Model Predictive Control of Nonlinear Latent Force Models

Model Predictive Control (MPC) has emerged as a potent approach for controlling nonlinear systems in the robotics field and various other engineering domains. Its efficacy lies in its capacity to predictively optimize system behavior while accommodating state and input constraints. Although MPC typically relies on precise dynamic models to be effective, real-world dynamic systems often harbor uncertainties. Ignoring these uncertainties can lead to performance degradation or even failure in MPC.

Nonlinear latent force models, integrating latent uncertainties characterized as Gaussian processes, hold promise for effectively representing nonlinear uncertain systems. Specifically, these models incorporate the state-space representation of a Gaussian process into known nonlinear dynamics, providing the ability to simultaneously predict future states and uncertainties.

This thesis delves into the application of MPC to nonlinear latent force models, aiming to control nonlinear uncertain systems. We formulate a stochastic MPC problem and, to address the ensuing receding-horizon stochastic optimization problem, introduce a scenario-based approach for a deterministic approximation. The resulting scenario-based approach is assessed through simulation studies centered on the motion planning of an autonomous vehicle. The simulations demonstrate the controller's adeptness in managing constraints and consistently mitigating the effects of disturbances. This proposed approach holds promise for various robotics applications and beyond.