An Algorithm for Iterative Identification and Control Design using an Improved Q-Markov Cover

Abstract

If a certain realizability condition is satisfied, the Q-Markov COVER identification algorithm provides a state-space realization which matches the first Q Markov parameters and the first Q covariance parameters of the identified plant. However, due to the presence of nonlinearities, often this realizability test fails and the measured Markov and covariance parameters cannot be realized by a linear time-invariant model. In this note, alternating projection techniques are used to compute the closest set of covariance parameters such that the realizability constraints are satisfied. In addition, fixed-order constraints and output covariance constraints can be enforced for the identified realization using the above techniques. This algorithm is used in an iterative closed-loop identification and control redesign scheme.