Data-Driven Tracking MPC for Changing Setpoints

Abstract

We propose a data-driven tracking model predictive control (MPC) scheme to control unknown discrete-time linear time-invariant systems. The scheme uses a purely data-driven system parametrization to predict future trajectories based on behavioral systems theory. The control objective is tracking of a given input-output setpoint. We prove that this setpoint is exponentially stable for the closed loop of the proposed MPC, if it is reachable by the system dynamics and constraints. For an unreachable setpoint, our scheme guarantees closed-loop exponential stability of the optimal reachable equilibrium. Moreover, in case the system dynamics are known, the presented results extend the existing results for model-based setpoint tracking to the case where the stage cost is only positive semidefinite in the state. The effectiveness of the proposed approach is illustrated by means of a practical example.

arXiv commentThis version fixes a minor error in the published version: definition of equilibrium (Definition 4) including minor implications throughout the paper, changes marked in blue color

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Cited by in corpus (13)

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• Linear tracking MPC for nonlinear systems Part II: The data-driven case
• Robust stability analysis of a simple data-driven model predictive control approach
• A nonlinear tracking model predictive control scheme for dynamic target signals
• Analysis and design of model predictive control frameworks for dynamic operation -- An overview
• Linear tracking MPC for nonlinear systems Part I: The model-based case
• An overview of systems-theoretic guarantees in data-driven model predictive control
• Robust Constraint Satisfaction in Data-Driven MPC
• Data-driven model predictive control: closed-loop guarantees and experimental results
• On the design of terminal ingredients for data-driven MPC
• Robust Data-Driven Tube-Based Zonotopic Predictive Control with Closed-Loop Guarantees
• Learning explicit predictive controllers: theory and applications
• A Linear Parameter-Varying Approach to Data Predictive Control