Application of input-signal design in system identification for adaptive control

An alternative approach to indirect adaptive control is considered. The proposed algorithm uses the input-signal design (probing action) in parameter estimation for the control (control action) of linear systems with unknown parameters. The probing-action input under the amplitude constraint is selected in order to achieve the parameter estimates that are most accurate with respect to the determinant ratio of the parameter covariance matrix. The control-action input is given by the cautious control law (CAUT) or alternatively by the active adaptive-control (AAC) law. The case of amplitude-constrained control input is also investigated. The parameter estimates obtained from the probing-action experiment are used to update the control-action scheme. During the control action it is still possible to update the controller parameters. For the adaptive control problem of finite horizon N = N₁ + N₂, it seems that an optimum action exists between the probing action of length N₁ and the control action of length N₂. This heuristic reasoning is illustrated by simulations. The performance of the proposed algorithm is compared with the innovation dual-control (IDC) approach.