Closed-form H-infinity optimal control for a class of infinite-dimensional systems

Research output: Contribution to journalArticle


H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems.


External organisations
  • University of Waterloo
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Control Engineering
  • Computational Mathematics


  • Distributed-parameter systems, H-infinity control, Linear systems, Optimal control, Optimal estimation
Original languageEnglish
Article number108916
Publication statusPublished - 2020 Jul
Publication categoryResearch