On constrained MMVC of discrete-time first-order linear stochastic systems with PSI I: The critically stable case

This paper is devoted to the study of the modified minimal variance control (MMVC) of discrete-time first-order linear critically stable stochastic systems with prospective strong intervention (PSI) and control input constraints. Due to different evolutionary characteristics of systems with PSI, that is, the two modes of tending to infinity and having bounded oscillations, the discrete-time first-order linear critically stable systems can be partitioned into two types regarding the signs of a key system parameter a. A necessary and sufficient condition for the state mean convergence of a system with a = 1 is derived and the corresponding design of MMVC is formulated. For the critical stable system with a =- 1, its oscillation amplitudes of state means can be effectively suppressed or the means can converge under control. Finally, the effectiveness and advantages of the proposed control strategies comparing with MVC are confirmed by numerical simulations.