Journal Article

The Optimal Sampling Pattern for Linear Control Systems

Enrico Bini, Giuseppe Buttazzo


In digital control systems, the state is sampled at given sampling instants and the input is kept constant between two consecutive instants. With the 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 derive a necessary condition of the LQR optimality of a set of sampling instants. Since the numerical solution of the optimal sampling problem is very time consuming, we also propose a new quantization-based sampling strategy that is computationally tractable and capable of achieving near-optimal cost. Finally, and probably most interesting of all, we prove that the quantization-based sampling is optimal in first-order systems for a large number of samples. Experiments demonstrate that quantization-based sampling has near-optimal performance even when
the system has a higher order. However, it is still an open question whether quantization-based sampling is asymptotically optimal in
any case.


IEEE Transactions on Automatic Control, 59:1, pp. 78–90,2014.

Download full document