Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems
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Xindong Si
Abstract
This paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.
Acknowledgment
The authors wish to thank the referees for their helpful and valuable comments which improve the quality of this paper.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Dynamic behavior of a stochastic SIRS model with two viruses
- Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems
- Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system
- Positive periodic solution for inertial neural networks with time-varying delays
- Stability analysis of almost periodic solutions for discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays
- Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method
- A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space
- Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps
- Stress wave propagation in different number of fissured rock mass based on nonlinear analysis
- Analytical predictor–corrector entry guidance for hypersonic gliding vehicles
- Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space
- Anthropogenic climate change on a non-linear arctic sea-ice model of fractional Duffing oscillator
- Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation
- Invariant solutions of fractional-order spatio-temporal partial differential equations
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Dynamic behavior of a stochastic SIRS model with two viruses
- Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems
- Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system
- Positive periodic solution for inertial neural networks with time-varying delays
- Stability analysis of almost periodic solutions for discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays
- Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method
- A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space
- Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps
- Stress wave propagation in different number of fissured rock mass based on nonlinear analysis
- Analytical predictor–corrector entry guidance for hypersonic gliding vehicles
- Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space
- Anthropogenic climate change on a non-linear arctic sea-ice model of fractional Duffing oscillator
- Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation
- Invariant solutions of fractional-order spatio-temporal partial differential equations
