Duality and H8-Optimal Control of Coupled ODE-PDE Systems

Sachin Shivakumar, Amritam Das, Siep Weiland, Matthew M. Peet

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

In this paper, we present a convex formulation of H8 -optimal control problem for coupled linear ODE-PDE systems with one spatial dimension. First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation (PIE) system and show that stability and H8 performance of the PIE system implies that of the ODE-PDE system. We then construct a dual PIE system and show that asymptotic stability and H8 performance of the dual system is equivalent to that of the primal PIE system. Next, we pose a convex dual formulation of the stability and H8 -performance problems using the Linear PI Inequality (LPI) framework. Next, we use our duality results to formulate the stabilization and H8 - optimal state-feedback control problems as LPIs. LPIs are a generalization of LMIs to Partial Integral (PI) operators and can be solved using PIETOOLS, a MATLAB toolbox. Finally, we illustrate the accuracy and scalability of the algorithms by constructing controllers for several numerical examples.

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers
Pages5689-5696
Number of pages8
ISBN (Electronic)978-1-7281-7447-1
DOIs
Publication statusPublished - 14 Dec 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: 14 Dec 202018 Dec 2020

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
CountryKorea, Republic of
CityVirtual, Jeju Island
Period14/12/2018/12/20

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