Multi-step H ∞ generalized predictive control

Abstract

An H∞ generalized control law is derived which has properties in common with both the GH∞ and GPC control laws. The stability and robustness properties are the same as for a GH∞ optimal controller but a cost on future predictive error and control action is dealt with in the same manner as for the GPC or model based predictive control laws. This type of long range predictive control algorithm has stability and robustness problems which are much improved through the H∞ formalism. The general two-block problem solution is considered first and this is then reduced to a novel one-block multi-step GH∞ control law which is very attractive computationally. This latter algorithm has all the benefits of one-block H∞ controllers and yet the equations can be written in a form where GPC type constrained solutions can be obtained.