Design and analysis of constrained nonlinear quadratic regulator

Area of Science:

• Control Systems Engineering
• Nonlinear Control Theory
• Optimization Techniques

Background:

• The constrained nonlinear quadratic regulator (CNLQR) problem presents challenges in achieving optimal control for nonlinear systems.
• Existing methods may struggle with stability and performance guarantees across different operating regions.

Purpose of the Study:

• To develop a suboptimal dual-mode control strategy for the CNLQR problem.
• To ensure stability and feasibility of the proposed control law.
• To demonstrate the controller's effectiveness through simulations.

Main Methods:

• Linearizing the nonlinear system around the origin to apply a linear-quadratic regulator (LQR) in a local neighborhood.
• Solving a finite horizon optimization problem (FHOP) with terminal inequality constraints for the region outside the LQR neighborhood.
• Designing terminal constraints to guide states into an LQR-invariant set.
• Combining the LQR and FHOP control laws to form the dual-mode controller.

Main Results:

• The proposed dual-mode controller is feasible.
• Asymptotic stability of the closed-loop system is proven.
• Simulation studies confirm the effectiveness of the suboptimal controller.

Conclusions:

• The dual-mode approach offers a viable solution for the CNLQR problem.
• This strategy effectively combines local LQR control with global optimization for enhanced system performance and stability.
• The controller demonstrates robustness by driving states into a stable region.