Data-Driven Adversarial Online Control for Unknown Linear Systems

Core Concepts

The author presents a novel data-driven online adaptive control algorithm to address the online control problem with unknown linear systems, leveraging behavioral systems theory and perturbation-based controllers to guarantee a regret bound matching the best-known result.

Abstract

The content discusses a data-driven approach for adversarial online control in unknown linear systems. It introduces an algorithm that bypasses system identification, providing simplicity and robustness. The method leverages non-parametric system representation and perturbation-based controllers to achieve sublinear regret bounds.

Key points include:

• Introduction of data-driven control approaches.
• Challenges in adversarial online control.
• Proposal of an adaptive control algorithm.
• Theoretical analysis and performance guarantees.
• Extension to output feedback cases.

The study emphasizes the importance of data-driven methods in addressing complex control problems efficiently.

Stats

Our algorithm guarantees an ˜O(T 2/3) regret bound with high probability.

Quotes

"Data-driven approaches offer simplicity, generality, and robustness."
"Our algorithm leverages non-parametric system representation for efficient control."

Key Insights Distilled From

Data-Driven Adversarial Online Control for Unknown Linear Systems

by Zishun Liu,Y... at arxiv.org 03-12-2024

https://arxiv.org/pdf/2308.08138.pdf

Deeper Inquiries

How can data-driven methods revolutionize traditional model-based controls

Data-driven methods can revolutionize traditional model-based controls by offering a more flexible and adaptive approach to control systems. Traditional model-based controls rely on accurate system identification, which can be challenging and time-consuming, especially for complex systems with unknown dynamics. Data-driven methods, on the other hand, bypass the need for explicit system identification by directly learning from data. This allows for more efficient implementation of control algorithms without the constraints of having a precise mathematical model.
One key advantage of data-driven methods is their ability to handle complex and nonlinear systems that may not have easily identifiable models. By leveraging large datasets and advanced machine learning techniques, data-driven approaches can capture intricate system behaviors and adapt in real-time to changing conditions. This flexibility enables better performance in dynamic environments where traditional models may fall short.
Furthermore, data-driven methods offer scalability and generalizability across different applications and domains. They are not limited by specific assumptions or simplifications inherent in traditional models, making them suitable for a wide range of control problems. Overall, the use of data-driven methods in control systems opens up new possibilities for optimizing performance, enhancing robustness, and enabling autonomous decision-making processes.

What are the implications of bypassing system identification in control algorithms

Bypassing system identification in control algorithms has several implications that can significantly impact the field:

Simplicity: Eliminating the need for explicit system identification simplifies the design process of control algorithms. Data-driven approaches focus on learning directly from input-output data without requiring detailed knowledge of underlying dynamics or parameters.

Robustness: By bypassing system identification steps that may introduce errors or uncertainties into models, data-driven algorithms can be more robust to variations or disturbances in the environment. The reliance on empirical observations allows for adaptive responses based on real-time feedback.

Flexibility: Without being tied down by specific model structures or assumptions about system behavior, data-driven approaches offer greater flexibility in handling diverse types of systems with varying complexities.

Real-Time Adaptation: Data-driven algorithms enable continuous adaptation based on incoming sensor information or feedback signals without needing re-identification each time there is a change in operating conditions.

5Efficiency: By focusing on utilizing available operational data rather than spending resources on identifying complex mathematical models upfront,data driven strategies streamline development processes leading to quicker deployment times
Overall,bypassing sysytem identifcation leads to improved efficiency,faster response times,and enhanced adaptability making it an attractive option particularly when dealing with uncertain,dynamic environments.

How can behavioral systems theory enhance adaptive control strategies

Behavioral Systems Theory (BST) enhances adaptive control strategies by providing a framework for understanding how systems behave based solely on observed input-output relationships.BST focuses on characterizing behavioral properties such as stability,reliability,and predictability through empirical observations rather than theoretical modeling.This approach aligns well with datadriven methodologies which also emphasize learning from observed patterns insteadof relying solelyon predefinedmodels.
By incorporating BST principles into adaptivecontrol strategies,data-drivensystems gainthe following advantages:
1**Non-parametric Representation:BSTallowsforanon-parametricrepresentationofsystembehaviorbasedondirectdataobservations.This eliminates theneedforprecisemodelidentificationalgorithmsandprovides amoreflexiblewaytoadapttochangingenvironments.
2Adaptive Learning:BSTemphasizeslearningfromempiricaldatatoidentifypatternsandtrendswhichcanbeusedtomakeinformeddecisionsinrealtime.Adaptivecontrolstrategiesbenefitfromthisapproachbybeingabletoadjusttheirparametersbasedoncurrentsystemstatesandinputs.
3Robustness:**Byfocusingonobservedbehaviorsratherthanassumptionsoridealizedmodels,BSTenhancesrobustnesstoadverseconditionsoruncertaintiesintheprocess.ByincorporatingBSTprinciples,intoadaptivecontrolschemes,thecontrollersbecomemorecapableofhandlingvariabilitiesindatawithoutrequiringrepeatedmodelupdates
Incorporating Behavioral Systems Theory into datadrivenadaptivecontrolstrategiesenablesmoreeffectiveandsophisticatedresponsestochangeabledynamicswhilemaintainingastablerobustperformanceacrossdiverseapplicationsandincomplexenvironments