Mixed Regular and Impulsive Sampled-data LQR

TL;DR

This paper explores combining regular and impulsive inputs in sampled-data LQR control, demonstrating that such hybrid control can enhance controllability and performance, especially when future disturbances are known.

Contribution

It introduces a new controllability condition for mixed regular and impulsive sampled-data systems and develops an optimal preview LQR controller leveraging both input types.

Findings

Impulsive inputs can enlarge controllability regions.

The proposed preview LQR improves disturbance rejection.

Numerical examples show significant performance gains.

Abstract

We investigate the benefits of combining regular and impulsive inputs for the control of sampled-data linear time-invariant systems. We first observe that adding an impulsive term to a regular, zero-order-hold controller may help enlarging the set of sampling periods under which controllability is preserved by sampling. In this context, we provide a tailored Hautus-like necessary and sufficient condition under which controllability of the mixed regular, impulsive (MRI) sampled-data model is preserved. We then focus on LQR optimal control. After having presented the optimal controllers for the sampled-data LQR control in the MRI setting, we consider the scenario where an impulsive disturbance affects the dynamics and is known ahead of time. The solution to the so-called preview LQR is presented exploiting both regular and impulsive input components. Numerical examples, that include an insulin infusion benchmark, illustrate that leveraging both future disturbance information and MRI controls may lead to significant performance improvements.