Stochastic MPC With Dynamic Feedback Gain Selection and Discounted Probabilistic Constraints

This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law incorporating dynamic feedback gain to minimise quadratic cost function subject single chance constraint. The is selected online we provide two selection methods based on minimising upper bounds predicted costs. constraint defined as discounted sum of violation probabilities an infinite horizon. By penalising close the initial time assigning in far future vanishingly small weights, this form constraints allows for MPC guarantees recursive feasibility without boundedness assumption disturbance. A computationally convenient optimisation problem formulated using Chebyshev's inequality introduce constraint-tightening technique ensure feasibility. closed loop system guaranteed satisfy stability condition. With selection, reduced conservativeness mitigated. Also, larger feasible set conditions can be obtained. Numerical simulations are given show these results.