Attitude control by means of explicit model predictive control, via multi-parametric quadratic programming

Explicit solutions to constrained linear MPC problems can be computed by solving multi-parametric quadratic programs (mpQP), where the parameters are the components of the state vector. The solution to the mpQP is a piecewise affine (PWA) function, which can be evaluated at each sample to obtain the optimal control law. The online computation effort is restricted to a table-lookup, and the controller can be implemented on inexpensive hardware as fixed-point arithmetics can be used. This is useful for systems with limited power and CPU resources. An example of such systems is micro-satellites, which is the focus of this paper. In particular, the explicit MPC (eMPC) approach is applied to the SSETI/ESEO micro-satellite, initiated by the European Space Agency (ESA). The theoretical results are supported by simulations.