Soft-Constrained Stochastic MPC of Markov Jump Linear Systems: Application to Real-Time Control With Deadline Overruns

Modern real-time control systems can sporadically exceed the computation deadlines, which may lead to a deterioration in performance or even instability if not actively accounted for. This letter proposes a stochastic model predictive control approach that incorporates deadline miss probabilities of subsequent control task executions in a scenario tree. To account for the effect of missed deadlines, we utilize Markov jump linear systems that allow us to prove mean-square stability and recursive feasibility under hard input and mixed hard/soft state constraints. The proposed stochastic controller is benchmarked using a Furuta pendulum, demonstrating improved performance and an increased feasible region compared to a nominal and a hard-constrained stochastic controller, respectively.