Optimization of bilinear systems using higher-order method

This paper derives some optimization results for bilinear systems using higher-order method by characterizing them over matrix Lie groups. In the derivation of the results, a bilinear system is first transformed to a left-invariant system on matrix Lie groups. The product of exponential representation is then used to express this system in a canonical form. The conditions for optimality are then obtained by the principles of variational calculus. It is demonstrated that closed-form analytical solutions exist for classes of bilinear systems whose Lie algebra is nilpotent.