Multi-objective active control policy design for commensurate and incommensurate fractional order chaotic financial systems

In this study, an active control policy design is proposed for a fractional order financial system, which considers multiple conflicting objectives. An active control template is used as a nonlinear state feedback mechanism and the controller gains are selected within a multi-objective optimization (MOO) framework to satisfy the conditions of asymptotic stability, which are derived analytically. The MOO obtains a set of solutions on the Pareto optimal front for the multiple conflicting objectives that are considered. We demonstrate that there is a trade-off between the multiple design objectives where better performance for one objective can only be obtained at the cost of degrading the performance for the other objectives. The multi-objective controller design was compared using three different MOO techniques, i.e., non-dominated sorting genetic algorithm-II, epsilon variable multi-objective genetic algorithm, and multi-objective evolutionary algorithm with decomposition. The robustness of the same control policy designed with the nominal system settings was also investigated with gradual decrease in the commensurate and incommensurate fractional orders of the financial system.