A passive type multiple-model adaptive control (MMAC) of linear discrete-time stochastic systems with uncertain observation subsystems

A passive type multiple-model adaptive control (MMAC) algorithm is presented for linear discrete-time stochastic systems with observation subsystems which involve unknown but constant parameters. The unknown parameters are assumed to belong to a finite set on which a prior probability distribution is available. A suboptimal control policy is adopted so that the problem of minimizing the original quadratic cost can be replaced by that of minimizing the ‘elemental quadratic cost’. It is shown that the present MMAC method is slightly different from the well known Lainiotis et al. (1973) method, viz. the elemental control is fed back to the elemental filter and, further, the solution method of the elemental filter gain depends on both the elemental and adaptive control decisions. It is also demonstrated, through some Monte Carlo simulations, that for unstable systems performance improvements over the Lainiotis et al. (1973) method are achieved using the present method.