Efficiently tunable real-time implementation of Riccati equation-based designs: general scheme and benchmark study.

Area of Science:

• Control Systems Engineering
• Computational Mathematics
• Aerospace Engineering

Background:

• Riccati equation (RE)-based designs are computationally intensive for real-time applications.
• The state-dependent Riccati equation (SDRE) scheme faces challenges due to the high computational burden of solving REs at each time step.
• Thrust vector control (TVC) is a benchmark application where computational efficiency is critical.

Purpose of the Study:

• To address the computational burden of SDRE-based designs, particularly for TVC.
• To develop a computationally efficient and flexible Riccati equation solver for real-time implementation.
• To guarantee the applicability and asymptotic stability of SDRE-based TVC without relying on extensive numerical checks.

Main Methods:

• An FPGA hardware implementation of the Structure-Preserving Doubling Algorithm for Riccati equation solving was developed.
• The extended solver was analyzed for computational efficiency (time and accuracy) and tuning flexibility.
• The performance was benchmarked against standard MATLAB routines, focusing on computation time and accuracy residuals.

Main Results:

• The proposed FPGA implementation achieved remarkable computational efficiency in both time and accuracy.
• The extended solver's computation time was significantly reduced compared to the MATLAB benchmark.
• Tuning flexibility was provided through the stopping criterion, utilizing the Frobenius norm of the RE's residual matrix.

Conclusions:

• The FPGA-based Riccati equation solver offers a practical solution to enhance the real-time computational efficiency of SDRE designs.
• The developed method provides a balance between computational speed and accuracy, crucial for applications like TVC.
• This approach avoids common compromises by efficiently guaranteeing system stability and applicability.