Change-Triggered INT in Control and Telemetry

• Change-triggered INT is a mechanism that uses threshold-based events to trigger intermittent control actions, event-driven telemetry, and plasma instability detection.
• It employs rigorous event laws, including delta change and Lyapunov/Barrier triggers, to ensure stability, safety, and resource efficiency in complex systems.
• Applications span hybrid control systems, in-band network telemetry, and plasma confinement, providing scalable solutions with reduced actuation and processing overhead.

Change-triggered INT (Intermittent Control, Event-based Network Telemetry, and Mode Instabilities) denotes a class of strategies and mechanisms that leverage detected changes—state transitions, signal thresholds, or confinement shifts—to trigger discrete events: the activation or deactivation of control input, the emission of network telemetry, or the onset of physical instabilities. This paradigm is employed within hybrid control, networked systems, and plasma physics to optimize resource usage, guarantee safety or stability properties, ensure scalability, and capture non-steady phenomena beyond periodic or steady-state analysis.

1. Fundamental Principles of Change-Triggered INT

Change-triggered INT architectures eschew periodic or uniformly event-driven actuation in favor of event laws or predicates contingent upon evolving system indicators. In event-triggered control, actuators apply feedback only upon specified state-dependent conditions, sometimes including explicit OFF periods. In programmable telemetry (in-band INT), events in the data plane drive the sampling and reporting of network metrics. In plasma confinement, changes in system rotation and transport can transiently lower thresholds for disruptive instabilities.

The key principles are:

• State- or change-dependent triggers: Activation and deactivation events are determined by measurable changes, such as threshold crossings in state, signal deltas, sampled errors, or transitions in plasma confinement (Ong et al., 2022, Vestin et al., 2019, Lei et al., 2023, Ghodrat et al., 2019).
• Intermittent/conditional control and reporting: Instead of continuous feedback or uniform sampling, resources are deployed only when indicators suggest performance or safety margins are at critical levels (Ong et al., 2022, Lei et al., 2023).
• Performance and stability/safety guarantees: Event laws are typically designed to maintain Lyapunov or barrier conditions, bounded error or disturbance influence, and to exclude Zeno (infinite event density) via dwell-time protections (Ong et al., 2022, Ghodrat et al., 2019, Lei et al., 2023).
• Scalability and efficiency: Change-triggered INT in telemetry scales to higher packet rates and reduces load by pre-filtering, while in control it saves actuation energy/fuel (Vestin et al., 2019, Lei et al., 2023).

2. Mathematical Event Laws and Trigger Conditions

Change-triggered INT schemes utilize rigorously defined predicates and dynamic thresholds, typically expressed via:

Trigger Type	Formal Expression	Context / Application
Counter Threshold	$E_i(f) = [C_i(f) > T_i]$	INT reporting (network)
Delta Change	$$\Delta X(f) = |X_{current}(f) - X_{prev}(f)| > \theta$$	INT reporting / Control
Moving Average	$$M_n(f) = \alpha X_{current}(f) + (1-\alpha)M_{n-1}(f)$$;	INT / Control
Lyapunov Trigger (Stability)	$$\sigma_{off}(t) = L_fV(x(t),e^{on}(t)) +(1-\sigma)\alpha(\|x(t)\|)$$; $$t^{off}_i = \min\{ t > t^{on}_i | \sigma_{off}(t) = 0, t^{on}_i + T_{max} \}$$	Intermittent control
Barrier Trigger (Safety)	$$t^{off}_i = \min\{ t > t^{on}_i | \dot h(x,e^{on},t) = -\omega(h(x,t)) + \theta d, t^{on}_i + T_{max} \}$$	Safety-critical control
Composite (ON/OFF)	See $t^{act}_k, t^{on}_{k+1}$ in (Lei et al., 2023)	Constrained spacecraft attitude

These triggers ensure feedback or reporting only when quantified conditions justify intervention, thereby reducing unnecessary effort and preserving stability/safety envelopes.

3. Implementation in Control Systems: Intermittent and Event-Triggered Control

In control applications, change-triggered INT formalizes ON/OFF switching of the controller or actuators:

• Architecture: The plant dynamics $\dot{x} = f(x,u)$ are controlled via a feedback law $u = k(x)$, implemented only in ON intervals $[t^{on}_i, t^{off}_i)$, while OFF intervals set $u=0$ (Ong et al., 2022, Lei et al., 2023).
• Lyapunov-based design: Stability is guaranteed via Lyapunov functions $V(x)$ and explicit OFF/ON triggers. During ON, $V$ strictly decreases; during OFF, $V$ must remain below a time-varying bound $S(t)$ (Ong et al., 2022).
• Barrier-based design: Safety is ensured via barrier functions $h(x, t)\geq 0$, with triggers designed to preserve set invariance (Ong et al., 2022).
• Composite control: Backstepping provides cascaded subsystem control; the event mechanism incorporates sampling error and rate tracking bounds, cascaded with saturation and disturbance compensation (Lei et al., 2023).
• Guarantees: The approach avoids Zeno phenomena via imposed dwell times $T_{max}$ and decaying or positive thresholds.

Numerical results indicate large reductions in actuator firings versus periodic control (e.g., 32 vs. 150 firings over 150 s for spacecraft attitude, with comparable tracking error) (Lei et al., 2023).

4. Applications in In-Band Network Telemetry (INT)

Change-triggered INT in networking denotes event-driven emission of telemetry reports instead of per-packet sampling:

• Programmable event detection: Using P4, an SDN controller installs per-flow rules to select trigger predicates (threshold, delta, moving average) and required metadata collection (Vestin et al., 2019).
• Data-plane execution: Each switch maintains per-flow registers for previous counters and threshold values; triggers are checked, reports emitted only on significant changes (Vestin et al., 2019).
• Conditional header stamping and emission: INT headers are attached only when events are detected; non-event packets are stripped and forwarded (Vestin et al., 2019).
• Backend integration: AF_XDP enables high-rate collection, and reports are streamed to Kafka for scalable analytics. Effective thresholding and smoothing parameters can provide 10–35× capacity increases for the monitoring backend (Vestin et al., 2019).
• Formal predicates: Counter-based, delta, or moving-average rules are the principal mechanisms, enabling highly customizable and efficient reporting.

5. Plasma Physics: Change-Triggered Instability Thresholds

In plasma confinement, notably in tokamak operation, change-triggered phenomena are critical in locked mode (LM) and error field (EF) penetration analyses:

• Mechanism: During confinement transitions (L–H), the natural rotation frequency of critical tearing modes collapses rapidly (from ≈10 kHz to ≈1 kHz within 1 ms), lowering the EF penetration threshold by a factor of two relative to steady state (Peterka et al., 2024).
• Threshold criterion: For COMPASS Ohmic plasmas, steady-state thresholds obey $$n_{e,crit}[10^{19} m^{-3}] \simeq 1.0\cdot on=1[10^{-4}] - 2.1$$. Change-triggered penetration occurs whenever $on=1_{transient} \gtrsim 4\times 10^{-4}$, independent of $n_{e}$ or NBI torque (Peterka et al., 2024).
• Locking processes: Sawtooth-induced 2/1 islands may lock even below penetration threshold if seeded during rotation reversal, accounting for ≈30% of observed disruptions post-L-H transition in COMPASS (Peterka et al., 2024).
• Implications: Conventional EF-correction strategies that use steady-state parametric fits systematically underpredict LM risk during non-steady phases, mandating active control precisely around transition windows (1–5 ms post-change) in future devices (e.g., ITER) (Peterka et al., 2024).

6. Composite Trigger Designs and Guarantees of Minimum Inter-Event Time (MIET)

Event-triggered designs with additional dynamic state variables and composite thresholds deliver robust guarantees:

• General framework: Triggering rule $$\Phi(t) = \phi(x(t),e(t)) - [k_1\varphi_1(t) + k_2\varphi_2(t)] = 0$$, where dynamic variables $\varphi_1, \varphi_2$ evolve to enforce enlarged minimum inter-event times and Lₚ-gain performance (Ghodrat et al., 2019).
• Algorithmic prescription: Initializations for $\varphi$ and decaying thresholds ensure that triggering does not occur more frequently than computed dwell-time bounds $\tau_m = \min\{\tau_*(1), \hat{\tau}\} > 0$ (Ghodrat et al., 2019).
• Performance: For a quadratic Lyapunov-based design, sampling rates are reduced (samples per second drop from ≈18.7 Hz to ≈3.25 Hz; MIET increases from ≈1.8 ms to ≈22 ms), with preserved asymptotic or finite-gain stability (Ghodrat et al., 2019).

7. Context, Trade-offs, and Implementation Considerations

Change-triggered INT mechanisms offer substantial trade-offs:

• Resource savings: The opportunity for extended OFF intervals yields lower energy or actuation burden in control, and lower CPU and disk load in networked telemetry (Ong et al., 2022, Vestin et al., 2019, Lei et al., 2023).
• Flexibility and customizability: Per-flow or per-subsystem thresholds are programmable, enabling fine-tuned responsiveness and selectivity (Vestin et al., 2019, Lei et al., 2023).
• Stability and safety: Lyapunov and barrier functions ensure invariance and robustness under both intermittent control and networked feedback scenarios (Ong et al., 2022, Ghodrat et al., 2019).
• Prevention of pathological behavior: Explicit dwell-time and threshold design nominally prevent Zeno execution and ensure ultimate boundedness in constrained control (Lei et al., 2023, Ghodrat et al., 2019).
• Limitations and challenges: Change-triggered thresholds can miss fast perturbations if thresholds are too high, or may yield slower convergence or tighter residual errors if dwell-times are maximized. In plasma systems, parametric fits from steady-state experiments may substantially misrepresent risk during transitions, necessitating dedicated change-phase studies (Peterka et al., 2024).

Change-triggered INT is a rigorously developed, highly adaptable paradigm that spans control theory, network monitoring, and plasma physics, leveraging system events for optimal intervention with formal theoretical guarantees.