Model Predictive Control
A large focus of my research has been on developing a theoretical framework for risk-aware model predictive control (MPC). Often times, in an MPC setting, uncertainty is considered either in a robust sense (worst-case analysis that is risk-averse) or using the expected cost with chance constraints (risk-neutral). My work combines these two settings into one framework through the use of coherent risk measures that allow a more continuous transition between being averse or neutral to risk. Coherent risk measures also provide distributional robustness based on the risk-level chosen.
MPC with moving obstacles
We consider the problem of risk-averse receding horizon motion planning for agents with uncertain dynamics, in the presence of stochastic, dynamic obstacles. We propose MPC scheme that formulates the obstacle avoidance constraint using coherent risk measures. To handle disturbances, or process noise, in the state dynamics, the state constraints are tightened in a risk-aware manner to provide a disturbance feedback policy.
MPC with distributionally robust chance constraints
We study distributionally robust MPC using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk reformulation of the MPC optimization problem that is distributionally robust in the expected cost and chance constraints. We show that, in this case, obtaining distributional robustness in the constraints is equivalent to a simple tightening of the chance constraint. The constraint tightenings provide intuitive approximations of the MPC optimization that reduce the number of optimization variables so as to make the complexity of the distributionally-robust MPC comparable to stochastic MPC.