Long-lived actinides transmutation in accelerator driven system (ADS) is considered in this paper. The objective is to improve the transmutation performance from the overall radiotoxity of nuclear waste point of view by means of an optimization approach based on control theory. Parameters subjected to determination are the initial values of actinides nuclear concentration in the loaded fuel. The change in time of actinides’ atomic concentration is described by a system of ordinary differential equations with initial conditions, that can be given with some inaccuracy. For such dynamical system a gradient-based optimization algorithm taking into account robustness of initial loading will be constructed. Moreover, constraint on value of effective multiplication factor is considered during numerical optimization. Based on this approach initial atomic concentration values providing the best indicators of actinides burnup can be obtained. Calculation results of actinides volume fraction and effective multiplication factor dynamics are presented.