Extended invariance and its use in model predictive control

The use of time invariant linear state feedback control laws for the definition of terminal invariant regions can be conservative, thereby reducing the efficacy of predictive control in terms of size of stabilisable sets and closed-loop performance. This difficulty, which is particularly pronounced in the case of nonlinear and/or uncertain dynamics, can be remedied through the use of time-varying control laws and terminal invariant sets. In existing MPC schemes, however, these have to be computed online thereby rendering implementation impracticable for anything other than low-dimensional systems. Here, the definition of invariance is extended to apply over ν predicted control moves, thereby enabling the use of pre-determined (offline) time-varying state feedback gains. More importantly, this extension allows for the use of local uncertainty or linear difference inclusion sets, and thus affords significant improvements, e.g. in terms of the size of terminal regions.