Approximate Robust Optimal Control of Periodic Systems with Invariants and High-Index Differential Algebraic Systems

Authors

• J. Sternberg, S. Gros, B. Houska, M. Diehl

Reference

• In Proceedings of the
  7th IFAC Symposium on Robust Control Design,
  Aalborg, Denmark, pages 690 - 695, June 20-22, 2012.

Abstract

In this paper we present solution approaches for uncertain periodic optimal control problems with invariants and high-index differential algebraic systems. There are two difficulties to be addressed: first, we encounter a redundancy in the periodic boundary constraints which is due to the presence of invariants. And second, we have to deal with the presence of uncertainties. To address the first problem we discuss both a projection and a null-space based reformulation approach which avoid the redundancies in the constraints. Concerning the uncertainties, we discuss an approximate robust optimal control formulation based on Lyapunov differential equations. Here, the invariants and periodic boundary constraints have to be taken into account, too. We illustrate our techniques by optimizing an open-loop controlled inverted pendulum which is affected by unknown forces.

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