Counterexamples to the Maximum Speed/Energy IMC Theory – A New Geometric Consideration Incorporates the Multivariable Perfect Control Defined in the LTI Discrete-Time State-Space Framework

Hunek, Wojciech P.; Feliks, Tomasz

doi:10.1080/01969722.2020.1758465

Cited by 1 publication

(3 citation statements)

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“…Indeed, the IMC continuous-time plants have effectively been analyzed in the context of the minimum energy of control input runs subjected to an assumed finite time horizon [3], [26], [27]. On the other hand, the inverse modelbased maximum-speed/maximum-accuracy control design for discrete-time systems has also been studied, and the resulted peculiarities have consequently been revealed to the control society [11], [25], [36]. Nevertheless, the received analytical outcomes in this matter have only been referred to the relatively simple objects involving a single output variable [4].…”

Section: Progress In the Minimum-energy-based Imc Theorymentioning

confidence: 99%

“…Notwithstanding, following the heuristic studies in this matter, it should be stated that the mentioned right Tinverse does not guarantee the minimum-energy IMC-based MV/PCD [11], [36]. Although the heuristic approaches could be contested in some way, the novel authors' analytical investigation undeniably confirms such an intriguing statement [4].…”

mentioning

confidence: 97%

“…speed and accuracy phenomena [6], [7], [8], [9], [10], [11]. The family of IMC-related algorithms constitutes the wellknown and broadly explored stochastic minimum variance (MV) and deterministic perfect control (PC) formulas strictly dedicated to the plants defined in both the transfer function [12], [13], [14], and state-space frameworks [4], [15], [16].…”

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confidence: 99%

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Application of Generalized Inverses in the Minimum-Energy Perfect Control Theory

Feliks

Hunek

Stanimirović

2023

IEEE Trans. Syst. Man Cybern, Syst.

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Application of generalized inverses in solving the inverse model control (IMC)-oriented minimum-energy perfect control design (PCD) problem for linear time-invariant multi-input/multi-output systems governed by the discrete-time d-state-space structure is presented in this article. For this reason, an appropriate class of polynomial generalized inverses is investigated. Moreover, it can be stated that the nonunique right σ -inverse, based on properly selected so-called degrees of freedom (DOFs), outperforms the well-known unique Moore-Penrose (MP) minimum-norm right T-inverse in terms of the energy consumption of perfect control (PC) input signals. However, the analytical confirmation of such an intriguing statement has only been established for the special class of the single-delayed plants with a zero reference value. Moreover, because of the complexity of the IMC, the objects with a time delay d > 1 having a nonzero setpoint have never been analytically explored in regard to the PC energy context until now. Thus, the newly introduced analytical methods defined in this article allow us to designate the proper forms of σ -inverse-related DOFs that guarantee the minimum-energy PCD for the entire set of LTI multivariable nonsquare systems with the delay d ≥ 1. Moreover, the new original results, supported by numerical examples, strongly contest the well-established control and systems theory canons related to the optimal minimum-energy-originated peculiarity of the MP pseudoinverse.

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