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Optimal control synthesis for the constrained bilinear biquadratic regulator problem

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Abstract

Optimal process control with control constraints is a challenging task related to many real-life problems. In this paper, a single input continuous time constrained linear quadratic regulator problem, is defined and fully solved. The constraints include both bilinear inequality constraints and customary control force bounds. As a first step, the problem is reformulated as an equivalent constrained bilinear biquadratic optimal control problem. Next, Krotov’s method is used to solve it. To this end, a sequence of improving functions suitable to the problem’s new formulation is constructed and the corresponding successive algorithm is derived. The required computational steps are arranged as an algorithm and proof outlines for the convergence and optimality of the solution are given. The efficiency of the suggested method is demonstrated by numerical example.

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Acknowledgements

The first author is grateful for the support of The Irving and Cherna Moskowitz Foundation for his scholarship.

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Authors and Affiliations

  1. Department of Civil Engineering, Ariel University, Ariel, Israel

    Ido Halperin & Yuri Ribakov

  2. Department of Electrical and Electronics Engineering, Ariel University, Ariel, Israel

    Grigory Agranovich

Authors
  1. Ido Halperin
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  2. Grigory Agranovich
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  3. Yuri Ribakov
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Correspondence to Ido Halperin.

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Halperin, I., Agranovich, G. & Ribakov, Y. Optimal control synthesis for the constrained bilinear biquadratic regulator problem. Optim Lett 12, 1855–1870 (2018). https://doi.org/10.1007/s11590-017-1218-6

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  • DOI: https://doi.org/10.1007/s11590-017-1218-6

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