Risk-Sensitive Model Predictive Control with Gaussian Process Models*

This paper proposes the use of risk-sensitive costs in a model predictive controller (MPC) with Gaussian process (GP) models, for more effective online learning and control. Being a probabilistic model, a GP incorporates the uncertainty information due to imperfect knowledge of the system. The MPC then utilises this uncertainty information in a risk-sensitive, especially risk-seeking fashion, to balance the exploration of the unknown characteristics and the exploitative control actions simultaneously. Comparison of MPCs with the risk-seeking cost and the risk-neutral cost, i.e. the standard quadratic cost, on the swing-up control of a cart-pendulum system demonstrates that the risk-seeking cost exhibits an effective exploratory behaviour which leads to a better learning of the unknown system and in turn gives improved control performance.