Constrained one step predictive control of discrete time Markovian jump linear systems

The one step receding horizon control(RHC) problcm is considered for discrete time Markovian jump linear system,subject to constraints on control inputs.At first,constrained one step receding horizon control low are designed to drive the state trajectory into a terminal invariant set,which guarantees stochastic stability of jump system.Then the situation with peak bounded noise inputs is also studied.And the invariant set depends on the existence of a fictitious state feedback control law,which guarantees stochastic stability of jump system out of the receding horizon.For computational tractability,the controller optimization problem is transformed into a semi-definite programming(SDP) problem which can be easily solved by means of LMI.The sinulation results of an economic dynamic system which described by a Markovian jump linear system demonstrates that the method are valid.