The explicit linear quadratic regulator for constrained systems

  • Authors:

  • Alberto Bemporad;Manfred Morari;Vivek Dua;Efstratios N. Pistikopoulos

  • Affiliations:

  • Automatic Control Laboratory, ETH Zentrum, ETL I 26, 8092 Zurich, Switzerland and Dip. Ingegneria dell'Informazione, Universití di Siena, Via Roma 56, 53100 Siena, Italy;Automatic Control Laboratory, ETH Zentrum, ETL I 26, 8092 Zurich, Switzerland;Centre for Process Systems Engineering, Imperial College, London SW7 2BY, UK;Centre for Process Systems Engineering, Imperial College, London SW7 2BY, UK

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2002

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Abstract

We present a technique to compute the explicit state-feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints. We show that this closed form solution is piecewise linear and continuous. As a practical consequence of the result, constrained linear quadratic regulation becomes attractive also for systems with high sampling rates, as on-line quadratic programming solvers are no more required for the implementation.