Spacecraft formation flight is an important technology for upcoming scientific and Earth observation missions. The topic of this work is the control of spacecraft formations specifically through the control of the differential, mean orbital elements of a spacecraft. Orbital perturbations can disturb formation geometry in an undesirable fashion so active control is required to maintain a precise relative trajectory.;A number of control strategies are proposed. The first is an impulsive thrust strategy that is valid for formations in both eccentric and circular orbits. A general N-thrust per orbit formulation is presented. For the two-thrust case, an analytical solution to the constraint equations is presented and the closed-loop stability of the formation is considered. Two-thrust performance is shown to achieve superior position control with similar delta-V over previously proposed control strategies.;The geomagnetic Lorentz force is a propellantless means of altering a spacecraft's orbit. A spacecraft with a significant surface charge experiences the Lorentz force due to the spacecraft's velocity relative to the Earth's magnetic field. Application of the Lorentz force to the formation control problem is a major contribution of this work. It is identified that the relative spacecraft state is not completely controllable with the Lorentz force alone, necessitating control strategies that combine conventional thruster actuation with the Lorentz force. Emphasis is placed on minimizing the thruster actuation and maximizing the use of the Lorentz force. Strategies that employ both continuous and impulsive thruster actuation with the Lorentz force are considered. Results show that the majority of the required actuation can be achieved using the Lorentz force.;Investigation of optimal impulsive thrusting with continuous Lorentz force actuation motivates the development of novel optimal control theory for linear time-varying systems with both continuous and impulsive inputs. The necessary conditions to minimize a hybrid quadratic performance index are derived. A continuous and a discrete Riccati equation are required to solve the optimal control problem: the former yields the continuous solution between impulsive actions; the latter provides a new boundary condition at impulsive application times. Necessary and sufficient conditions are derived for optimal impulsive application times. Numerical simulations validate the solutions.
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