Computationally Efficient Continuous-Time Model Predictive Control of a 2-DOF Helicopter via B-Spline...

Area of Science:

• Control Engineering
• Computational Mathematics

Background:

• Continuous-time model predictive control (MPC) faces significant computational challenges in real-time applications.
• Efficient implementation of MPC is crucial for advanced control systems, especially on hardware with limited resources.

Purpose of the Study:

• To investigate the use of B-spline functions for approximating signals and models in continuous-time MPC.
• To develop a computationally efficient MPC framework that reduces online computational effort.
• To demonstrate the practical applicability of the proposed method in real-time control scenarios.

Main Methods:

• Representing input/output signals and models using B-spline functions.
• Formulating control signals as continuous polynomial spline functions.
• Expressing prediction horizon constraints as constraints on B-spline control polygon vertices.
• Implementing an adaptive control mode with recursive least squares (RLS) parameter estimation.
• Adapting stabilizing terminal sets and terminal cost calculations.

Main Results:

• Significant reduction in computational burden, evidenced by fewer decision variables and input constraints.
• Successful real-time experimental validation on a 2-DOF laboratory helicopter setup.
• Effective tracking of pitch and yaw trajectories despite parameter uncertainties.
• Demonstrated potential for real-time applications on embedded control hardware.

Conclusions:

• B-spline approximation offers an effective strategy to reduce the computational complexity of continuous-time MPC.
• The proposed adaptive MPC framework enhances robustness against parameter uncertainties.
• The method is well-suited for real-time control applications, including those with embedded systems.