Brief A receding-horizon approach to the nonlinear H∞ control problem

  • Authors:

  • L. Magni;H. Nijmeijer;A. J. Van Der Schaft

  • Affiliations:

  • Dipartimento di Informatica e Sistemistica, Universití di Pavia, via Ferrata 1, 27100 Pavia, Italy;Faculty of Mechanical Engineering, Dynamics and Control Group, Eindhoven University of Technology, WH 0.139/141, P.O. Box 513, 5600 MB Eindhoven, Netherlands;Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2001

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Abstract

The receding-horizon (RH) methodology is extended to the design of a robust controller of H"~ type for nonlinear systems. Using the nonlinear analogue of the Fake H"~ algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input-output map of the closed-loop system obtained with the RH control law has a bounded L"2-gain. Robustness properties of the nonlinear H"~ control law in face of dynamic input uncertainty are considered.