Conditions and a computation method of the constrained regulation problem for a class of fractional-order nonlinear continuous-time systems

• Main Authors: Si Xindong, Yang Hongli, Ivanov Ivan G.
• Format: Article
• Language: English
• Published: Sciendo 2021-03-01
• Series: International Journal of Applied Mathematics and Computer Science
• Subjects: fractional-order nonlinear systems; constrained regulation; positively invariant set; linear programming
• Online Access: https://doi.org/10.34768/amcs-2021-0002

The constrained regulation problem (CRP) for fractional-order nonlinear continuous-time systems is investigated. New existence conditions of a linear feedback control law for a class of fractional-order nonlinear continuous-time systems under constraints are proposed. A computation method for solving the CRP for fractional-order nonlinear systems is also presented. Using the comparison principle and positively invariant set theory, conditions guaranteeing positive invariance of a polyhedron for fractional-order nonlinear systems are established. A linear feedback controller model and the corresponding algorithm of the CRP for fractional nonlinear systems are also proposed by using the obtained conditions. The presented model of the CRP is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Numerical examples illustrate the proposed method.