Distributed stochastic model predictive control for cyber–physical systems with multiple state delays and probabilistic saturation constraints

In this paper, a stochastic distributed model predictive control (DMPC) architecture is investigated for cyber–physical systems subject to probabilistic input saturations. We present a systematic approach to design the stochastic DMPC by extending the deterministic DMPC. The input saturation constraints are relaxed and characterized by a Bernoulli-distributed white sequence, which can provide a trade-off between the satisfaction of input saturations and control performance. The probabilistic input constraints are transformed into a convex hull of linear feedback laws, therefore, can make the controller design less conservative. Then, the optimization problem of the stochastic DMPC is designed and cast into solving an online optimization problem. The probabilistic input saturations are dealt with a distributed fashion by developing an iterative algorithm of the DMPC. The recursive feasibility and closed-loop stability subject to probabilistic input saturations are given. Finally, a numerical example and an industrial electric heater system are used to demonstrate the effectiveness of the proposed approach.