A Recursive System Identification With Non-Uniform Temporal Feedback Under Coprime Collaborative Sensing

A common assumption for real-time control systems design is that the sampling of input and output signals is uniform, periodic, and synchronous. In the information-rich world, however, data streams are often non-uniform and asynchronous. (In fact, real-time control system implementations often have to adjust the sampling rate to deal with irregular data.) While non-uniformly sampled data intuitively contain more temporal information for system analysis and controls, they violate the classical real-time control framework, and most existing methods for non-uniformly sampled systems are heuristic and specific. It remains not well understood how to systematically leverage non-uniform data streams for real-time dynamic systems. In particular, as the first critical step in real-time controls, classic system identification requires synchronous input and output data when building the model of a dynamical system. This paper contributes to a novel system identification that leverages the temporal advantage of non-uniform sampling but overcomes the obstacle imposed by non-uniform data collection for general input-output models. We first propose a coprime collaborative sensing scheme, which generates one set of data that appears non-uniform with respect to time while, in the meantime, having systematic underlying sampling patterns. Next, we implement a model reparameterization tailored for the selected sensing scheme based on polynomial transformation to construct an auxiliary model that can be directly identified with the available observations. Then, a recursive leastsquares-based algorithm is designed to identify the auxiliary model and to illustrate the feasibility of working with the mechanism of collaborative sampling and model reparameterization. Lastly, the parameters of the original fast system model are recovered by removing the highest common factors between the denominator and numerator polynomials.

Journal article