Computationally Efficient Nonlinear Model Predictive Control Using the L₁ Cost-Function

Area of Science:

• Control Engineering
• Applied Mathematics
• Artificial Intelligence

Background:

• Model Predictive Control (MPC) commonly employs L2 cost functions for minimizing squared errors, offering good numerical stability.
• While L1 norm control offers superior quality by minimizing absolute errors, its non-differentiable nature complicates nonlinear model predictions.
• Existing methods face challenges with nonlinear cost functions in MPC, limiting practical implementation.

Purpose of the Study:

• To develop a computationally efficient alternative for Model Predictive Control (MPC) utilizing the L1 norm for improved control quality.
• To address the challenges posed by non-differentiable cost functions in nonlinear MPC.
• To demonstrate the effectiveness of a novel approach combining neural approximation and advanced linearization techniques.

Main Methods:

• Utilizing a neural approximator to replace the non-differentiable absolute value function within the cost function.
• Implementing advanced on-line trajectory linearization for nonlinear prediction models.
• Transforming a complex nonlinear optimization problem into a solvable quadratic optimization task.

Main Results:

• The proposed method achieves computationally efficient L1 norm optimization in MPC.
• Simulated results on a neutralization benchmark show trajectories comparable to nonlinear optimization methods.
• The L1 norm demonstrates superior performance over the L2 norm, even when evaluated by traditional squared error metrics.

Conclusions:

• The integration of neural approximation and trajectory linearization provides an effective and efficient solution for L1 norm MPC.
• This approach significantly simplifies the optimization problem without sacrificing control performance.
• The findings suggest a promising direction for enhancing control quality in nonlinear systems using MPC.