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| In this paper, a new control problem, namely, opportunity-awaiting control problem is proposed and investigated thoroughly for a class of discrete stochastic systems. The main purpose of the opportunity-awaiting control problem is to design a controller, for a system subjected to external stochastic disturbances, such that the following two requirements meet specified admissible values simultaneously: 1) the controlled output resides within a given rectangular target area  for time Tin(residence time); and 2) the controlled output waits outside the area  for time Tout(waiting time). Statistical characteristics for admissible residence time and waiting time are derived with respect to a given rectangular target area, and the relationship between residence time and waiting time is discussed. It is shown that both the residence time and waiting time are determined by the steady-state output variance and the correlation coefficient of the system output. Based on the linear matrix inequality approach, a controller design method is then developed so that the prescribed performance constraints on the residence time, waiting time and poles’ location are satisfied. An illustrative numerical example is included to demonstrate the effectiveness of the developed design method. |
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| Keywords:Stochastic control, opportunity-waiting control, satisfactory control, Linear matrix inequality |
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