Numerical robustness and efficiency of generalised predictive control algorithms with guaranteed stability

Three recent publications proposed modifications to the generalised predictive control algorithm which guarantee closed-loop stability. Of these the first two adopt the same philosophy, namely that of constrained receding horizon predictive control (CRHPC), whereas the third adopts a stable generalised predictive control (SGPC) strategy by first stabilising then controlling the plant. The purpose of the paper is to examine the relationship between CRHPC and SGPC. It is shown that, theoretically, the two approaches are equivalent, but is is also shown that CRHPC could be subject to significant numerical instability problems. Two alternative improved implementations of CRHPC are proposed, but SGPC is shown to have the advantage in terms of numerical stability and computational efficiency