Hybrid RSSI-Throughput Control Strategy

• Hybrid RSSI-Throughput Control Strategy is a closed-loop TXP framework that integrates transmission power management, event-triggered sampling, and dual-loop PID control for optimized wireless performance.
• It employs adaptive event-triggered transmission policies and observer-based methods to balance reduced communication overhead with robust stability in diverse control systems.
• The strategy unifies rapid RSSI-based response with throughput regulation, achieving significant energy savings and consistent performance in dynamic wireless environments.

A closed-loop TXP (Transmission/Task Execution Planning) control framework refers to a class of architectures in which system outputs are continuously monitored and the control policy is updated dynamically—typically based on a quantifiable error signal relative to a reference or planned trajectory. These frameworks ensure robust stability, improve resource efficiency (e.g., communication or energy usage), and often unify different feedback modalities within a hybrid systems context. This article surveys the principles, methodologies, architectures, and guarantees underlying closed-loop TXP frameworks, synthesizing perspectives from modern wireless communication control, hybrid plant–controller system design, and task execution planning.

1. System Modeling and Interconnection

Closed-loop TXP control frameworks model the problem as an interconnection between a controlled process ("plant"), a controller, and digital communication or planning infrastructures:

• Linear Plant and Controller via Digital Channel: Consider a continuous-time linear plant $\dot x_p = A_p x_p + B_p u$, with output $y = C_p x_p$, connected to a controller $\dot x_c = A_c x_c + B_c y_k$, $u = C_c x_c$, over a digital channel. Here, $y_k$ represents the last transmitted output sample. Control updates occur discretely at transmission events, with the controller holding its state constant between arrivals (Forni et al., 2013).
• Wireless Communication Context: In transmission-power control (TXP), system signals include the transmission power $TXP$, received signal strength indicator (RSSI), and throughput $T$. Received RSSI depends on TXP and path-loss models:

$RSSI(d) \approx TXP - PL(d)$

with $PL(d)$ described by log-distance path-loss and shadowing (Zhou et al., 6 Jan 2026).

• Robotic and Symbolic Planning Context: In closed-loop robotic planning, a planner produces goal states ($\hat{O}_i$ or sub-tasks $T_i$), error is computed in an embedding space, and feedback controllers adapt actions dynamically (Bu et al., 2024). TXP frameworks can substitute symbolic planners, embedding spaces, and error metrics for discrete control tasks.

2. Transmission-Lazy Event-Triggered Sampling

The transmission-lazy (TXP) methodology aims to minimize communication events in networked control without sacrificing closed-loop stability. At each sensor/control node:

• Error Definition: $e(t) := y_k - y(t)$, quantifying deviation between held output and true plant output.
• Event-Triggered Policies: Transmission is triggered only when

$\|e(t)\| \geq \sigma\|x(t)\|$

or the Lyapunov dissipation rate falls below a specified threshold $-\gamma_x|x|^2$. This balances reduced communication with robustness (Forni et al., 2013).

There are two principal policies:

• State-Available Policy: If $x_p$ is known, transmission triggers on error–state norm ratios.
• Observer-Based Policy: If only output feedback is available, a Luenberger observer provides state estimates; the triggering uses estimated state $\hat x_p$.

3. Closed-Loop PID and Hybrid Control Strategies

In wireless TXP control, event-triggered frameworks are implemented via discrete-time PID controllers:

$$\Delta TXP[k] = K_p\,e[k] + K_i\sum_{i=0}^{k}e[i] + K_d (e[k] - e[k-1])$$

The control variable may be RSSI or throughput:

• RSSI-based PID: Provides rapid adaptation to signal fluctuations.
• Throughput-based PID: Offers accurate rate control but slower responsiveness.
• Hybrid Architecture: A cascaded dual-loop combines the advantages: the outer loop (throughput) determines RSSI set-points; the inner loop (RSSI) rapidly regulates TXP to maintain RSSI at target (Zhou et al., 6 Jan 2026).

Table: Response Characteristics of Closed-Loop TXP Control Methods (0–50m tests) (Zhou et al., 6 Jan 2026)

Method	Mean RSSI (dBm)	Mean Throughput (kbps)	Recovery Time
RSSI-based	–58.5	–	150 ms
Throughput-based	–51.5	781.1	3 s
Hybrid	–50.6	788.3	150 ms

4. Stability Analysis and Guarantees

Closed-loop TXP architectures employ Lyapunov (or related) stability arguments to ensure robust convergence:

• Lyapunov-Based Guarantees: A quadratic Lyapunov function $V(x,e)$ is constructed such that it decreases on system "flows" and jumps, ensuring global asymptotic—and under rank conditions, exponential—stability (Forni et al., 2013).
• Tube-Based Predictive Control: In data-driven settings, robust Tube-Based Zonotopic Predictive Control (TZPC) computes invariant "tubes" around nominal trajectories using matrix-zonotope approximations of dynamics and additive disturbance sets. MPC optimizations are solved over tightened constraints guaranteeing recursive feasibility and robust exponential stability (Farjadnia et al., 2024).
• Hybrid Control Responsiveness: In BLE wireless control, hybrid PID architectures balance rapid recovery (sub-150 ms to 20 dB drops) with steady-state throughput regulation (within 5% target), precluding Zeno phenomena by enforcing minimum dwell-times and bounded transmission updates (Zhou et al., 6 Jan 2026).

5. Design Guidelines and Practical Implementation

Closed-loop TXP control allows explicit trade-offs between performance, resource consumption, and robustness. Notable practices include:

• Parameter Selection: For sampling-based TXP: choose $\gamma_x$ for desired decay/convergence rate, and $\sigma$ as large as feasible while maintaining Lyapunov dissipation (Forni et al., 2013).
• PID Control Gains: RSSI-loop $K_p \in [0.1, 0.3], K_i$ low to manage overshoot/speed; throughput-loop $K_p \approx 0.005$–$0.01$, $K_d \approx 10^{-4}$–$10^{-3}$ (Zhou et al., 6 Jan 2026).
• Update Frequencies: RSSI at high frequency (100 Hz), throughput at lower frequency (1 Hz) for noise management.
• Implementation: On Nordic BLE hardware, hybrid TXP control achieves up to 60% energy savings versus fixed maximum TXP, adapts robustly to diverse channel conditions, and is compatible with mesh/multi-node topologies.
• Planning Substitutions: In advanced symbolic/robotic TXP settings, replace video diffusion with LLM-based planners, embed symbolic states, and adapt error quantification for closed-loop replanning (Bu et al., 2024).

6. Extensions and Contextual Variants

TXP frameworks generalize across domains:

• Wireless Communication: TXP for BLE and similar systems, employing RSSI and throughput as control signals.
• Networked Control Systems: Transmission-lazy sampling for linear (and linear–observer) plant–controller interconnections over rate-limited, unreliable channels.
• Robotic Planning: Closed-loop planners quantify embedding–goal error, use symbolic planners, and hybridize with low-level feedback policies.
• Data-Driven Predictive Control: Tube-based zonotopic predictive control applies set-theoretic disturbance compensation for learned models with noisy data (Farjadnia et al., 2024).

A plausible implication is that advances in symbolic embedding and error quantification using closed-loop principles can unify task-oriented robotic planning and resource-constrained networked control.

7. Summary of Impact and Recommendations

Closed-loop TXP control frameworks present a robust, parameterizable, and hybrid approach for maintaining system performance with minimal resource expenditure—whether in wireless communication, digital control, or symbolic planning settings. Key features include global (and exponential) stability guarantees, adjustable performance–resource trade-offs, and prevention of pathological behaviors (e.g., Zeno phenomena). These architectures enable responsive, scalable, and resource-efficient control adaptable to highly dynamic or mission-critical environments (Forni et al., 2013, Zhou et al., 6 Jan 2026, Farjadnia et al., 2024, Bu et al., 2024).

For practitioners: select event-triggering and controller designs tuned to required response latency and steady-state performance; use hybrid strategies for high dynamism or robustness; and adapt embedding/error quantification methodologies for planning-based implementations.