ABSTRACT
By the dual control problem we mean the problem of simultaneous estimation of the system’s parameters and optimal control of that system.
In 1974 Mandl [11] presented the solution of that problem in the case when the system is discrete, linear, cost functional, quadratic, and of the “average cost per unit of time” type. The paper considers a general discrete, homogeneous system with unknown parameters which are to be estimated. The system is to be controlled in such a way as to minimize a cost functional of the “average cost per unit of time” type. It is shown that if the system is regular enough, then any method of estimation which gives strong consistency and which assures that the control sequence is stabilizing, is good in the sense that the cost approaches its minimal value.
A method of on-line estimation which should be best in the considered case is suggested, and the links of that method with the sensitivity analysis by Wierzbicki [8,9,10] are indicated.
198The paper is not, however, a generalization of Mandl’s results, as we do not analyze the problem of stability of the system and do not generalize Mandl’s conditions assuring that optimal (for the sequentially estimated models of the given systems) control is stable for the real process.
