Control architectures and algorithms

In this chapter, a few algorithms to derive a control law are presented. Both closed- and open-loop architectures are discussed, focusing on two techniques, namely, the state-dependent Riccati equation and the particle swarm optimization. The former is a systematic and effective methodology to design a suboptimal feedback controller, which allows for capturing system nonlinearities and accounting for state or input constraints. It has been widely used in a variety of control applications, and more recently it has been applied to satellite maneuvering problems. The particle swarm optimizer is a stochastic approach to solving the optimal control problem. Inspired by the behavior of the socially organized swarm population in nature, such as bird flocks or fish schools, it has become popular in the control community because of its simplicity and straightforward implementation. Several examples are presented to show the effectiveness of the aforementioned algorithms, with a strong emphasis on their application to “real” spacecraft control problems.