Infinite horizon stable predictive control

Model predictive control of nonlinear systems: Stability region and feasible initial control

“…Using the transforms (20), (23) and (26), one can see that (29) is equivalent to condition (18). Similar to [6], it is easy to prove that condition (19) guarantees that input constraints are satisfied.…”

“…Theorem 1. For those discrete-time vertex systems given in (14), suppose there exist S ands such that conditions (18) and (19) hold. Then the SMPC proposed in Section 3 is feasible to steer any initial state from M into ν.…”

Properties of extended predictive control

“…Infinite horizon MPC are in any case a practical route to achieving stability as there exist very efficient ways to solve the corresponding huge quadratic programming problems [17]. Therefore, it is assumed that as the prediction horizon P → ∞, α 11 ∼ = α 12 ∼ = · · · ∼ = α n u n u .…”

A modified model predictive control scheme

“…The first category, e.g. infinite horizon predictive control [6] , terminal constraints [7∼12] and fake algebraic Riccati equations [5] , focuses on introducing some terminal penalties into the performance index function, so that stability is guaranteed by satisfying some special conditions which are employed to prevent the performance index from increasing. The second category puts emphasis on imposing extra state constraints on the online optimization process rather than modifying the performance index function itself [13∼16] .…”