arXiv subjects

Zheng Qu

Publications and source records attributed to Zheng Qu.

39 records · Page 3Linked to original sources

arXiv2013

Squaring-Up Method In the Presence of Transmission Zeros

This paper presents a method to square up a generic MIMO system that already possesses transmission zeros. The proposed method is developed based on and therefore can be incorporated into the existing method that has been proven effective on a system without transmission zeros. It has been shown that for the generic system considering here, the squaring-up problem can be transformed into a state-feedback problem with uncontrollable modes.

math.OC↗

arXiv2012

The contraction rate in Thompson metric of order-preserving flows on a cone - application to generalized Riccati equations

We give a formula for the Lipschitz constant in Thompson's part metric of any order-preserving flow on the interior of a (possibly infinite dimensional) closed convex pointed cone. This provides an explicit form of a characterization of Nussbaum concerning non order-preserving flows. As an application of this formula, we show that the flow of the generalized Riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its Lipschitz constant by a matrix inequality. We also show that the same flow is no longer a contraction in other natural Finsler metrics on this cone, including the standard invariant Riemannian metric. This is motivated by a series of contraction properties concerning the standard Riccati equation, established by Bougerol, Liverani, Wojtowski, Lawson, Lee and Lim: we show that some of these properties do, and that some other do not, carry over to the generalized Riccati equation.

math.MG↗

arXiv2011

Curse of dimensionality reduction in max-plus based approximation methods: theoretical estimates and improved pruning algorithms

Max-plus based methods have been recently developed to approximate the value function of possibly high dimensional optimal control problems. A critical step of these methods consists in approximating a function by a supremum of a small number of functions (max-plus "basis functions") taken from a prescribed dictionary. We study several variants of this approximation problem, which we show to be continuous versions of the facility location and $k$-center combinatorial optimization problems, in which the connection costs arise from a Bregman distance. We give theoretical error estimates, quantifying the number of basis functions needed to reach a prescribed accuracy. We derive from our approach a refinement of the curse of dimensionality free method introduced previously by McEneaney, with a higher accuracy for a comparable computational cost.

math.OC↗