Optimal boundary control of reaction-diffusion partial differential equations via weak variations

Scott J. Moura, Hosam K. Fathy

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


This paper derives linear quadratic regulator (LQR) results for boundary-controlled parabolic partial differential equations (PDEs) via weak variations. Research on optimal control of PDEs has a rich 40-year history. This body of knowledge relies heavily on operator and semigroup theory. Our research distinguishes itself by deriving existing LQR results from a more accessible set of mathematics, namely weak-variational concepts. Ultimately, the LQR controller is computed from a Riccati PDE that must be derived for each PDE model under consideration. Nonetheless, a Riccati PDE is a significantly simpler object to solve than an operator Riccati equation, which characterizes most existing results. To this end, our research provides an elegant and accessible method for practicing engineers who study physical systems described by PDEs. Simulation examples, closed-loop stability analyses, comparisons to alternative control methods, and extensions to other models are also included.

Original languageEnglish (US)
Article number034501
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Issue number3
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications


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