Spectral Analysis and Optimal Energy Control for a Spacecraft System

In this paper, a spacecraft system is investigated. The system is formulated by partial differential equations with the initial and the boundary conditions. The spectral analysis and semigroup generation for the system are employed and discussed in the appropriate Hilbert spaces, and some exponential stability-type results are obtained. Finally, a significant optimal energy control is proposed, and existence and uniqueness of the optimal energy control are demonstrated. Eventually, an approximation theorem for minimum energy control is proved in terms of semigroup approach and geometric method.