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On the Positive LQ-Problem for Linear Discrete Time Systems

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Book cover Positive Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 389))

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Abstract

The finite horizon Linear-Quadratic (LQ) optimal control problem with nonnegative state constraints (denoted by LQ + ) is studied for positive linear systems in discrete time. Necessary and sufficient optimality conditions are obtained by using the maximum principle. These conditions lead to a computational method for the solution of the LQ +  problem by means of a corresponding Hamiltonian system. In addition, necessary and sufficient conditions are reported for the LQ + -optimal control to be given by the standard LQ-optimal state feedback law. Sufficient conditions are also reported for the positivity of the LQ-optimal closed-loop system. In particular, such conditions are obtained for the problem of minimal energy control with penalization of the final state. Moreover a positivity criterion for the LQ-optimal closed-loop system is derived for positive systems with a positively invertible (dynamics) generator.

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Author information

Authors and Affiliations

  1. Department of mathematics, University of Namur (FUNDP), Rempart de la Vierge, 8, 5000, Namur, Belgium

    Charlotte Beauthier & Joseph J. Winkin

Authors
  1. Charlotte Beauthier
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  2. Joseph J. Winkin
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Editor information

Editors and Affiliations

  1. Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camí de Vera s/n, 46022, Valencia, Spain

    Rafael Bru  & Sergio Romero-Vivó  & 

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Beauthier, C., Winkin, J.J. (2009). On the Positive LQ-Problem for Linear Discrete Time Systems. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-02894-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02893-9

  • Online ISBN: 978-3-642-02894-6

  • eBook Packages: EngineeringEngineering (R0)

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