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

Abstract

A new geometric approach providing the minimum-energy issue for inverse model control-related perfect regulation of linear time-invariant multi-input/single-output plants described in the discrete-time state-space framework is proposed in the paper. Recent results have shown that the minimum-norm T -inverse does not guarantee the minimum-energy perfect control design, which has been confirmed by heuristic studies only. The new proposal, postulated throughout the manuscript, certifies the potential of nonunique σ -inverse regarding the minimum-energy behavior of inverse model control-based structures. After application of the proposed geometric approach dedicated to some class of state-space systems, we can precisely calculate the total energy of the multivariable perfect control runs. Thus, the analytical new methodology allows to obtain the minimum-energy inverse model control schemes, what constitutes the main accomplishment of the paper. Additionally, the aim of future analytical exploration covering the entire class of right-invertible state-space systems is clearly focused.

Keywords

• Geometric solution
• perfect control
• minimum-energy problem
• inverses of nonsquare matrices
• discrete-time state-space domain
• LTI MIMO