamic mode decomposition with control (DMDc) has emerged as a powerful tool for data-driven system identification in recent years. Our work provides an extension to DMDc, namely the ability to identify systems with a delayed input. Specifically, we propose dynamic mode decomposition with input-delayed Control (DMDidc), which allows the identification of input-delayed linear time-invariant (LTI) systems given sufficient input-output data. We prove the method is able to identify delays that are a fraction of a discrete controllers sampling period and provide an extended predictive feedback control scheme that accommodates such delays. A numerical simulation illustrates the benefits of our method.