Direct Data-Driven Synthesis of Stabilizing and Performance-Optimal LPV State-Feedback Controllers

Belangrijkste concepten

This paper derives novel methods that allow to synthesize LPV state-feedback controllers directly from a single sequence of data, guaranteeing stability and performance of the closed-loop system, without knowing the model of the plant.

Samenvatting

The key highlights and insights from the content are:

The authors derive data-driven open-loop and closed-loop LPV state-space representations from a single sequence of input-scheduling-state measurement data of an unknown LPV system with affine dependence. This allows them to formulate data-based analysis and synthesis methods for LPV state-feedback controllers.

They develop data-driven methods to synthesize LPV state-feedback controllers that guarantee closed-loop stability. These methods can be efficiently solved as semi-definite programs (SDPs) with a finite set of linear matrix inequality (LMI) constraints, constructed using only the measurement data.

The authors further extend their data-driven synthesis approach to design LPV state-feedback controllers that guarantee quadratic, generalized H2-norm, and ℓ2-gain-based performance of the closed-loop system. These performance-oriented synthesis methods are also formulated as SDPs with LMI constraints.

The proposed data-driven analysis and synthesis techniques are demonstrated to achieve competitive performance compared to model-based synthesis methods that have complete knowledge of the true system model, through multiple simulation studies.

Statistieken

The following sentences contain key metrics or important figures used to support the author's key logics:
"If the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data."
"The controllers are synthesized by solving an SDP with a finite set of LMI constraints."

Citaten

"We derive novel methods that allow to synthesize LPV state-feedback controllers directly from a single sequence of data and guarantee stability and performance of the closed-loop system, without knowing the model of the plant."
"Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis that have complete knowledge of the true system model in multiple simulation studies."

Belangrijkste Inzichten Gedestilleerd Uit

Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems

by Chri... om arxiv.org 04-05-2024

https://arxiv.org/pdf/2211.17182.pdf

Diepere vragen

How can the proposed data-driven methods be extended to handle more complex LPV system structures, such as state-dependent or nonlinear parameter dependencies

The proposed data-driven methods can be extended to handle more complex LPV system structures by incorporating techniques to deal with state-dependent or nonlinear parameter dependencies. For state-dependent dependencies, the data-driven approach can be adapted to include state-dependent matrices in the system representation. This would involve collecting data that includes state information along with input and scheduling signals. By incorporating state-dependent matrices in the data-driven representations, the controller synthesis algorithms can be modified to account for these dependencies.
For nonlinear parameter dependencies, the data-driven methods can be extended by incorporating nonlinear modeling techniques such as neural networks or Gaussian processes. These models can capture the nonlinear relationships between parameters and system behavior, allowing for the synthesis of controllers that can handle nonlinear parameter dependencies. By training these models on data that captures the nonlinearities in the system, the data-driven synthesis methods can be adapted to handle more complex LPV system structures.

What are the potential limitations or challenges in applying these data-driven LPV control techniques to real-world systems with practical considerations like measurement noise, model uncertainties, and computational constraints

When applying data-driven LPV control techniques to real-world systems, there are several potential limitations and challenges to consider.

Measurement Noise: Real-world systems often have measurement noise that can affect the quality of the data used for controller synthesis. Robustness to measurement noise should be considered in the data-driven methods to ensure the controllers are effective in the presence of noise.

Model Uncertainties: Practical systems may have uncertainties in the model parameters, which can impact the performance of the controller. Data-driven methods should be robust to model uncertainties and be able to adapt to variations in the system dynamics.

Computational Constraints: Data-driven synthesis methods may require significant computational resources, especially for large-scale systems. Efficient algorithms and optimization techniques should be employed to address computational constraints and ensure scalability to real-world applications.

Validation and Testing: Validating the data-driven controllers on real-world systems is essential to ensure their effectiveness and performance. Testing the controllers in simulation and on physical systems can help identify any discrepancies between the data-driven approach and traditional model-based methods.

The paper focuses on state-feedback control, but many practical systems have access to output measurements rather than full state information. How could the data-driven synthesis methods be adapted to handle output-feedback control problems for LPV systems

To adapt the data-driven synthesis methods for output-feedback control problems in LPV systems, the following modifications can be made:

Observer Design: Incorporate observer design techniques to estimate the system states based on output measurements. By combining state estimation with output feedback, the data-driven synthesis methods can be adapted for output-feedback control.

Data Collection: Collect data that includes output measurements along with input and scheduling signals. This data can be used to construct data-driven representations of the system dynamics and design controllers that operate based on output feedback.

Controller Synthesis: Modify the controller synthesis algorithms to account for the use of output measurements instead of full state information. This may involve adapting the LMI conditions and constraints to ensure stability and performance of the closed-loop system based on output feedback.

By incorporating these adaptations, the data-driven synthesis methods can be effectively applied to output-feedback control problems in LPV systems, enabling the design of controllers based on output measurements.