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Pilot-Free Optimal Control over Wireless Networks: A Control-Aided Channel Prediction Approach

Minjie Tang, Zunqi Li, Photios A. Stavrou, Marios Kountouris

TL;DR

A pilot-free framework for optimal control over wireless channels in which control commands are generated from plant states together with control-aided channel prediction together with a stochastic approximation algorithm is proposed.

Abstract

A recurring theme in optimal controller design for wireless networked control systems (WNCS) is the reliance on real-time channel state information (CSI). However, acquiring accurate CSI a priori is notoriously challenging due to the time-varying nature of wireless channels. In this work, we propose a pilot-free framework for optimal control over wireless channels in which control commands are generated from plant states together with control-aided channel prediction. For linear plants operating over an orthogonal frequency-division multiplexing (OFDM) architecture, channel prediction is performed via a Kalman filter (KF), and the optimal control policy is derived from the Bellman principle. To alleviate the curse of dimensionality in computing the optimal control policy, we approximate the solution using a coupled algebraic Riccati equation (CARE), which can be computed efficiently via a stochastic approximation (SA) algorithm. Rigorous performance guarantees are established by proving the stability of both the channel predictor and the closed-loop system under the resulting control policy, providing sufficient conditions for the existence and uniqueness of a stabilizing approximate CARE solution, and establishing convergence of the SA-based control algorithm. The framework is further extended to nonlinear plants under general wireless architectures by combining a KalmanNet-based predictor with a Markov-modulated deep deterministic policy gradient (MM-DDPG) controller. Numerical results show that the proposed pilot-free approach outperforms benchmark schemes in both control performance and channel prediction accuracy for linear and nonlinear scenarios.

Pilot-Free Optimal Control over Wireless Networks: A Control-Aided Channel Prediction Approach

TL;DR

A pilot-free framework for optimal control over wireless channels in which control commands are generated from plant states together with control-aided channel prediction together with a stochastic approximation algorithm is proposed.

Abstract

A recurring theme in optimal controller design for wireless networked control systems (WNCS) is the reliance on real-time channel state information (CSI). However, acquiring accurate CSI a priori is notoriously challenging due to the time-varying nature of wireless channels. In this work, we propose a pilot-free framework for optimal control over wireless channels in which control commands are generated from plant states together with control-aided channel prediction. For linear plants operating over an orthogonal frequency-division multiplexing (OFDM) architecture, channel prediction is performed via a Kalman filter (KF), and the optimal control policy is derived from the Bellman principle. To alleviate the curse of dimensionality in computing the optimal control policy, we approximate the solution using a coupled algebraic Riccati equation (CARE), which can be computed efficiently via a stochastic approximation (SA) algorithm. Rigorous performance guarantees are established by proving the stability of both the channel predictor and the closed-loop system under the resulting control policy, providing sufficient conditions for the existence and uniqueness of a stabilizing approximate CARE solution, and establishing convergence of the SA-based control algorithm. The framework is further extended to nonlinear plants under general wireless architectures by combining a KalmanNet-based predictor with a Markov-modulated deep deterministic policy gradient (MM-DDPG) controller. Numerical results show that the proposed pilot-free approach outperforms benchmark schemes in both control performance and channel prediction accuracy for linear and nonlinear scenarios.
Paper Structure (28 sections, 5 theorems, 63 equations, 8 figures, 4 algorithms)

This paper contains 28 sections, 5 theorems, 63 equations, 8 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Prior Art
  4. Main Contributions
  5. System Model
  6. Decision-Making at the Dynamic Plant
  7. Signal Generation and Transmission at the Remote Controller
  8. Signal Reception at the Dynamic Plant
  9. Pilot-Free Communication Paradigm for the WNCS
  10. Linear Systems over OFDM
  11. Problem Formulation
  12. Solution to Problem \ref{['problem: channel_estimation']}
  13. Solution to Problem \ref{['problem:decision_making']}
  14. Extensions to Nonlinear Systems
  15. Generic System Modeling
  16. ...and 13 more sections

Key Result

Theorem 1

Under the proposed pilot-free control framework, suppose the channel state evolves according to the linear dynamics eq: channel dynamic model and is related to the plant evolution through the linear observation model eq: channel observation model. Then, the one-step lookahead channel prediction erro

Figures (8)

  • Figure 1: Typical WNCS architecture under the proposed pilot-free framework.
  • Figure 2: Data flow between Algorithm \ref{['algorithm:channel_estimation_linear']} and Algorithm \ref{['algorithm:decision_making_linear']}, which solve Problem \ref{['problem: channel_estimation']} and Problem \ref{['problem:decision_making']}, respectively. Algorithm \ref{['algorithm:decision_making_linear']} generates the control input $\mathbf{u}_k$ using the one-step channel prediction $\widehat{\mathbf{h}}(k+1|k)$ from Algorithm \ref{['algorithm:channel_estimation_linear']}. In turn, Algorithm \ref{['algorithm:channel_estimation_linear']} exploits the control history $\mathbf{u}_0^{k-1}$ produced by Algorithm \ref{['algorithm:decision_making_linear']}. This illustrates the mutual dependence between Problem \ref{['problem: channel_estimation']} and Problem \ref{['problem:decision_making']}.
  • Figure 3: Normalized MSE (NMSE) of channel prediction versus received SNR at the plant for Case (i) (linear model).
  • Figure 4: NMSE of channel prediction versus received SNR at the plant for Case (ii) (nonlinear model).
  • Figure 5: Average plant state energy versus received SNR at the plant for Case (i).
  • ...and 3 more figures

Theorems & Definitions (7)

  • Remark 1: Coupling Between Problems \ref{['problem: channel_estimation']} and \ref{['problem:decision_making']}
  • Remark 2: Equivalence of MMSE Prediction for $\mathbf{H}_k^c$ and $\mathbf{h}_k^c$
  • Theorem 1: Stability of Channel Prediction
  • Theorem 2: Markov-Modulated Bellman Equation
  • Theorem 3: Plant Stability
  • Theorem 4: Sufficient Conditions for Existence and Uniqueness of a Stabilizing Solution to \ref{['eq: discrete riccati']}
  • Lemma 1: Convergence of Algorithm \ref{['algorithm:decision_making_linear']}