Contribution of the generalized nonunique inverses to the minimum-energy control theory: The inverse model control investigation

The innovative analytical approach to the minimum-energy design problem of the inverse model control (IMC) state-space structures is presented in this work. Following the recent papers, it should be concluded that the optimal behavior of the IMC strategy cannot longer be associated with the application of the well-known Moore–Penrose minimum-norm inverse. However, the minimum-energy IMC-oriented scheme has only be obtained through heuristic methods. Nevertheless, in the recent authors’ work, it has been proven for the first time that such an issue can be considered in an analytical manner. Yet, the obtained results have only been valid for the second-order state-space systems. Therefore, the motivation instance proposed in the manuscript, confirming the possibility of extending such paradigm to higher-order plants, will certainly contribute to the introduction of the new unified minimum-energy IMC theory canon. Since the nonunique σ and H inverses can successfully be employed in the robustification of the discussed control strategy, they can also be helpful in the case of our essential considerations. Thus, from now on the yet unexplored research area can now be investigated in the analytical manner, what has never been seen before in the modern IMC-originated control theory and practice. The predefined methodology clearly fills the gap in the analytical control design procedures and opens a new chapter in the knowledge related to the well-known and broadly accepted multivariable control canons.

An Algebraic Approach to Identifiability

This paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on distinguishability and observability. Employing techniques from algebraic geometry such as polynomial ideals and Gröbner bases, local as well as global results are derived. The methods are illustrated on some example systems.