Computation of Limit Cycles for Uncertain Nonlinear Fractional-order Systems using Interval Constraint Propagation

The present paper proposes an algorithm to compute limit cycle points for an uncertain nonlinear fractional-order system with separable nonlinearities using interval constraint propagation. It is first shown that the problem of finding limit cycle points can be formulated as an interval constraint satisfaction problem and then solved using branch and prune algorithm. The algorithm guarantees that all the points on the limit cycle locus are computed to prescribed accuracy, i.e., the error in the computation of limit cycle point can never exceed the accuracy tolerance specified by the user. The algorithm also guarantees that all the limit cycle points in the given search domain are found. The other advantage of the method is that it does not need any kind of approximation of the fractional-order system. It must be noted that any errors resulting in the limit cycle locus due to approximate nature of describing function method cannot be avoided. The proposed algorithm is illustrated on two examples taken from the literature.