A short note on constrained linear control systems with multiplicative ellipsoidal uncertainty

Authors

• B. Houska, A. Mohammadi, M. Diehl

Reference

• IEEE Transactions on Automatic Control,
  Volume 61(12), pages 4106-4111, 2017.

Abstract

This paper revisits the classical robust control question of how to design linear control laws for uncertain linear dynamic systems. We formulate this robust control design problem from a modern optimal control perspective which allows us to take into account control and state constraints that have to be satisfied by the closed-loop system for all possible uncertainty scenarios. The contribution of this paper is the derivation of a conservative but computationally tractable robust control design problem formulation for the case that multiplicative uncertainties are present in the linear dynamic systems, which render the robust control problem non-convex in general. Here, our approximation technique relies on propagating ellipsoidal bounds on the reachable states of the closed-loop system. The methods developed in this paper can also be used as a building block for tube based model predictive control schemes, where robustly designed linear control laws can help to reduce the conservatism of open-loop predictions. We illustrate the proposed techniques with a numerical case study.

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