Abstract
The advanced analytical study in the field of fractional-order non-full rank inverse model control design is presented in the paper. Following the recent results in this matter it is certain, that the inverse model control-oriented perfect control law can be established for the non-full rank integer-order systems being under the discrete-time state-space reference with zero value. It is shown here, that the perfect control paradigm can be extended to cover the multivariable non-full rank plants governed by the more general Grünwald-Letnikov discrete-time state-space model. Indeed, the postulated approach significantly reduces both iterative and non-iterative computational effort, mainly derived from the approximation of the Moore-Penrose inverse of the non-full rank matrices to finally be inverted. A prevention provided by the new method excludes the detrimental matrix behavior in the form of singularity, often avoided due to the observed ill-conditioned sensitivity. Thus, the new defined robust fractional-order non-full rank instance of such control strategy, supported by the pole-free mechanism, gives rise to the introduction of the general unified non-full rank perfect control-originated theory. Numerical algorithms with simulation investigation clearly confirm the innovative peculiarities provided by the manuscript.
References
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© 2021 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 24–4–2021)
- Research Paper
- Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
- Tutorial paper
- The bouncing ball and the Grünwald-Letnikov definition of fractional derivative
- Research Paper
- Fractional diffusion-wave equations: Hidden regularity for weak solutions
- Censored stable subordinators and fractional derivatives
- Variational methods to the p-Laplacian type nonlinear fractional order impulsive differential equations with Sturm-Liouville boundary-value problem
- Multivariable fractional-order PID tuning by iterative non-smooth static-dynamic H∞ synthesis
- Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity
- The rate of convergence on fractional power dissipative operator on compact manifolds
- Fractional Langevin type equations for white noise distributions
- Local existence and non-existence for a fractional reaction–diffusion equation in Lebesgue spaces
- Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function
- The Crank-Nicolson type compact difference schemes for a loaded time-fractional Hallaire equation
- Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework
- Properties of the set of admissible “state control” pair for a class of fractional semilinear evolution control systems
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 24–4–2021)
- Research Paper
- Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
- Tutorial paper
- The bouncing ball and the Grünwald-Letnikov definition of fractional derivative
- Research Paper
- Fractional diffusion-wave equations: Hidden regularity for weak solutions
- Censored stable subordinators and fractional derivatives
- Variational methods to the p-Laplacian type nonlinear fractional order impulsive differential equations with Sturm-Liouville boundary-value problem
- Multivariable fractional-order PID tuning by iterative non-smooth static-dynamic H∞ synthesis
- Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity
- The rate of convergence on fractional power dissipative operator on compact manifolds
- Fractional Langevin type equations for white noise distributions
- Local existence and non-existence for a fractional reaction–diffusion equation in Lebesgue spaces
- Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function
- The Crank-Nicolson type compact difference schemes for a loaded time-fractional Hallaire equation
- Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework
- Properties of the set of admissible “state control” pair for a class of fractional semilinear evolution control systems