Optimal control of spacecraft attitude motion using Port-Hamiltonian systems

In this study, a concept of optimality is introduced into Port-Hamilton systems for attitude control of spacecraft. Port-Hamiltonian systems make it possible to design asymptotically stable controllers in a uniform procedure for a wide variety of physical systems. By introducing optimality to Port-Hamilton system, conventional error systems of Port-Hamilton systems are expanded to minimize a quadratic form of evaluation function. In this study, as an optimal control method of Port-Hamiltonian system, Hamilton-Jacobi-Bellman (HJB) equation is considered. Since solving HJB equation is not easy, the equation is simplified through generalized canonical transformation, which is a unique conversion of Port-Hamiltonian system. Furthermore, by considering the minimum evaluation function as a Hamiltonian transformed through the generalized canonical transformation, the analytical solution of the HJB equation can be derived. This method can be used for a time-varying error system and applied for tracking control of spacecraft to specified trajectories. The optimality of the control input obtained from the proposed procedure is verified in numerical simulations.