Calculus of Variations and Geometric Measure Theory

E. Bini - G. Buttazzo

The optimal sampling pattern for linear control systems

created by buttazzo on 05 Oct 2017


Published Paper

Inserted: 5 oct 2017

Journal: IEEE Trans. Automat. Control
Volume: 59
Number: 1
Pages: 78-90
Year: 2014
Doi: 10.1109/TAC.2013.2279913
Links: file from the journal web site


In digital control systems the state is sampled at given sampling instants and the input is kept constant between two consecutive instants. By \emph{optimal sampling problem} we mean the selection of sampling instants and control inputs, such that a given function of the state and input is minimized. In this paper we formulate the optimal sampling problem and we propose a numerical method to solve it. Being the solving procedure time consuming, we also propose a new \emph{quantization-based} sampling strategy that is computationally tractable and capable to achieve a near-optimal cost. Finally, we prove that the quantization-based sampling is optimal in scalar systems for large number of samples.

Keywords: optimal control problems, sampling patterns, quantization