The availability of increasing computational power together with algorithmic developments make computation times in the milli- or micro-second range possible even for large-scale optimization problems. This offers new possibilities in MPC, where an optimal control problem has to be solved online at each sampling instant.
A main challenge for the application of MPC to high-speed embedded processes is the presence of real-time constraints, i.e. a limit on the online computation time that is available. Since computation times for solving the MPC problem vary significantly with the current system state, a real-time constraint may require early termination of the online optimization, in which case the control theoretic properties of MPC are generally lost.
Our goal is to provide safety certificates for the real-time MPC problem with fixed computational bounds. The two main considered approaches are: derivation of tight a priori bounds on the worst-case computational complexity and development of suboptimal methods with the desired theoretical properties (e.g. stability, invariance). Our work considers second-order (interior-point) and first-order (fast gradient) methods and comprises both theory as well as implementation aspects.