The attitude determination and control subsystem (ADCS) is a critical part of any satellite conducting scientific experiments that require accurate positioning (such as Earth observation and solar spectroscopy). The engineering design process of this subsystem has a long heritage; yet, it is surrounded by several limitations due to the stringent physical constraints imposed on small satellites. These limitations (e.g., limited computational capabilities, power, and volume) require an improved approach for the purpose of attitude determination (AD) and control. Previous space missions relied mostly on the extended Kalman filter (EKF) to estimate the relative orientation of the spacecraft because it yields an optimal estimator under the assumption that the measurement and process models are white Gaussian processes. However, this filter suffers from several limitations such as a high computational cost. This thesis addresses all the limitations found in small satellites by introducing a computationally efficient algorithm for AD based on a fuzzy inference system with a gradient decent optimization technique to calculate and optimize the bounds of the membership functions. Also, an optimal controller based on a fractional proportional-integral-derivative controller has been implemented to provide an energy-efficient control scheme. The AD algorithm presented in this thesis relies on the residual information of the Earth magnetic field. In contrast to current approaches, the new algorithm is immune to several limitations such as sensitivity to initial conditions and divergence problems. Additionally, its computational cost has been reduced. Simulation results illustrate a higher pointing stability, while maintaining satisfying levels of pointing accuracy and increasing reliability. Moreover, the optimal controller designed provides a shorter time delay, settling time, and steady-state error. This demonstrates that accurate attitude determination and control can be conducted in small spacecraft.