Linear–quadratic optimal sampled-data control problems: Convergence result and Riccati theory

• Autores: Loïc Bourdin, Emmanuel Trélat
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 79, 2017, págs. 273-281
• Idioma: inglés
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• Resumen

  • Abstract We consider linear–quadratic optimal sampled-data control problems, where the state evolves continuously in time according to a linear control system and the control is sampled, i.e., is piecewise constant over a subdivision of the time interval, and the cost is quadratic. As a first result, we prove that, as the sampling periods tend to zero, the optimal sampled-data controls converge pointwise to the optimal permanent control. Then, we extend the classical Riccati theory to the sampled-data control framework, by developing two different approaches: the first one uses a recently established version of the Pontryagin maximum principle for optimal sampled-data control problems, and the second one uses an adequate version of the dynamic programming principle. In turn, we obtain a closed-loop expression for optimal sampled-data controls of linear–quadratic problems.