Optimal boundary control & estimation of diffusion-reaction PDEs

Scott J. Moura, Hosam K. Fathy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Scopus citations


This paper considers the optimal control and optimal estimation problems for a class of linear parabolic diffusion-reaction partial differential equations (PDEs) with actuators and sensors at the boundaries. Diffusion-reaction PDEs with boundary actuation and sensing arise in a multitude of relevant physical systems (e.g. magneto-hydrodynamic flows, chemical reactors, and electrochemical conversion devices). We formulate both the control and estimation problems using finite-time optimal control techniques, where the key results represent first order necessary conditions for optimality. Specifically, the time-varying state-feedback and observer gains are determined by solving Riccati-type PDEs. These results are analogous to the Riccati differential equations seen in linear quadratic regulator and optimal estimator results. In this sense, this paper extends LQR and optimal estimation results for finite-dimensional systems to infinite-dimensional systems with boundary actuation and sensing. These results are unique in two important ways. First, the derivations completely avoid discretization until the implementation stage. Second, they bypass formulating infinite-dimensional systems on an abstract Hilbert space and applying semigroup theory. Instead, Riccati equations are derived by applying weak-variations directly on the PDEs. Simulation examples and comparative analyses to backstepping are included for demonstration purposes.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 American Control Conference, ACC 2011
Number of pages8
StatePublished - 2011
Event2011 American Control Conference, ACC 2011 - San Francisco, CA, United States
Duration: Jun 29 2011Jul 1 2011

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2011 American Control Conference, ACC 2011
Country/TerritoryUnited States
CitySan Francisco, CA

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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