Data-Driven Predictive Control with Adaptive Disturbance Attenuation for Constrained Systems

Core Concepts

Combining H∞ control and MPC for adaptive disturbance attenuation in data-driven predictive control.

Abstract

The paper proposes a novel data-driven predictive control approach that combines H∞ control for disturbance rejection and Model Predictive Control (MPC) for constraint handling. The method dynamically adapts disturbance attenuation performance based on system state and forecasted disturbances to ensure constraint satisfaction. The theoretical properties include closed-loop stability, disturbance attenuation, and constraint satisfaction under noisy data. The approach is illustrated with a numerical example.
Abstract:

Proposes a data-driven predictive control approach.
Combines H∞ control and MPC.
Dynamically adapts disturbance attenuation.
Ensures constraint satisfaction under noisy data.
Introduction:

Importance of disturbance rejection and constraint satisfaction.
H∞ control minimizes the effect of disturbances.
MPC handles time-domain constraints explicitly.
Data-Driven Methods:

Data availability spurs development of data-driven methods.
End-to-end solutions bypass modeling steps.
Extending model-based methods to data-driven counterparts.
Existing Data-Driven Control Methods:

Reinforcement Learning used for training optimal controllers.
DeePC technique based on behavioral systems theory shows superior performance but has higher computational cost.
Proposed Approach:

Novel data-driven predictive control method combining H∞ control and MPC.
Focuses on H∞ type disturbance attenuation for systems with time-domain constraints.
Moving-Horizon Control:

Strategy for implementing the proposed control approach in a moving-horizon manner.
Problem Statement and Preliminaries:

Control of dynamic systems represented by linear time-invariant models.
Constrained H∞Control:

Designing feedback gain K using optimization problem (20).
Moving-Horizon Control Implementation:

Strategy for implementing the proposed control approach in a moving-horizon manner.

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Key Insights Distilled From

Data-Driven Predictive Control with Adaptive Disturbance Attenuation for Constrained Systems

by Nan Li,Ilya ... at arxiv.org 03-25-2024

https://arxiv.org/pdf/2403.14935.pdf

Deeper Inquiries

How can this data-driven approach be applied to real-world systems

This data-driven approach can be applied to real-world systems by leveraging historical and real-time data from the system's operation. By collecting trajectory data, including state variables, control inputs, and disturbances, the system's behavior can be modeled without relying on complex first-principle models. This approach allows for adaptive control strategies that adjust based on measured system states and forecasted disturbances. In practical applications such as aerospace engineering or industrial automation, this method can enhance performance by dynamically adapting to changing conditions in the environment.

What are the potential drawbacks or limitations of combining H∞ control and MPC

While combining H∞ control and Model Predictive Control (MPC) offers advantages in terms of disturbance rejection and constraint handling, there are potential drawbacks to consider. One limitation is the computational complexity of implementing both approaches simultaneously in a real-time setting. The optimization required for MPC solutions combined with robustness analysis for H∞ control may lead to increased computational burden. Additionally, tuning the parameters for both controllers to work harmoniously together can be challenging and may require extensive testing and validation.

How can advancements in sensing technologies impact the effectiveness of this approach

Advancements in sensing technologies play a crucial role in enhancing the effectiveness of this data-driven approach. Improved sensors provide more accurate measurements of system states and disturbances, leading to better modeling accuracy. High-resolution sensors with faster sampling rates enable capturing detailed dynamics of the system in real time, facilitating precise feedback control adjustments based on current operating conditions. Furthermore, advancements like IoT integration allow for seamless data collection across distributed systems, enabling comprehensive monitoring and control capabilities over interconnected components within a larger networked environment.