Toward Improved Performance of Inner Convex Approximation for Suboptimal Nonlinear MPC.

Area of Science:

• Control Engineering
• Applied Mathematics

Background:

• Inner convex approximation enables real-time suboptimal nonlinear model predictive control (MPC).
• Conventional methods suffer from slow convergence, limiting performance within sample times.

Purpose of the Study:

• To accelerate the convergence rate of inner convex approximation for suboptimal MPC.
• To enhance the overall performance of real-time MPC systems.

Main Methods:

• Reformulated inner convex approximation as a nonlinear root-finding problem.
• Performed functional analysis on the nonlinear equation (continuity, differentiability, Jacobian invertibility).
• Applied Broyden's method to accelerate the root-finding procedure.

Main Results:

• Achieved a locally superlinear convergence rate for the improved algorithm.
• Demonstrated enhanced convergence without significant additional computational cost.
• Validated effectiveness through obstacle avoidance simulations.

Conclusions:

• The proposed Broyden's method-accelerated algorithm significantly improves convergence speed for inner convex approximation in MPC.
• This advancement allows for better real-time suboptimal MPC performance and efficiency.