Suboptimal stabilization and tracking control for nonlinear systems with general input constraints

Area of Science:

• Control Theory
• Nonlinear Systems Analysis
• Optimization Techniques

Background:

• Nonlinear systems often face challenges with control input limitations.
• Achieving optimal stabilization and trajectory tracking under these constraints is crucial.
• Existing methods may struggle to guarantee both stability and constraint satisfaction simultaneously.

Purpose of the Study:

• Introduce a novel State-Dependent Riccati Equation (SDRE) based control strategy.
• Address and satisfy control input constraints in nonlinear systems.
• Enable optimal stabilization and trajectory tracking.

Main Methods:

• Utilize an augmented system with integral control and input-barrier states.
• Employ a State-Dependent Coefficient (SDC) representation for system formulation.
• Develop a systematic procedure for SDC matrix construction to ensure Riccati equation solvability.
• Establish conditions for pointwise stabilizability and detectability of the augmented system.

Main Results:

• Guaranteed asymptotic closed-loop stability for nonlinear systems.
• Ensured strict satisfaction of control input constraints.
• Successfully extended the method for time-varying trajectory tracking under input constraints.
• Demonstrated effectiveness and robustness through four simulation case studies.

Conclusions:

• The proposed SDRE framework provides a robust solution for optimal control of nonlinear systems with input constraints.
• The method ensures both stability and constraint satisfaction through rigorous theoretical analysis.
• The approach is effective for both stabilization and complex trajectory tracking tasks.