Learning‐Based Model Predictive Control for Multi‐Agent Systems using Gaussian Processes

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AbstractModel Predictive Control (MPC), also referred to as Moving Horizon Control (MHC), experienced a massive growth of interest over the last decades due to increasing computing power and the ability to naturally incorporate state and input constraints. As a model‐based controller, the performance of Model Predictive Control heavily relies upon the quality of the model used. One can leverage measurement data to improve upon a nominal model, e.g., based on first principles, using Gaussian Processes, or other regression techniques. We instead opt for the introduction of (nonlinear) rate constraints to force the system to stay within regions of the state space where a simple, possibly linear, model describes the underlying dynamics well, while still robustly accounting for small model mismatches introduced with the simple model. These rate constraints can again be learned using any parametric or non‐parametric regression method, making the approach very flexible. As an exemplary system, we choose an omnidirectional mobile robot moving in an environment with changing friction coefficients, putting state‐dependent limits on the maximal rate of change of its speed.