TY - GEN
T1 - Duality and H8-Optimal Control of Coupled ODE-PDE Systems
AU - Shivakumar, Sachin
AU - Das, Amritam
AU - Weiland, Siep
AU - Peet, Matthew M.
N1 - Funding Information:
of the ODE-PDE are inherited from the PIE. Our duality results allow can be used with LPIs to find stabilizing and H∞-optimal state-feedback controllers for PIEs and these controllers can then be used to regulate the associated ODE-PDEs. We have demonstrated the accuracy and scalability of the resulting algorithms by applying the results to several illustrative examples. While the scope of the paper is limited to inputs entering through the ODE or in-domain, we believe the results can be extended to inputs at the boundary. ACKNOWLEDGMENT This work was supported by Office of Naval Research Award N00014-17-1-2117, and National Science Foundation grants CMMI-1935453 and CNS-1739990. REFERENCES
Publisher Copyright:
© 2020 IEEE.
PY - 2020/12/14
Y1 - 2020/12/14
N2 - 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.
AB - 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.
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U2 - 10.1109/CDC42340.2020.9303989
DO - 10.1109/CDC42340.2020.9303989
M3 - Conference contribution
AN - SCOPUS:85099877224
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5689
EP - 5696
BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 59th IEEE Conference on Decision and Control, CDC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -