<p>A data-driven model predictive control (MPC) algorithm based on the input-mapping method is proposed for piecewise affine (PWA) systems. These systems are characterized by unknown but constant parameters and are subject to disturbances, as well as state and input constraints. To support the control strategy, an offline algorithm is developed to compute a non-convex robust positively invariant set that serves as the terminal set within the MPC framework tailored for PWA systems. The online MPC algorithm directly maps the future control input and predicted state to the historical input-state data associated with the corresponding state subregion. This mapping process leverages the more accurate relationships contained in the historical input-state data to enhance the prediction accuracy of future states. A state-dependent weight embedded in the cost function enables the controller to balance prediction accuracy against convergence speed, enhancing overall performance. Moreover, conditions ensuring the recursive feasibility of the optimization problem and stability of the closed-loop system are established. The effectiveness of the proposed algorithm is demonstrated through a numerical example, which highlights its ability to handle complex system dynamics and constraints while maintaining robust performance.</p>

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Online data-driven MPC for PWA systems with unknown parameters

  • Rui Gu,
  • Aoyun Ma,
  • Dewei Li,
  • Yunwen Xu,
  • Shaoying He

摘要

A data-driven model predictive control (MPC) algorithm based on the input-mapping method is proposed for piecewise affine (PWA) systems. These systems are characterized by unknown but constant parameters and are subject to disturbances, as well as state and input constraints. To support the control strategy, an offline algorithm is developed to compute a non-convex robust positively invariant set that serves as the terminal set within the MPC framework tailored for PWA systems. The online MPC algorithm directly maps the future control input and predicted state to the historical input-state data associated with the corresponding state subregion. This mapping process leverages the more accurate relationships contained in the historical input-state data to enhance the prediction accuracy of future states. A state-dependent weight embedded in the cost function enables the controller to balance prediction accuracy against convergence speed, enhancing overall performance. Moreover, conditions ensuring the recursive feasibility of the optimization problem and stability of the closed-loop system are established. The effectiveness of the proposed algorithm is demonstrated through a numerical example, which highlights its ability to handle complex system dynamics and constraints while maintaining robust performance.