Optimization of bilinear systems using a higher-order variational method

This paper derives some optimization results for bilinear systems using a h igher-order method by characterizing them over matrix Lie groups. In the de rivation of the results, first a bilinear system is transformed to a left-i nvariant system on matrix Lie groups. Then, the product of exponential repr esentation is used to express this system in canonical form. Next, the cond itions for optimality are obtained by the principles of variational calculu s, It is demonstrated that closed-form analytical solutions exist for class es of bilinear systems whose Lie algebra are nilpotent.