Randomized Algorithm of Constrained MPC for Linear Systems with Bounded Additive Disturbances

The major drawback to the deterministic method for MPC robust design is computational complexity on-line and control conservatism. From the probabilistic point of view, Randomized Algorithm of constrained MPC is developed in this paper, in which the additive disturbances are taken as random variables and then the control algorithm is simplified into on-line QP problem at each sampling time with off-line computation of the empirical mean of the cost function based on quasi-Monte Carlo method. This is quite different from Min-Max MPC that is formulated as an optimization of the worst case of the cost function at each sampling time. Although the proposed algorithm is similar to Stochastic MPC in some principle, it provides another feasible and computationally efficient approach for Robust MPC. Finally, a simulation result of liquid level control of two-tank network demonstrates the effectiveness of the proposed algorithm.