Stochastic Model Predictive Control with Discounted Probabilistic Constraints
It addresses the challenge of ensuring recursive feasibility in stochastic MPC for systems with unbounded disturbances, which is a known bottleneck in the field.
This paper develops a stochastic MPC method for linear systems with additive disturbances, using discounted probabilistic constraints to ensure recursive feasibility without requiring bounded disturbances. The approach guarantees closed-loop satisfaction of the chance constraint and quadratic stability.
This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law to minimise a quadratic cost function subject to a chance constraint. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and ignoring violation probabilities in the far future, this form of constraint enables the feasibility of the online optimisation to be guaranteed without an assumption of boundedness of the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility based on knowledge of a suboptimal solution. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition.