Safe Adaptive-Sampling Control via Robust M-Step Hold Model Predictive Control

Abstract

In adaptive-sampling control, the control frequency can be adjusted during task execution. Ensuring that these on-the-fly changes do not jeopardize the safety of the system being controlled requires careful attention. We introduce robust M-step hold model predictive control (MPC) to address this. This MPC formulation provides robust constraint satisfaction for an uncertain discrete-time system model with a fixed sampling time subject to an adaptable multi-step input hold (referred to as M-step hold). We show how to ensure recursive feasibility of the MPC utilizing M-step hold extensions of robust invariant sets, and demonstrate how to use our framework to enable safe adaptive-sampling control via the online selection of M. We evaluate the utility of the robust M-step hold MPC formulation in a cruise control example.

Figures (5)

• Figure 1: An $M$-step hold MPC is a receding horizon controller that solves an optimization every $M$ steps and applies a constant input between solves.
• Figure 2: A platoon of $P$ vehicles behind an uncontrolled front car.
• Figure 3: Slices of $\mathcal{C}^1$, $\mathcal{C}^5$, and $\mathcal{C}^{10}$ at discrete values of $v_{0}$.
• Figure 4: Larger $M$-step holds stay farther behind the front car to be robust to more open-loop uncertainty propagation, and all controllers safely stop the ego when the front car full-breaks until stopped ($\geq15s$).
• Figure 5: Online adaptation to smaller $M$-step holds expands the safe operating region to include smaller following distances. The slices $\mathbb{C}^M_{v_{0}}$ are nested for factors of $M$ for all $v_0$ ($25$ m/s shown).

Theorems & Definitions (7)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Remark 1
• Remark 2