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.
Highlights
The perfect control strategy, i.e. the deterministic case of the minimum variance control algorithm, is an attractive method due to its valuable properties [1]–[7]
In the case of examination of nonsquare MIMO systems with different number of input and output signals, we can effectively impact the robustness of the IMC-related perfect control schemes
PROBLEMS The original observation covering the minimum-energy perfect control design problem is proposed in this paper
Summary
The perfect control strategy, i.e. the deterministic case of the minimum variance control algorithm, is an attractive method due to its valuable properties [1]–[7]. In the case of examination of nonsquare MIMO systems with different number of input and output signals, we can effectively impact the robustness of the IMC-related perfect control schemes. It can only be done for rightinvertible plants described by both input-output and statespace LTI multivariable frameworks [26]–[28]. 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]. The final conclusions and open problems are indicated
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