A norm-based approach to the minimum-energy multivariable perfect control design

A New Non-Full Rank Algorithm for the IMC-Derived d-Step MIMO Structures in the Pole-Free State Space

“…Proof. Immediately, after considering the entire investigations, in particular the expressions (26) and (27).…”

“…The inverse model control (IMC) has widely been investigated over the past decades due to its application in many scientific and engineering fields [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25]. The unique behaviors of the discussed technique such as robustness, maximumspeed or minimum-energy properties make it attractive in many practical implementations [1], [9], [12], [23], [26], [27], [28]. The widely known IMC-based perfect control law, which constitutes the deterministic instance of the minimum variance control (MVC), has not only been associated with the full-rank square MIMO systems, including SISO ones [1].…”

“…systems with greater number of input than output variables, can also be subjected by such noise-free control law [3]. In such a case, through the application of nonunique parameter/polynomial right inverses, we can redefine the special properties of the closed-loop state-feedback plant [1], [9], [26]. The IMC methodology, both in the input-output and the state-space domains, has necessitated the system to be under full-rank regulation, hence the non-full rank instance has not been considered, in general [29], [30].…”

A New Geometric-Oriented Minimum-Energy Perfect Control Design in the IMC-Based State-Space Domain

“…However, while the heuristic approach seems to be rather not to complex, the analytical approach is more difficult to solve. It should be emphasized, that the broadly known Moore-Penrose minimum-norm T -inverse does not provide the minimum-energy of the perfect control input runs, for instance see [4]. Notwithstanding, the formal analytical proof has not been given, up to now.…”