Learning event-triggered controllers for linear parameter-varying systems from data

arXiv:2506.08366 · eess.SY, cs.SY · Submitted 2025-06-10 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Learning event-triggered controllers for linear parameter-varying systems from data".

Dev: The gist: This paper develops data-driven control strategies for event-triggered linear parameter-varying (LPV) systems, providing theoretical analysis and stability verifications that bypass complex model knowledge.

Rosa: First, who's behind it and why it matters.

Title and authors: Rosa: So we’re looking at this paper called "Learning event-triggered controllers for linear parameter-varying systems from data." It basically shows how you can build a control strategy for these complex LPV systems without needing to know the exact internal model of the system beforehand.

Dev: Right, so it focuses on using collected data to figure out how to control these things, which sounds really useful when you don't have perfect mathematical descriptions available.

Taro: I’m interested in how it handles when things go wrong, like external perturbations that are always there in the real world. Does this approach give us a handle on those disturbances?

Rosa: Well, the core idea is developing data-driven control for event-triggered LPV systems with stability verifications. They start by looking at a condition called theta-persistence of excitation for LPV systems, which tells you the minimum amount of data you need before you can even start doing this kind of analysis.

Dev: So, that theta-persistence of excitation condition seems to be the first big hurdle they tackle; it sets a baseline for how much data we need to collect before we can rely on this method.

Taro: If you have that condition, what does that actually let us do? Can we just plug the data into a controller right away, or is there still a lot of heavy math involved?

Rosa: They use that condition to find feasible data-based representations of the system first, and then they derive stability certificates for event-triggered LPV systems using tools like Petersen’s lemma in the sense of robust control.

Dev: So they are using these lemmas and these matrix techniques to turn the data into something concrete, like those computationally tractable semidefinite programmings that give us optimal gain schedulings.

Taro: That sounds a bit heavy for something we might try on a mobile robot or something small-scale; how does this abstract mathematical framework actually translate into real-time performance?

Rosa: The paper then goes on to three main control problems, including deriving stability certificates for the data-based LPV closed-loop representation under bounded external perturbations.

Dev: And they specifically focus on incorporating event-triggered communication, which means the control input only updates when something significant happens in the data stream.

Taro: When you introduce triggering parameters into those stability certificates, what does that actually change about how we think about system reliability or safety?

Rosa: They show that if certain matrix inequalities hold for a specific data set D s, then the event-triggered LPV system is practically exponentially ISS.

Dev: That ISS guarantee, when tied to the data set and those inequalities, means they are proving some kind of stability bound even when dealing with noise or disturbances present in the measured data.

Taro: I wonder about tracking; if we're just stabilizing, that’s one thing, but what about keeping the system locked onto a desired output reference as well?

Rosa: For tracking, they extend this by constructing an auxiliary integral compensator to create an augmented LPV system, which then allows them to derive stability certificates for a data-driven event-triggered LPV tracking controller.

Dev: So they’ve built something that handles both stabilizing the system and keeping it following a target signal simultaneously using that same data-driven approach.

Taro: What’s the practical implication for someone who just listens to this show—what does this mean for their day-to-day work with autonomous systems?

Rosa: It suggests that you don't necessarily need a perfect, pre-defined model of the system to develop a controller; you can learn and control it directly from experimental data.

Dev: The method provides concrete procedures: first, determine the required data length using that theta-persistence of excitation criterion; second, find the feasible solutions for those theorems to get your decision variables like P, F Q and constant beta one; and third, use Theorem four to verify the stability.

Taro: So it’s a structured workflow: identify what you need from data, solve the optimization problem derived from that data, and then verify the resulting controller.

Rosa: Exactly; they finish by deploying the resulting data-based event-triggered LPV controller and testing it in three simulations: a circle reference, a one-dimension tracking scenario, and a plane output tracking scenario.

Dev: The simulations show how the state responds to these controllers and what those inter-event intervals look like when you are doing both stabilization and tracking.

Taro: So it’s not just theory on paper; they showed that this approach works in practice across different types of reference problems, which is a big step for autonomy.

Rosa: It's definitely a solid demonstration of how data-driven methods can handle the complexity inherent in LPV systems without needing perfect prior knowledge.

Dev: It’s about finding those convex programmings that are solvable, even when dealing with the uncertainty introduced by external perturbations in the data.

Taro: This whole paper, "Learning event-triggered controllers for linear parameter-varying systems from data," seems to be a step toward making control design much more adaptable to real-world conditions where models are messy.

Rosa: It really is; it lays out a path from raw data to a guaranteed stable, event-triggered controller that handles tracking too.

Dev: We’ll leave it there for now, but keep an eye on how these stability certificates translate into actual hardware implementation constraints.

The paper's summary: Rosa: So, this paper is all about taking raw data and using that to build a controller for these LPV systems without needing a perfect mathematical blueprint of what they are doing inside.

Dev: Exactly, so they’re bypassing the whole modeling headache by letting the data itself tell them how to control it in real-time.

Rosa: They start with this idea of theta-persistence of excitation, which is essentially figuring out how much data you actually need before you can even begin building a reliable control strategy for these variable systems.

Dev: That condition sets the baseline, right? It tells us the minimum amount of data we have to collect to make this whole data-driven approach even possible.

Rosa: Once they have that foundation, they use tools like Petersen’s lemma and S-procedures to turn that collected data into actual stability certificates for the closed-loop system.

Dev: So instead of just guessing a controller, they use these matrix techniques to generate convex programming problems that we can actually solve.

Rosa: And what they’re solving is finding the right scheduling signal—basically, figuring out when and how to apply the control action based on what’s happening in the data stream.

Dev: That means they can find a data-based control law, which is something you could deploy on a system that's changing constantly.

Rosa: They also tackle event-triggered communication here—meaning the system only sends updates when necessary, which saves bandwidth and processing power in the field.

Dev: And for tracking, they build an extra component called an integral compensator to make sure the system doesn't just stabilize but actually follows a desired reference signal.

Rosa: The big implication is that we can design controllers for these complex systems using only what we measure, which is huge for things like autonomous vehicles where you can't always get a perfect model.

Dev: It’s about moving from needing a detailed mathematical description to just needing enough good data to make the system behave correctly.

Rosa: This whole process, from collecting the right amount of data to verifying the stability of that event-triggered controller, gives us a structured way to handle these systems in messy real-world scenarios.

Dev: It shows that with enough smart math and enough sensor data, we can get a controller running even when things are changing unpredictably.

Rosa: We’ve seen how they test this on a circle reference, tracking one dimension, and even plane tracking scenarios in simulations to show it works across the board.

Dev: Those simulations give us a sense of the actual response time and how often those events trigger in practice, which is important for latency concerns.

Rosa: So, it’s not just about proving stability on paper; they actually showed how this data-driven approach performs in these varied scenarios.

Dev: This opens up a new way to think about control design where the complexity of the system doesn't automatically mean we need an impossibly complex model upfront.

Rosa: Next time, we’ll look at how these stability guarantees hold up when there are actual external disturbances and perturbations messing with the data measurements.

The paper's improvements: Rosa: We just talked about how this paper uses data to build a controller for these shifting LPV systems, and now we’re going to look at what they suggest as improvements to that process.

Dev: So, what are the actual suggested fixes or next steps in their methodology? I want to know if there’s a way to make this even more robust for real-world deployment.

Rosa: Well, one major improvement is how they handle the uncertainty from external perturbations; they explore ways to refine those stability certificates when the environment isn't perfectly predictable.

Dev: So you think there’s a better way to guarantee stability when things go sideways outside of just assuming a bounded perturbation? I need more concrete failure mode handling.

Rosa: They suggest focusing on how the system handles "noisy" data streams, basically making the trigger logic smarter so it reacts less to random spikes in sensor readings.

Dev: That makes sense for loop rate issues; if the triggering mechanism is too sensitive to noise, you’re just going to get jittery control signals.

Rosa: They also look at extending this idea into more complex scenarios where the system needs to track a reference signal, not just keep itself stable.

Dev: Tracking is harder than stabilization, especially with event-triggered systems; how do they manage the increased complexity of keeping that output locked onto a target?

Rosa: For tracking, they propose adding an extra component, an integral compensator again, but they refine how that compensation interacts with the data-driven scheduling.

Dev: So it’s not just slapping on a standard tracking term; it's integrating the tracking error directly into the data-based control law structure.

Rosa: That means the controller is actively learning to compensate for both internal system dynamics and external disturbances at the same time.

Dev: That sounds like a significant step toward handling more dynamic, unpredictable systems in hardware, which is exactly what I need to hear for loop stability.

Rosa: The authors also touch on how this approach might be adapted if the underlying LPV parameters themselves were changing in a very complex way, not just bounded variations.

Dev: If the parameters are shifting faster than they can be captured by that data set, does this method still hold up? I’m worried about the "data set" becoming outdated too fast.

Rosa: They suggest looking at how the required data length scales with how fast those LPV parameters are changing; it gives a hint on how much more monitoring you’ll need.

Dev: So it provides a practical guideline for data collection planning, which is useful for someone actually deploying this controller on a remote robotic platform.

Rosa: It’s about giving the field engineer a checklist: check your data rate against the system's parameter variation rate to make sure you don't run out of reliable information.

Dev: That moves it from just being a theoretical tool to something with some actionable engineering constraints, which is what I really want to see.

Rosa: So the next big thing here is applying these refined stability certificates to physical hardware testing under realistic, noisy conditions.

Conclusion: Rosa: So we've gone through how this paper, "Learning event-triggered controllers for linear parameter-varying systems from data," uses collected data to build a robust controller without needing a perfect model.

Dev: Right, it’s about turning experimental measurements into actual control actions via these structured mathematical proofs.

Rosa: The big picture is that we can design systems for things like autonomous robots where the physical parameters are always changing or uncertain, just by learning from what the robot actually experiences in the field.

Dev: I still have to worry about the loop rate and latency; how fast this data-driven decision-making happens when you’re driving something that needs rapid response?

Rosa: They do address that in their methodology by deriving conditions on data collection length, which gives us a hint on how much time we need for those decisions.

Dev: So it’s not instant control; it requires a minimum amount of historical data to ensure the stability certificates hold up during the decision-making delay.

Rosa: That’s the caveat—it’s not magic, you still have to collect enough information upfront for that analysis to be valid.

Dev: It changes things because it makes the required data collection a necessary part of the control design process, not just an afterthought.

Rosa: For autonomy research, this means we can build systems that adapt their control strategy based on real-time sensory input rather than being locked into a fixed set of rules.

Taro: I think what’s most interesting is how they handle the tracking problem alongside stabilization; it shows the same data-driven framework can manage both keeping things stable and following a specific target.

Dev: It’s good to see that complexity handled in one package, but I still want to see how this plays out when the environment misbehaves unexpectedly, outside of these controlled simulations.

Rosa: That’s where we need to look next—testing these controllers in messy, real-world environments where the data quality might be inconsistent or the system dynamics are even more volatile than they assumed.

Taro: I'm curious if this data-driven approach could be used to create more resilient autonomous agents that can self-correct their control laws during unexpected failures.

Dev: Well, yeah, that’s the goal, but for now we have to stick to verifying these stability certificates under the specific conditions they laid out in "Learning event-triggered controllers for linear parameter-varying systems from data."

Rosa: It’s a solid piece of work showing how data can replace some of the hard modeling work in control design.

eess.SY, cs.SY

Submitted: 2025-06-10

Updated: 2026-10-09

Comments: 15 pages, 5 figures

Code: https://github.com/Renjie-Ma/Learning-EventTriggered-Controller-LPV-Systems-From-Data

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 76/100

The gist: The gist: This paper develops data-driven control strategies for event-triggered linear parameter-varying (LPV) systems, providing theoretical analysis and stability verifications that bypass complex

Key concepts

$\theta$-persistence of excitation condition: This is a prerequisite for applying data-driven control to LPV systems. It defines the smallest amount of collected data required so that the system's behavior can be reliably analyzed and controlled using only that data, ensuring the feasibility of the data-based representations.
Data-based representation: Instead of knowing every parameter exactly, this method describes an LPV system using matrices derived directly from collected input/output data. This allows control design to proceed even when the exact system parameters are unknown or changing over time.
Event-triggered communication: This scheme modifies standard control by only transmitting data or performing computations when a specific trigger condition is met, rather than continuously. This reduces communication load while maintaining stability guarantees for the LPV system.

Terminology

Verification — 1× in this paper · explained in 2 episodes

Summary

The gist: This paper develops data-driven control strategies for event-triggered linear parameter-varying (LPV) systems, providing theoretical analysis and stability verifications that bypass complex model knowledge.

Theoretical Foundation and Prerequisites

The work first establishes a prerequisite for data-driven control of perturbed LPV systems by exploring the θ-persistence of excitation condition for LPV systems which reveals the smallest value of the length of collected data as a prerequisite for data-driven analysis and control (Page 1). This condition is derived using Petersen’s lemma in the sense of robust control, resulting in computationally tractable semidefinite programmings that yield optimal gain schedulings (Page 1). The authors also provide a theoretical analysis of θ-persistence of excitation for LPV systems, which leads to the feasible data-based representations (Page 1).

Data Representation and Stability Certificates

The system is formulated using a data-based representation where the LPV system (3) is described by X+ =AdZ +BdU +W, Y =CdZ +DdU, based on collected data matrices Ds (Page 2). The authors utilize techniques such as linear fractional transformation, full-block matrix S-lemma, Petersen’s lemma, Young’s inequality relaxation, and Farkas’s lemma to obtain data-dependent performance certificates of closed-loop systems (Page 2). These methods lead to either semidefinite programmings or sum-of-squares programmings whose feasibility implies an available data-driven control strategy (Page 2).

Control Synthesis for Stabilization and Tracking

The paper addresses three main problems:

For the data-based LPV closed-loop representation with the bounded specification of external perturbations, it derives data-based stability certificates and implements convex programmings feasible at the vertices of the polytopic set of scheduling signal (Page 2).
By deploying event-triggered communication, it incorporates triggering parameters into data-based stability certificates to develop a data-driven event-triggered LPV controller (Page 2).
For extending stabilization to robust tracking, it constructs an auxiliary integral compensator leading to augmented LPV systems and derives the corresponding stability certificates for developing the data-driven event-triggered LPV tracking controller (Page 2).

The state-feedback control strategy is designed as uk = Kd(pk)xk, where Kd: P 7→Rm×n has an affine-dependent form (Page 3). The resulting closed-loop dynamics are formulated with the form xk+1 =N Col(zk, pk⊗pk⊗xk)+ωk (Page 3).

Event-Triggered Communication Scheme and Robustness

The paper develops an event-triggered communication scheme where the control input is depicted by uk=Kd(pkˆi)xkˆi, k∈N[kˆi,kˆi+1) (Page 7). The closed-loop LPV system is rewritten in the data-based form as xk+1 = (X+−Wc)VCol(zk, pk⊗pk⊗xk)+νk+ωk (Page 7). The triggering logic is specified by the form ˆki+1 =inf n k > ˆki ν⊤k Ψ1νk ≥ x⊤k Ψ2xk + v o (Page 7).

The authors establish that for the event-triggered LPV system (37) together with the data set Ds, if there exist µ, ε2 ∈ R+ and Ψ1, Ψ2∈S n++, such that a specific matrix inequality (39) holds, then the system is practically exponentially ISS (Page 7). This stability guarantee is achieved by reducing the problem to a finite number of constraints using Theorem 4 (Page 8).

Application on Reference Tracking

The theoretical results are extended to the scenario of output reference tracking by defining an auxiliary state χk∈Rr with the form χk+1=χk+(yk−rk) (Page 9). This leads to an augmented LPV system expressed as ψk+1=Abd(pk)ψk+Bbd(pk)uk+Ebd(pk)̟ k (Page 9). The authors establish that for the event-triggered LPV system (67), if there exist µ, εˆ4 ∈ R+ and Ψb 1, Ψ2∈S n¯++, such that a specific matrix inequality (71) holds, then the system is practically exponentially ISS (Page 9).

The paper concludes by presenting a procedure for robust stabilization:

Construct the data-based description of event-triggered LPV system (37) and determine the length T of collected data in terms of θ-persistence of excitation criterion in Lemma 1 (Page 8).
Seek for the feasible solution of Theorem 2 and obtain the available decision variables P, FQ and constant β1 (Page 8).
Calculate the feasible solution of Theorem 4 and verify the stability of event-triggered LPV systems (37) (Page 8).
Deploy the data-based event-triggered LPV controller (34) (Page 8).

The paper also includes numerical simulations to verify the effectiveness of these theoretical derivations in three examples: a circle reference, a one-dimension output tracking scenario, and a plane output tracking scenario (Page 11). The simulation results illustrate the state responses and inter-event intervals of event-triggered LPV systems actuated by data-driven controller (34) for both stabilization and tracking cases (Page 13).

References

[1] J. Mohammadpour and C. W. Scherer, Control of Linear Parameter Varying Systems with Applications. Springer Science & Business Media, 2012 (Page 13).

[2] T. Martin, T. B. Sch¨on, and F. Allg¨ower, ”Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey”, Annual Reviews in Control, vol. 56, num. 100911, 2023 (Page 13).

[3] X. Ping, J. Yao, B. Ding, and Z. Li, ”Tube-based output feedback robust MPC for LPV systems with scaled terminal constraint sets”, IEEE Transactions on Cybernetics, vol. 52, no. 8, pp. 7563-7576, 2022 (Page 13).

[4] A. P. Pandey and M. C. de Oliveira, ”A new discrete-time stabilizability condition for linear parameter-varying systems”, Automatica, vol. 79, pp. 214-217, 2017 (Page 13).

[5] A. N. Vargas, C. M. Agulhari, R. C. L. F. Oliveira, and V. M. Preciado, ”Robust stability analysis of linear parameter-varying systems with Markov jumps”, IEEE Transactions on Automatic Control, vol. 67, no 11, pp 6234-6239 (Page 13).

[6] P. B. Cox, S. Weiland, and R. T´oth, ”Affine parameter-dependent Lyapunov functions for LPV systems with affine dependence”, IEEE Transactions on Automatic Control, vol. 63, no. 11, pp 3865-3872 (Page 13).

[7] J. A. Gallegos and K. A. Barbosa, ”Set-theoretical stability analysis of LPV systems via Minkowski-Lyapunov functions”, IEEE Transactions on Automatic Control, DOI: 10.1109/TAC.2024.3441325 (Page 13).

[8] S. K. Mulagaleti, M. Mejari, and A. Bemporad, ”Parameter-dependent robust control invariant sets for LPV systems with bounded parametervariation rate”, IEEE Transactions on Automatic Control, DOI: 10.1109/TAC.2024.3454528 (Page 13).

[9] J. Cheng, M. Wu, F. Wu, C. Lu, X. Chen, and W. Cao, ”Modeling and control of drill-string system with stick-slip vibrations using LPV technique”, IEEE Transactions on Control Systems Technology, vol. 29, no 2, pp 718-730 (Page 13).

[10] P. Polcz, B. Kulcsar, T. Peni, and G. Szederkenyi, ”Passivity analysis of rational LPV systems using Finsler’s lemma”, in IEEE 58th Conference on Decision and Control, pp 3793-3798 (Page 13).

[11] C. E. de Souza, K. A. Barbosa, and A. T. Neto, ”Robust H∞ filtering for discrete-time linear systems with uncertain time-varying parameters”, IEEE Transactions on Signal Processing, vol 54, no 6, pp 2110-2118 (Page 13).

[12] G. Cai, T. Wu, M. Hao, H. Liu, and B.

Improvements for AI systems

Data-driven control synthesis for perturbed LPV systems allows for developing control strategies directly from data, bypassing complex modeling processes which is crucial for real-world applications like autonomous vehicles or hypersonic aircrafts [1].
The method establishes the condition of θ-persistence of excitation for LPV systems, which acts as the prerequisite of direct data-driven LPV control synthesis, providing a necessary benchmark for data collection length [1].
The derived stability certificates, obtained by Petersen’s lemma and full-block S-procedure, lead to computationally tractable convex programming solvable at the vertices of the polytopic set of scheduling signal, enabling data-based LPV control synthesis [2].
The event-triggered communication scheme allows for refining communication efficiency by using a triggering logic based on the sequence of transmission instants and the resulting error term, which is embedded in the data-based representation [10].
For reference tracking, an auxiliary integral compensator is developed to construct an augmented LPV system, enabling the synthesis of a data-driven event-triggered LPV tracking controller for systems where the output converges to a desired signal [12].