Computing ellipsoidal robust forward invariant tubes for nonlinear MPC

Authors

• M.E. Villanueva, J.C. Li, X. Feng, B. Chachuat, B. Houska

Reference

• In Proceedings of the
  20th IFAC World Congress,
  Toulouse, France, July, 2017.

Abstract

Min-max differential inequalities (DIs) can be used to characterize robust forward invariant tubes with convex cross-section for a large class of nonlinear control systems. The advantage of using set-propagation over other existing approaches for tube MPC is that they avoid the discretization of control policies. Instead, the conservatism of min-max DIs in tube MPC arises from the discretization of sets in the state-space, while the control law is never discretized and remains defined implicitly via the solution of a min-max optimization problem. The contribution of this paper is the development of a practical implementation of min-max DIs for tube MPC using ellipsoidal-tube enclosures. We illustrate these developments with a spring-mass-damper system.

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