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Feedback Control via Integrated Sensing and Communication: Uncertainty Optimisation

Touraj Soleymani, Mohamad Assaad, John S. Baras

TL;DR

It is shown that the threshold region, defined as the set of estimation covariance pairs for which communication is preferred over sensing, expands with increasing source uncertainty and contracts with increasing base-station uncertainty.

Abstract

This paper studies strategic design in an integrated sensing and communication (ISAC) architecture for feedback control of cyber-physical systems. We focus on a setting in which the regulation of a physical process (i.e., remote source) is performed via an ISAC-enabled base station. The base station can alternate between tracking the state of the source and delivering control-relevant information back to the source. For a Gauss-Markov source subject to i.i.d. Bernoulli sensing and communication links, under a finite-horizon linear-quadratic-Gaussian cost, we rigorously characterise the optimal policies through an uncertainty-aware synthesis. We establish that the optimal switching policy, for the ISAC system at the base station, is threshold-based in terms of the source and base-station estimation covariances, while the optimal control policy, for the actuator at the source, is linear in the source state estimate. We show that the threshold region$\unicode{x2014}$defined as the set of estimation covariance pairs for which communication is preferred over sensing$\unicode{x2014}$expands with increasing source uncertainty and contracts with increasing base-station uncertainty.

Feedback Control via Integrated Sensing and Communication: Uncertainty Optimisation

TL;DR

It is shown that the threshold region, defined as the set of estimation covariance pairs for which communication is preferred over sensing, expands with increasing source uncertainty and contracts with increasing base-station uncertainty.

Abstract

This paper studies strategic design in an integrated sensing and communication (ISAC) architecture for feedback control of cyber-physical systems. We focus on a setting in which the regulation of a physical process (i.e., remote source) is performed via an ISAC-enabled base station. The base station can alternate between tracking the state of the source and delivering control-relevant information back to the source. For a Gauss-Markov source subject to i.i.d. Bernoulli sensing and communication links, under a finite-horizon linear-quadratic-Gaussian cost, we rigorously characterise the optimal policies through an uncertainty-aware synthesis. We establish that the optimal switching policy, for the ISAC system at the base station, is threshold-based in terms of the source and base-station estimation covariances, while the optimal control policy, for the actuator at the source, is linear in the source state estimate. We show that the threshold regiondefined as the set of estimation covariance pairs for which communication is preferred over sensingexpands with increasing source uncertainty and contracts with increasing base-station uncertainty.
Paper Structure (18 sections, 6 theorems, 28 equations, 3 figures)

This paper contains 18 sections, 6 theorems, 28 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Sensor Scheduling and Sensor Selection
  4. Communication Scheduling and Event-Triggered Sampling
  5. Integrated Sensing and Communication
  6. Contributions and Outline
  7. Notation
  8. Problem Statement
  9. System Model
  10. Performance Criterion and Optimisation Problem
  11. Main Results and Derivation
  12. Separation and Reformulation
  13. Uncertainty Dynamics
  14. Dynamic Programming Formulation
  15. Monotonicity and Submodularity of $V_k$
  16. ...and 3 more sections

Key Result

Proposition 1

Let $\check{x}_k = \mathop{\mathrm{\mathsf{E}}}\nolimits[x_k | \mathcal{I}^b_k, y_{0:k}]$ and $Q_k = \mathop{\mathrm{\mathsf{cov}}}\nolimits[x_k - \check{x}_k | \mathcal{I}^b_k, y_{0:k}]$. The optimal estimator at the base station satisfies the recursive equation for $k \in \mathbb{N}_{[1,N]}$ with initial conditions $\check{x}_{0} = m_{0} + K_{0} (y_0 - Cm_0)$, $Q_{0} = (M_{0}^{-1} + C^T V^{-1}

Figures (3)

  • Figure 1: Illustration of an unmanned aerial vehicle leveraging ISAC support from a base station to enhance situational awareness when onboard sensing is limited.
  • Figure 2: Value function at time $k=0$ as a function of the source and the base-station variances. This value function captures the expected closed-loop performance impact of estimation errors and reflects the cumulative effect of uncertainty.
  • Figure 3: Optimal ISAC switching decision map at time $k=0$ as a function of the source and base-station variances. The boundary exhibits the covariance-threshold structure predicted by the theoretical analysis.

Theorems & Definitions (6)

  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Lemma 1: Monotonicity of covariance maps
  • Lemma 2
  • Lemma 3