A novel robust model predictive control approach with pseudo terminal designs.

Robust model predictive control (RMPC) has gained much attention in the past two decades. For classic finite-horizon RMPC, a terminal constraint set together with a terminal cost function are usually employed for the purpose of closed-loop stability. However, computational burden and feasibility region may need to be carefully addressed when the prediction horizon length becomes large, especially for the cases with additive disturbances. In this paper, a novel RMPC approach with pseudo terminal designs is proposed. Specifically, a bank of pseudo terminal sets (PTSs) are designed given a predefined terminal constraint set. Besides, a pseudo terminal cost (PTC) term is considered for each PTS. With the proposed approach, a long-horizon RMPC problem can be divided into several short-horizon ones. It is shown that both the PTSs and the corresponding PTCs can be computed off-line recursively. In the online implementation, selecting a PTS is realized in a self-triggered way. Meanwhile, a time-varying cost function, which is always an upper bound of the infinite-horizon cost function, is optimized online.