Model Reduction by Least Squares Moment Matching for Linear and Nonlinear Systems

The paper studies the model reduction problem using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation conditions imposed by moment matching are satisfied in a least squares sense. The paper revisits this idea using tools from output regulation theory to develop a nonlinear enhancement of the notion of least squares moment matching and a unifying model reduction framework both for linear and nonlinear systems. The proposed framework allows for the direct computation of models through optimization, the use of weights to modulate the quality of approximation, and the possibility of enforcing prescribed properties, such as stability and passivity, via additional constraints. Parameterized families of models achieving least squares moment matching are also determined and shown to admit natural geometric and system-theoretic interpretations. The theory is illustrated by numerical examples.