Performance guarantees and performance optimization of MRAC for non-minimum phase systems

Non-minimum phase systems pose a challenge in the design of MRAC. While some methods that can handle non-minimum phase systems are available in the literature, it is not always easy to guarantee tracking performance with these methods. This paper offers a partial solution to this problem. The method of generating an augmented plant by adding some dynamics in parallel to the original plant is used to make the adaptation scheme see a minimum phase system. The drawback of this method is that the error between original plant and original reference model does not asymptotically converge to zero, and even analysis of this error is not available in the literature. This paper offers a way to find an upper bound on the tracking error and design an alternative reference model to minimize the error. The application of the new reference model leads to improved tracking performance with respect to the original reference model. The alternative reference model is designed by iteratively solving linear matrix inequalities. Performance guarantees are given in terms of an £2-gain bound from the reference to the tracking error, and this £2-gain bound is minimized when the matrix inequalities are solved. An aerospace example is given to illustrate the effectiveness of our approach.