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 language | English |
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| Title of host publication | 59th IEEE Conference on Decision and Control (CDC 2020) |
| Publisher | Institute of Electrical and Electronics Engineers |
| Pages | 5689-5696 |
| Number of pages | 8 |
| ISBN (Electronic) | 978-1-7281-7447-1 |
| DOIs | |
| Publication status | Published - 11 Jan 2021 |
| Event | 59th IEEE Conference on Decision and Control, CDC 2020 - Virtual/Online, Virtual, Jeju Island, Korea, Republic of Duration: 14 Dec 2020 → 18 Dec 2020 Conference number: 59 https://cdc2020.ieeecss.org/ |
Publication series
| Name | Proceedings of the IEEE Conference on Decision and Control |
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| Volume | 2020-December |
| ISSN (Print) | 0743-1546 |
| ISSN (Electronic) | 2576-2370 |
Conference
| Conference | 59th IEEE Conference on Decision and Control, CDC 2020 |
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| Abbreviated title | CDC |
| Country/Territory | Korea, Republic of |
| City | Virtual, Jeju Island |
| Period | 14/12/20 → 18/12/20 |
| Internet address |