Piecewise Linear Quadratic Optimal Control

Anders Rantzer, Mikael Johansson

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Abstract

The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex optimization problem using the given control law. A compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy
Original languageEnglish
Pages (from-to)629-637
JournalIEEE Transactions on Automatic Control
Volume45
Issue number4
DOIs
Publication statusPublished - 2000

Subject classification (UKÄ)

  • Control Engineering

Free keywords

  • optimal control
  • semidefinite programming
  • Nonlinear systems

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