Infinite-horizon optimal scheduling for feedback control

TL;DR

This article investigates infinite-horizon optimal scheduling for resource-aware networked control systems by addressing the rate-regulation tradeoff and derives the optimal scheduling law for feedback control based on the VoI and shows that it is deterministic and stationary.

Abstract

Emerging cyber-physical systems impel the development of communication protocols that optimize resource utilization. This article investigates infinite-horizon optimal scheduling for resource-aware networked control systems by addressing the rate-regulation tradeoff. Consider a scenario where the sensor and the controller communicate via a networked channel, the transmission scheduling problem is formulated as a Markov decision process on unbounded general state space controlled by scheduling decisions. The value of information (VoI) serves as a metric to assess the importance of sensory data for transmission. We derive the optimal scheduling law for feedback control based on VoI and show that it is deterministic and stationary, with an explicit expression obtained via value iteration. The closed-loop system under the designed scheduling law is shown to be stochastically stable. By analyzing the dynamic behavior of the iteration process, we show that the VoI function and the optimal scheduling law exhibit symmetry. Furthermore, when the system matrix is diagonalizable, the VoI function is monotone and quasi-convex. Consequently, the optimal scheduling law is shown to exhibit a threshold structure and takes a quadratic form, with the threshold region explicitly characterized. Finally, the numerical simulation illustrates the theoretical result of the VoI-based scheduling.

Figures (5)

• Figure 1: NCS architecture
• Figure 2: The differential cost $h(e)$, the expected differential cost $\mathbf{E}[h(Ae+\xi)]$ and their contour lines.
• Figure 3: The optimal thresholds of optimal scheduling law $\hat{\gamma}^\ast$, and two state-based scheduling law $\gamma_1$ and $\gamma_2$ under different multiplier $\theta$.
• Figure 4: The regulation and communication costs \ref{['eq:Vk']} achieved by the optimal scheduling \ref{['eq:threshold triggering']}, the greedy scheduling \ref{['eq:greedy']} and two state-based scheduling \ref{['eq:triggering 1']}, \ref{['eq:triggering 2']} under different multiplier $\theta$.
• Figure 5: Tradeoff between regulation cost and communication rate under the optimal scheduling \ref{['eq:threshold triggering']}, the greedy scheduling \ref{['eq:greedy']} and two state-based scheduling \ref{['eq:triggering 1']}, \ref{['eq:triggering 2']} .

Theorems & Definitions (19)

• Lemma 1
• Lemma 2
• Proposition 1
• Remark 1
• Lemma 3
• Proposition 2
• Remark 2
• Definition 1
• Theorem 1
• Remark 3