The Ellipsoid Algorithm for Probabilistic Robust Controller Design

This paper presents a new iterative approach to probabilistic robust controller design, which is an alternative to the recently proposed Subgradient Iteration Algorithm (SIA). In its original version [12] the SIA possesses the useful property of guaranteed convergence in a finite number of iterations, but requires that the radius of a non-empty ball contained in the solution set is known a-priori. This rather restrictive assumption was later on released in [3], but only at the expense of an increased number of iterations. The approach in this paper does also not require the knowledge of such a radius, and offers a significant improvement even over the original SIA in terms of the maximum number of possible correction steps that can be executed before a feasible solution is reached. Given an initial ellipsoid that contains the solution set, the approach iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the solution set. A method for finding an initial ellipsoid containing the solution set is also proposed. The approach is illustrated on a real-life diesel actuator benchmark model. keywords: probabilistic robustness, robust LMIs, robust control.