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

Mohammad Hosein Sabzalian1, Yazdan Batmani2

  • 1Department of Mechanical Engineering, Faculty of Engineering, University of Santiago of Chile (USACH), Avenida Libertador Bernardo O'Higgins 3363, 9170022, Santiago, Chile.

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|October 27, 2025
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Summary
This summary is machine-generated.

This study presents a new State-Dependent Riccati Equation (SDRE) control strategy for nonlinear systems, ensuring stability and precise trajectory tracking while respecting input constraints. The method guarantees system stability and strict adherence to control input limits.

Keywords:
Input constraintsNonlinear systemsStabilizationState-dependent riccati equationsTrajectory tracking controller

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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.