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In this paper, an active control policy design for a fractional order (FO)financial system is attempted, considering multiple conflicting objectives. Anactive control template as a nonlinear state feedback mechanism is developedand the controller gains are chosen within a multi-objective optimization (MOO)framework to satisfy the conditions of asymptotic stability, derivedanalytically. The MOO gives a set of solutions on the Pareto optimal front forthe multiple conflicting objectives that are considered. It is shown that thereis a trade-off between the multiple design objectives and a better performancein one objective can only be obtained at the cost of performance deteriorationin the other objectives. The multi-objective controller design has beencompared using three different MOO techniques viz. Non Dominated SortingGenetic Algorithm-II (NSGA-II), epsilon variable Multi-Objective GeneticAlgorithm (ev-MOGA), and Multi Objective Evolutionary Algorithm withDecomposition (MOEA/D). The robustness of the same control policy designed withthe nominal system settings have been investigated also for gradual decrease inthe commensurate and incommensurate fractional orders of the financial system.

Multi-objective Active Control Policy Design for Commensurate and Incommensurate Fractional Order Chaotic Financial Systems