Quadratically constrained least squares identification and nonlinear system identification using Hammerstein/nonlinear feedback models.

摘要

Empirical or data-based modeling, generally referred to as system identification, plays an essential role in control systems engineering as well as many other branches of science and engineering. Models obtained from system identification, incorporate the “real-world” dynamics of the system in a direct manner through measured data, and thus reduce the dependence on analytical modeling assumptions.; Of all the empirical modeling techniques, least squares optimization is the most commonly used method. Although, this technique may introduce a bias in the identified model, it remains one of the most fundamental methods due to its simplicity. This dissertation generalizes the standard least squares technique, develops specific overparameterizations for obtaining parameter consistency, and develops a computationally tractable nonlinear identification method that utilizes least squares optimization. First, a generalization of least squares identification is considered. Standard least squares identification proceeds by fixing a system parameter, namely, the lead coefficient of the denominator polynomial of the system's transfer function. The present work introduces a quadratically constrained least squares (QCLS) problem, which uses the same least squares criterion, but uses a more general quadratic constraint on the parameters of the system. This generalization leads to a method that is capable of reducing the bias in the parameter estimates.; Furthermore, μ-Markov parameterizations are developed. These transfer function parameterizations are nonminimal, and have sparse denominator structure and Markov parameters as numerator coefficients. When using least squares identification, these parameterizations lead to consistent estimates of the Markov parameters of the system, and is an extension of the consistency result for finite impulse response (FIR) models.; Finally, nonlinear identification using a Hammerstein/nonlinear feedback model structure is considered. Nonlinear static maps in this model are parameterized in terms of a special point-slope parameterization. The resulting nonlinear least squares cost is then bounded by a sub-optimal cost that leads to a computationally tractable optimization problem that involves the linear least squares solution, and a singular value decomposition. This approach allows the linear dynamic and static nonlinear blocks in the model to be simultaneously identified.