Robust Data-Driven Iterative Control Method for Linear Systems with Bounded Disturbances

Grunnleggende konsepter

This paper proposes a new robust data-driven iterative control method for linear systems with bounded disturbances, where the system model and disturbances are unknown.

Sammendrag

The paper presents a new robust data-driven control method for linear systems with bounded disturbances, where the system model and disturbances are unknown.
Key highlights:

Due to disturbances, accurately determining the true system becomes challenging using the collected dataset. Instead of designing controllers directly for the unknown true system, the proposed method designs controllers for all systems compatible with the dataset.
To overcome the limitations of using a single dataset and benefit from collecting more data, multiple datasets are employed in this paper.
A new iterative method is developed to address the challenges of using multiple datasets. This allows for the incorporation of numerous datasets, potentially reducing the conservativeness of the designed controller.
The paper develops both offline and online robust data-driven iterative control methods. The online controller is iteratively designed by continuously incorporating online collected data into the historical data to construct new datasets.
The effectiveness of the proposed methods is demonstrated using a batch reactor.

Statistikk

The system (1) satisfies the following data matrices:
Ui = [ui(0), ui(1), ..., ui(Ti-1)]
Xi = [xi(0), xi(1), ..., xi(Ti-1)]
Xi,+ = [xi(1), xi(2), ..., xi(Ti)]
Yi = [yi(0), yi(1), ..., yi(Ti-1)]
Wi = [ωi(0), ωi(1), ..., ωi(Ti-1)]
The disturbance ωi(k) is bounded such that ωi(k)ωi(k)' ≤ Υi, where Υi = TiΥ.

Sitater

"Due to disturbances, accurately determining the true system becomes challenging using the collected dataset. Therefore, instead of designing controllers directly for the unknown true system, an available approach is to design controllers for all systems compatible with the dataset."
"To overcome the limitations of using a single dataset and benefit from collecting more data, multiple datasets are employed in this paper."
"A new iterative method is developed to address the challenges of using multiple datasets. Based on this method, this paper develops an offline and online robust data-driven iterative control method, respectively."

Viktige innsikter hentet fra

A Robust Data-Driven Iterative Control Method for Linear Systems with Bounded Disturbances

by Kaijian Hu,T... klokken arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02537.pdf

Dypere Spørsmål

How can the proposed iterative method be extended to handle nonlinear systems or time-varying systems

The proposed iterative method can be extended to handle nonlinear systems by incorporating techniques such as linearization or approximation. For nonlinear systems, the system matrices A, B, C, and D are functions of the state variables and inputs, making it challenging to directly apply the iterative method. One approach is to linearize the nonlinear system around an operating point and treat it as a series of linear time-invariant systems. The iterative method can then be applied to each linearized system, updating the system sets and controllers iteratively. Another approach is to use model predictive control (MPC) techniques, where a nonlinear model of the system is used to predict future behavior and optimize control inputs iteratively. Additionally, for time-varying systems, the iterative method can be extended by updating the system sets and controllers at each time step based on the latest data, allowing for adaptation to changing system dynamics.

What are the potential limitations or drawbacks of the offline and online data-driven control methods when dealing with high-dimensional or complex systems

Limitations of Offline Data-Driven Control:

Curse of Dimensionality: Offline data-driven control methods may face challenges with high-dimensional systems, as the size of the system sets and LMIs grows exponentially with the number of states and inputs. This can lead to increased computational complexity and longer computation times.
Conservativeness: Offline methods may design conservative controllers when dealing with complex systems, as the intersection of system sets may become smaller, limiting the achievable control performance.
Data Dependency: Offline methods rely heavily on pre-collected data, which may not capture all system behaviors in high-dimensional or complex systems, leading to suboptimal controller designs.

Limitations of Online Data-Driven Control:

Real-Time Computation: Online data-driven control methods require real-time computation to update the controller at each time step, which can be computationally intensive for high-dimensional or complex systems.
Data Quality: Online methods are sensitive to the quality and consistency of the collected data, and noisy or inaccurate data can impact the performance of the controller.
Adaptation Speed: Online methods may have limitations in adapting to rapid changes in system dynamics, especially in high-dimensional systems where the control updates need to be fast and accurate.

Can the proposed approach be combined with other data-driven techniques, such as machine learning or reinforcement learning, to further enhance the control performance

The proposed approach can be combined with other data-driven techniques, such as machine learning or reinforcement learning, to further enhance control performance:

Machine Learning: Machine learning algorithms can be used to learn the system dynamics from data and improve the accuracy of the system identification process. This can help in constructing more precise system sets and designing controllers that better capture the system behavior.
Reinforcement Learning: Reinforcement learning algorithms can be employed to optimize the control policy iteratively based on the collected data and system responses. By incorporating reinforcement learning, the control strategy can adapt and improve over time, leading to enhanced performance in complex systems.
Hybrid Approaches: Hybrid approaches combining data-driven control with machine learning or reinforcement learning can leverage the strengths of each method. For example, using machine learning for system identification and reinforcement learning for controller optimization can lead to more robust and efficient control strategies in high-dimensional or complex systems.