Conditions and a computation method of the constrained regulation problem for a class of fractional-order nonlinear continuous-time systems
The authors study stability conditions and methods of controller synthesis to ensure the stability performance of the resulting system under some special state-and-input constraints. The authors call this problem the constraint regulation problem (CRP). A control law is a solution to the CRP for the system if and only if the closed-loop system is asymptotically stable at the origin, while the corresponding trajectory does not violate the constraints. In the paper CRP for fractional-order nonlinear continuous-time systems is investigated. The system is assumed to be affine in control. The linear part of the system is employed for designing a linear state feedback controller that provides asymptotic stability of the closed-loop system. First, three theorems with conditions guaranteeing positive invariance of some polyhedral sets for the systems are established, using the comparison principle and positively invariant set theory. Then, the authors propose a controller model for the CRP and the corresponding algorithm, by using the obtained invariance conditions. The presented model is formulated as a linear programming problem, which can be easily implemented from a computational point of view. At last, numerical examples illustrate the proposed method.
scientific article; zbMATH DE number 7373806
scientific article