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Nonlinear self-triggered MPC without terminal conditions for trajectory tracking.

Hai Zhao1, Hongjiu Yang1, Yuanqing Xia2

  • 1The Tianjin Key Laboratory of Intelligent Unmanned Swarm Technology and System, School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, China.

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|June 17, 2025
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Summary
This summary is machine-generated.

This study introduces a practical model predictive control (MPC) strategy for nonlinear systems. The novel approach simplifies parameters and uses a self-triggered mechanism to reduce computational load for trajectory tracking.

Keywords:
Discrete-time systemMPCNonlinear systemSelf-triggered mechanismTrajectory tracking

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Area of Science:

  • Control Systems Engineering
  • Robotics
  • Nonlinear System Dynamics

Background:

  • Trajectory tracking is crucial for autonomous systems.
  • Standard Model Predictive Control (MPC) can be computationally intensive due to terminal conditions.
  • Nonlinear discrete-time systems present unique control challenges.

Purpose of the Study:

  • To develop a simplified and computationally efficient MPC strategy for trajectory tracking in nonlinear discrete-time systems.
  • To enhance the practicability of MPC by removing terminal constraints and penalties.
  • To introduce a self-triggered mechanism for reducing computational burden.

Main Methods:

  • A novel Model Predictive Control (MPC) strategy is proposed, omitting terminal penalty terms and state constraints.
  • A self-triggered mechanism is implemented, utilizing cost function discrepancies between time instants.
  • An additional compensation variable is introduced to address redundancy from the self-triggered mechanism.
  • Mathematical proof of recursive feasibility for the optimization problem is provided.

Main Results:

  • The proposed MPC strategy demonstrates high practicability due to fewer required parameters.
  • The self-triggered mechanism effectively reduces the computational load.
  • Recursive feasibility of the optimization problem is mathematically proven.
  • Simulations and experimental results on a mobile vehicle platform validate the strategy's effectiveness.

Conclusions:

  • The novel self-triggered MPC strategy offers a practical and computationally efficient solution for trajectory tracking in nonlinear discrete-time systems.
  • The removal of terminal conditions simplifies the control design without compromising performance.
  • The method is validated through rigorous simulations and real-world experiments on a mobile robot.