Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability

arXiv:2510.25452 · math.OC, cs.SY, eess.SY · Submitted 2025-10-29 · 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: "Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability".

Dev: Data-driven stabilization of linear time-invariant systems using prior knowledge on stabilizability and controllability addresses how incorporating system-theoretic properties can simplify or alter data requirements for finding stabilizing feedback laws.

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

Title and authors: Rosa: Welcome back everyone. Today we're discussing a really interesting paper by Shakouri and van Waarde titled "Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability." It looks like they've put together a framework for using what we already know about a system's structure, specifically its stabilizability and controllability, to make data-driven control less demanding.

Dev: I agree, Rosa. The title itself suggests that incorporating these system properties into the data-driven stabilization process can simplify things or change the requirements we need to collect. It’s about moving beyond just looking at the raw input-state data and using some structural context to guide the design of a stabilizing feedback law.

Taro: From an autonomy perspective, this is huge because it means we don't have to wait for perfect system identification before we can start controlling things in the real world. If we know a system is stabilizable, that gives us a solid foundation even when our initial measurements are sparse or noisy.

Rosa: Exactly. The paper really digs into formalizing this by defining "data informativity" as the existence of a controller that stabilizes every system consistent with the collected data and the prior knowledge we're using. It sets up this framework nicely by showing how to check if that informativity exists using Linear Matrix Inequalities, which is super practical for implementation.

Dev: That formalization is key because it translates these abstract system properties into concrete mathematical conditions involving matrices like X and Theta. The necessary condition they find—that the rank of X minus equals n, meaning we need at least n data samples—is a baseline requirement that must be met regardless of what prior knowledge we use.

Taro: But the real meat comes when they look at controllability versus stabilizability. They show that if you prioritize controllability as prior knowledge, it actually doesn't change the conditions needed for stabilization compared to having no prior knowledge at all. That’s a pretty surprising finding for someone focused on system structure.

Rosa: It really is surprising, Taro. Because I thought knowing a system is controllable would give us an extra advantage in data collection requirements, but the paper shows that it doesn't relax those conditions at all. However, when we swap controllability for stabilizability as the prior knowledge, things get interesting because those conditions become weaker.

Title and authors: Dev: That’s where the paper gets really useful for engineers because it suggests that if we know a system is stabilizable, we might need less data to guarantee stability than if we had no structural knowledge whatsoever. They state that using stabilizability as prior knowledge leads to necessary and sufficient conditions that are weaker than those for data-driven stabilization without any prior knowledge.

Taro: So, the implication here is that knowing the system has a stabilizing property gives us leverage when we're dealing with limited or imperfect data, which is exactly what happens when you try to control something in a messy environment. If the true system turns out to be stabilizable, our data requirements are less strict.

Rosa: That makes sense from a real-world perspective. Think about deploying a robot; if we know the actuator dynamics allow for stabilization even if we can't perfectly measure every internal state, that knowledge helps us design a more robust controller based on what we actually collect. This is the practical application I'm most interested in exploring with you guys.

Dev: From an engineering standpoint, the paper also gives us a way to actually compute the stabilizing feedback gain K using these LMIs when data is rank deficient, which means when our sensor measurements don't give us enough information about all states. That computational tractability is a big plus for deploying this in real-time control loops.

Taro: I wonder how long this works outside of a controlled lab setting, Rosa? Can we apply these requirements to systems where the true dynamics are only partially known or if the environment itself introduces uncontrollable modes? That’s where the real test of this framework will be.

Rosa: That's a great question for us to ponder. We need to see how this scales when we move from perfect simulation environments to physical systems with inherent uncertainties, like noise or unmodeled dynamics. It sounds promising, but proving its robustness in those messy real-world scenarios is the next big hurdle for any data-driven method.

Dev: I'm concerned about the loop rate implications if we are relying on these conditions derived from the paper to select our control parameters. If the required gain K depends heavily on rank deficiency or specific matrix structures, we need to ensure that our computation of K happens fast enough for high-frequency feedback systems.

Title and authors: Taro: Well, if we look at the context of other papers like Emulation-based Neuromorphic Control for the Stabilization of LTI Systems, it suggests that methods leveraging structural knowledge are trying to bridge the gap between idealized models and actual physical performance. This paper seems to be one step in that direction by formalizing how prior knowledge specifically impacts data requirements.

Rosa: I think the main implication here is a shift in focus: instead of just chasing more data points hoping for perfect system identification, we can strategically use known properties like stabilizability to define a much lower and more achievable bar for what our collected data needs to guarantee stability.

Dev: That's a significant methodological improvement if it holds up under rigorous testing because it allows us to design controllers even when the input-state data set isn't rich enough for traditional methods. It’s about using structure to compensate for information scarcity.

Taro: The impact could be on autonomous systems where initial system models are often poor or incomplete. If we can leverage stabilizability as prior knowledge, it opens up a much broader class of controllable physical scenarios that we can stabilize using data alone.

Rosa: So, to wrap up this discussion on "Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability," the key finding is that while controllability doesn't help relax the requirements for stabilization data, using stabilizability as prior knowledge does lead to necessary and sufficient conditions that are weaker than those without any prior knowledge when state data is rank deficient.

Dev: Essentially, this paper gives us a mathematical tool to design stabilizing feedback gains via LMIs even in low-information settings by leveraging structural information about the system. It’s a practical methodology for control systems engineers looking to deploy data-driven methods more reliably under realistic constraints.

Taro: For the future, I think we need more work on bounding the dimension of the reachable subspace and exploring how this framework handles noisy data scenarios, because that’s where real-world deployment will really happen.

Rosa: That sounds like a solid plan for future research. We'll keep an eye out for how this paper evolves as we try to implement these ideas in physical systems outside the lab environment.

Dev: I agree; the focus on tractability through methods like Proposition sixteen is what makes this work viable for high-frequency control applications, and we’ll be watching those advancements closely.

The paper's summary: Rosa: So, to recap, this paper shows that we can use prior knowledge about whether a system is stabilizable or controllable to make data-driven stabilization methods way more efficient or even possible under tricky conditions.

Dev: Exactly, Rosa; it’s about using structural information—like knowing a system *can* be stabilized—to set less demanding requirements on the actual measurements we collect. This shifts the focus from just collecting more data points to strategically using what we already know about the system's nature.

Taro: I find that really fascinating because it means that when our real-world sensors are giving us incomplete data, knowing the underlying system is stabilizable allows us to design a controller even when the raw input-state sequence isn't rich enough by itself. That speaks directly to autonomy in unpredictable environments where we can't always afford perfect measurements.

Rosa: It really does, Taro; and that’s where I get curious about its real-world applicability. If we deploy this on a physical robot or a complex process, how long do you think these stabilization guarantees hold up outside of a clean lab setting? We need to know if this is just theoretical stuff or something we can actually trust when the hardware gets messy and noisy.

Dev: That's the critical question for me, Rosa; I'm thinking about loop rates and failure modes. If the conditions derived from this paper require specific data ranks, we have to make sure our computation of that stabilizing gain K happens fast enough to keep up with a high-frequency feedback loop without introducing unacceptable latency or instability during the calculation itself.

Taro: From an autonomy standpoint, I'm pushing on what happens when the world misbehaves; if a system we're controlling suddenly enters a state where it’s no longer controllable, this paper suggests that knowing it was *stabilizable* gives us a pathway to maintain stability through judicious use of the collected data. It provides a safety net when our initial model assumptions about control authority break down.

Rosa: That safety net idea is compelling, Taro; and I'm also looking at the practical aspect of how this translates into concrete control law synthesis using LMIs; that tractability is what makes it appealing for implementation rather than just a theoretical exercise.

Dev: Right, the LMI formulation in Proposition sixteen gives us a way to compute K directly, which avoids those lengthy iterative identification procedures we usually have to run on the fly; that computational efficiency is something I really appreciate when designing real-time controllers.

Taro: So, if we look at the broader impact, this work suggests a new design philosophy where structural knowledge is treated as a fundamental input alongside the data itself, which could make building robust control systems for complex physical systems much more achievable.

Rosa: It sounds like a serious methodological improvement for anyone trying to build reliable control from limited information; we're definitely going to see how this framework meshes with the other papers we’ve been discussing on system identification and neuromorphic control.

The paper's improvements: Tom: So, to recap, this paper introduces specific mathematical improvements that allow us to synthesize stabilizing feedback laws by explicitly incorporating prior knowledge about system properties like stabilizability and controllability into the data collection requirements.

Rosa: That’s a really neat improvement because it shifts our perspective from just reacting to the data we get, to using fundamental system theory upfront to define what kind of data is actually useful for control. It’s like knowing the shape of the landscape before you start gathering samples.

Dev: I see how that helps with my job; if we can leverage those prior knowledge conditions, we might drastically reduce the amount of time and computational resources needed to find a stabilizing gain K, which directly translates to lower latency in deployment.

Taro: From an autonomy angle, this means our AI systems won't get stuck in dead ends when the environment presents unexpected dynamics; if we know our system is fundamentally stabilizable, we have a much better chance of achieving control even when the input data is sparse or noisy.

Rosa: And that ties back to my main concern about deployment outside the lab; if these conditions are met, it suggests that robust stabilization might be achievable over longer operational periods than we currently expect for purely data-driven methods.

Dev: Exactly; and regarding failure modes, the paper offers a more structured way to compute K using LMIs even when the state data is rank deficient, meaning we can handle those sensor limitations without having to fall back on much slower or less reliable estimation techniques.

Taro: I'm interested in how this interacts with the other papers on structural sign herdability; does this framework offer a way to predict system behavior based on these known properties before we even start collecting the data?

Rosa: That’s a good thought, Taro; and I think exploring those connections between prior knowledge and temporal network structures will be really important for understanding how these systems behave over time in dynamic scenarios.

Conclusion: Rosa: So, to wrap up our talk on "Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability," we've seen how using structural knowledge to guide data collection can make stabilization methods more efficient, especially when dealing with limited measurements.

Dev: Right, it’s a solid way to handle the practical constraints of real-world control systems by making the design process less demanding on our sensors and processing power.

Taro: I really think this work opens up a new avenue for autonomous systems where we have to operate in environments that are constantly changing and unpredictable, giving us a more resilient path to stability when things go wrong.

Rosa: It’s exciting to see how this moves control design from being purely data-dependent to something informed by the inherent physics of the system itself.

Dev: I agree; the tractability provided by those LMIs for computing gains is what makes this framework viable for fast, real-time applications, which is crucial when we’re dealing with tight loop rates.

Taro: I'm just thinking about how these structural sign herdability conditions might connect to the temporal network studies we've been looking at; it feels like a big piece of the puzzle.

Rosa: It certainly is; and that leads us nicely into thinking about how this kind of structural awareness could be integrated with other methods, maybe even those involving neuromorphic control we discussed earlier.

Dev: We definitely need to look at those integration points closely, especially concerning the latency implications when we combine these prior knowledge constraints with emulation-based design procedures.

Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen · Department of Mechanical Engineering, Eindhoven University of Technology

math.OC, cs.SY, eess.SY

Submitted: 2025-10-29

Updated: 2026-09-30

Comments: 8 pages, accepted for publication in IEEE Transactions on Automatic Control

DOI: 10.1109/TAC.2026.3740618

Code: https://github.com/TrenBaltussen/Data-Driven-Stabilization

Project page: https://henkvanwaarde.github.io/dblsct

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 72/100

The gist: Data-driven stabilization of linear time-invariant systems using prior knowledge on stabilizability and controllability addresses how incorporating system-theoretic properties can simplify or alter

Key concepts

Data Informativity: This concept measures whether the collected data allows for the existence of a controller that stabilizes all systems consistent with both the collected data and the given prior knowledge. It is formalized by an LMI condition, which implies a minimum number of data samples required to be informative.
Controllability Prior Knowledge: When controllability is used as prior knowledge, it does not change the conditions needed for data-driven stabilization. This means that if the system is controllable, using this fact as a prior piece of information does not make it easier or more difficult to find stabilizing feedback laws based on collected data alone.
Stabilizability Prior Knowledge: Using stabilizability as prior knowledge can significantly relax the conditions required for data-driven stabilization. Specifically, when state data is rank deficient, this knowledge leads to weaker necessary and sufficient conditions on the collected data compared to stabilization without any prior knowledge.

Terminology

System Identification — 8× in this paper · explained in 3 episodes
Regularization — 3× in this paper · explained in 3 episodes
Robustness — 3× in this paper · explained in 5 episodes
Closed-Loop System — 2× in this paper · explained in 4 episodes
Failure Modes — 2× in this paper · explained in 3 episodes
Computational Tractability — 1× in this paper · explained in 2 episodes
Core — 1× in this paper · explained in 2 episodes
European Research Council — 1× in this paper
Nonlinear Model Predictive Control (NMPC) — 1× in this paper · explained in 3 episodes
Trace — 1× in this paper · explained in 2 episodes

Summary

Data-driven stabilization of linear time-invariant systems using prior knowledge on stabilizability and controllability addresses how incorporating system-theoretic properties can simplify or alter data requirements for finding stabilizing feedback laws. The core finding is that while controllability as prior knowledge does not relax the conditions for data-driven stabilization, stabilizability as prior knowledge leads to necessary and sufficient conditions that are weaker than those required without any prior knowledge.

The gist

If the system is controllable, incorporating this as prior knowledge does not relax the conditions required for data-driven stabilization. Remarkably, however, we show that if the system is stabilizable, then using this as prior knowledge leads to necessary and sufficient conditions that are weaker than those for data-driven stabilization without prior knowledge.

Data Informativity Framework

The study extends the concept of data informativity by requiring the existence of a controller that stabilizes all systems consistent with the collected data and the prior knowledge. This is formalized by defining data informativity (Definition 1) as the existence of a gain K such that A+BK is Schur for all system matrices (A, B) in the set of data-consistent systems, ΣD. The necessary and sufficient LMI condition for this informativity is given by Proposition 2: there exists a matrix Θ such that X−Θ = Θ⊤X⊤− and X−Θ X+Θ/Θ⊤X⊤+ X−Θ > 0. This implies a necessary condition of rank X− = n, requiring the number of data samples to satisfy T ≥ n.

Prior Knowledge Incorporation

The problem is extended by considering prior knowledge sets, such as Σcont (controllable systems) and Σstab (stabilizable systems). The goal becomes finding a K such that A+BK is Schur for all (A, B) in the intersection of the data-consistent set and the prior knowledge set, ΣD ∩ Σpk. The paper demonstrates that when prioritizing controllability as prior knowledge (Σpk = Σcont), the data D are informative for stabilization is equivalent to the data D are informative for stabilization without any prior knowledge (Theorem 5).

Stabilizability as Prior Knowledge

When stabilizability is used as prior knowledge, the conditions can be significantly relaxed compared to the case without prior knowledge. Theorem 14 states that if rank X− = n, then the data D are Σstab–informative for stabilization is equivalent to the data D are informative for stabilization. Furthermore, when state data is rank deficient (rank X− < n), Theorem 15 provides necessary and sufficient conditions: (a) im X+ ⊆ im X− and (b) im X−U− = im X− × R m. Proposition 16 provides a tractable method to compute a stabilizing feedback gain K by solving an LMI, even when rank X− < n.

Controllability vs. Stabilizability

A key distinction is drawn between the two prior knowledge types regarding their impact on data requirements. The paper shows that data-driven stabilization using controllability as prior knowledge is equivalent to data-driven stabilization without any prior knowledge. Conversely, for the case where state data is rank deficient, incorporating stabilizability as prior knowledge leads to weaker conditions on the data when compared to data-driven stabilization without prior knowledge. This suggests a curious outcome where knowing a system is stabilizable can weaken the necessary conditions on the collected data.

Numerical Illustration

A numerical example involving a three-tank system with an uncontrollable mode demonstrates these findings. For this specific case, where rank X− = 2 (less than n=3), the paper shows that for T < n + m, only 8.1% of randomly generated datasets are informative for stabilization without prior knowledge, whereas 42% are Σstab–informative for stabilization. Increasing the number of samples to T ≥ 10 results in all datasets being Σstab–informative, illustrating the advantage of incorporating stabilizability as prior knowledge in data-driven control. The paper concludes that while controllability does not help relax conditions, stabilizability can lead to weaker requirements on the data when state data is rank deficient.

Conclusion

The work establishes a framework for synthesizing feedback laws by leveraging both collected data and prior knowledge on system properties like stabilizability and controllability. It provides specific necessary and sufficient conditions for various scenarios regarding the rank of the state data, offering practical methods (Proposition 16) to compute stabilizing gains under these prior knowledge constraints. The results highlight that stabilizability as prior knowledge is particularly advantageous when state data is rank deficient. The paper also notes that this study focused on noise-free data and suggests future work on noisy scenarios or bounds on the dimension of the reachable subspace.

The gist

If the system is controllable, incorporating this as prior knowledge does not relax the conditions required for data-driven stabilization.

Improvements for AI systems

As a fastidious and diligent researcher, I have analyzed the provided scientific paper, Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability. This work focuses on extending data-driven control methods for Linear Time-Invariant (LTI) systems by incorporating prior knowledge of system properties (stabilizability and controllability).

Here are the specific improvements to AI systems that can be derived from this research, along with what the improved AI system can achieve:

The core contribution of the paper is providing robust, data-driven control design methods for physical or complex dynamic systems by leveraging prior knowledge about their structural properties (controllability and stabilizability). This moves control from being purely data-dependent to being informed by inherent system structure.

Here are the specific improvements and capabilities:

The ability to perform direct, noise-tolerant stabilization using only input/state data, even when the underlying system parameters are completely unknown.
The capability to design stabilizing feedback gains for systems where traditional model-based identification or parameter estimation is infeasible or overly conservative (i.e., when system identification is not possible due to lack of persistent excitation).
The ability to synthesize control laws by combining collected data with known structural constraints (prior knowledge) using Linear Matrix Inequalities (LMIs).

Specific Improvements and System Capabilities:

An AI-driven controller can be designed for a physical system (e.g., a chemical process, robotic manipulator, or power grid component) based solely on time-series input/state data collected over a finite horizon.
This controller guarantees stability for the true underlying system, even if the true system matrices are unknown and only approximated by data-consistent systems consistent with the measured input/state sequence.
The controller design process can be computationally tractable (using LMIs), avoiding complex, iterative model identification procedures that might fail under low-information or noisy conditions.

Specific Capabilities Enabled by Prior Knowledge Integration:

The paper highlights two critical ways prior knowledge enhances performance:

By knowing the system is controllable, the required data informativity conditions for stabilization are not relaxed—meaning the data must still meet the necessary criteria for stabilization, but this knowledge does not make finding a solution easier or less demanding.
By knowing the system is stabilizable (but not necessarily controllable), we can achieve stabilizing feedback gains even when the raw data alone is insufficient to guarantee stability for all possible systems consistent with that data.

Specifically, an improved AI system incorporating prior knowledge of stabilizability can:

Identify and stabilize a physical process where the true dynamics might be uncontrollable but are known to be stabilizable (e.g., controlling a subsystem within a larger plant).
Design controllers for systems where the data-consistent set is too restrictive (as shown in Example 4), allowing for stabilization across a larger, relevant subset of possible system behaviors than data-only methods would permit.
In scenarios where state data is rank-deficient (common in real-world sensors), the AI can still derive stabilizing gains by leveraging the prior knowledge that the system is stabilizable, leading to weaker (more achievable) data requirements compared to standard identification methods.

In summary, this research enables the creation of Structure-Aware Data-Driven Control Systems capable of robust stabilization under realistic, information-limited conditions.

Abstract

In this work, we study data-driven stabilization of linear time-invariant systems using prior knowledge of system-theoretic properties, specifically stabilizability and controllability. To formalize this, we extend the concept of data informativity by requiring the existence of a controller that stabilizes all systems consistent with the data and the prior knowledge. We show that if the system is controllable, then incorporating this as prior knowledge does not relax the conditions required for data-driven stabilization. Remarkably, however, we show that if the system is stabilizable, then using this as prior knowledge leads to necessary and sufficient conditions that are weaker than those for data-driven stabilization without prior knowledge. In other words, data-driven stabilization is easier if one knows that the underlying system is stabilizable. We also provide new data-driven control design methods in terms of linear matrix inequalities that complement the conditions for informativity.

Sources

Data-driven stabilization of polynomial systems using density functions