Data-Driven Linear Quadratic Optimization for Controller Synthesis With Structural Constraints.

Area of Science:

• Control Theory
• Optimization
• Data-Driven Methods

Background:

• Linear Quadratic Regulator (LQR) is attractive for optimal control.
• Structural constraints on gain matrices can prevent direct Algebraic Riccati Equation (ARE) application.
• Classical model-based control requires precise system modeling.

Purpose of the Study:

• To present an alternative optimization approach for optimal control problems with structural constraints.
• To develop a data-driven method that bypasses the need for precise system models.
• To accommodate model uncertainties in controller synthesis.

Main Methods:

• Utilizes a gradient projection optimization approach.
• Employs a data-driven methodology to obtain the gradient.
• Projects the gradient onto constrained hyperplanes for gain matrix updates.
• Refines the gain matrix iteratively.

Main Results:

• The gradient projection method effectively handles structural constraints in optimal control.
• The data-driven approach avoids precise modeling, reducing complexity.
• The method accommodates various model uncertainties.
• Illustrative examples validate the theoretical findings.

Conclusions:

• The proposed data-driven gradient projection method offers an effective alternative for controller synthesis with structural constraints.
• This approach enhances robustness by handling model uncertainties.
• It provides a viable solution when traditional methods like ARE are not directly applicable.