Constrained Optimal Synthesis and Robustness Analysis by Randomized Algorithms

TL;DR

This paper advances robust control by extending order statistics theory to constrained, non-continuous distributions, proposing two solution approaches, and analyzing computational efficiency and sample size bounds.

Contribution

It introduces new distribution inequalities for order statistics with constraints and develops two methods for robust analysis and synthesis under these constraints.

Findings

Extended order statistics distribution theory to non-continuous, constrained cases.

Proposed two approaches for robust control synthesis and analysis.

Derived bounds on sample size and computational effort.

Abstract

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order statistics is associated with certain constraints. In particular, we derive an inequality on distribution for related order statistics. Moreover, we also propose two different approaches in searching reliable solutions to the robust analysis and optimal synthesis problems under constraints. Furthermore, minimum computational effort is investigated and bounds for sample size are derived.