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Learning-based stochastic Model Predictive Control with scalable Gaussian process regression
One of the key ingredients in Model Predictive Control (MPC) schemes
is an effective model of the dynamical system’s response to external inputs. However, first-
principles models are often not accurate enough, as there might be unknown external disturbances and model mismatches. To address this, learning-based control aims at
complementing nominal models with data-based ones, which can be refined online as new system
observations are gathered. Thus, such a model should be both expressive and fast to update.
This project focuses on a learning-based stochastic
MPC scheme, where uncertainty in the model is learned
with an approximate Gaussian process, namely the regularized trigonometric regression stemming from the so-
called sparse-spectrum Gaussian processes. To this
aim, the candidate will review the available uncertainty
bounds around these approximate Gaussian-process-based estimates and incorporate them in the
MPC formulation. The chance-constraints thereby obtained are then to be analyzed to rigorously prove recursive feasibility and stability of the closed-loop system.
Keywords: stochastic model predictive control, Gaussian process regression, learning-based control, uncertainty bounds
SparseSpectrumSMPC.pdf
