Robustly Invariant Polytopes based on the L1-Norm

T.B. Blanco and B. De Moor (Belgium)


Polytopic invariant sets; Optimization; Constrained control


Invariant sets are tools that are used in practice as terminal sets for model predictive control (MPC) in order to ensure stability. By enforcing the terminal state to lie inside an in variant set stability and feasibility with respect to the constraints can be ensured. In this work the main focus will go to sets based on the L1-norm invariant for linear systems with polytopic uncertainty description subject to input constraints. The paper first proposes a method to determine an initial robustly feasible invariant set. This set is used as starting point for an optimization scheme that increases the volume of the set by solving a sequence of convex programs. A numerical example shows the efficiency of the proposed methods.

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