4 Continuous-time systems: Tracking control

Eli Gershon, Uri Shaked, Isaac Yaesh

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this chapter we treat the problem of H∞ tracking with stochastic multiplicative white noise. We extend the work of [98], which does not involve stochastic uncertainties, to the case where there are stochastic white noise parameter uncertainties in the matrices of the state-space model that describes the system. We treat the case where correlated parameter uncertainties appear in both the system dynamics and the input matrices for the state-feedback case, and in both, the input and the measurement matrices in the outputfeedback case. An optimal finite-horizon state-feedback tracking strategy is derived which minimizes the expected value of the standard H∞ performance index with respect to the unknown parameters and which applies game theoretic considerations. The solution of the latter problem and the stationary state-feedback case, appear in Section 4.3. In Section 4.4 we solve the outputfeedback control problem where we allow for a state-multiplicative noise in the measurement matrix. We first introduce in Section 4.4.1 an auxiliary stochastic BRL for systems that contain, in addition to the standard stochastic continuous-time BRL [10], a reference signal in the system dynamics. The BRL is solved as a max-min problem and results in a modified Riccati equation. controller.

Original languageEnglish
Title of host publicationH-Control and Estimation of State-multiplicative Linear Systems
PublisherSpringer Verlag
Number of pages19
ISBN (Print)1852339977, 9781852339975
StatePublished - 21 Sep 2005

Publication series

NameLecture Notes in Control and Information Sciences
ISSN (Print)0170-8643


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