Parameter-perturbation adaptive control systems with imposed constraints

The general problem of continuously adjusting the parameters of a control system, in order to minimize a performance index, is briefly discussed. Some features of systems which achieve parameter adjustment by measuring the derivatives of the performance index are mentioned, and a system is proposed for the particular problem of seeking optimal parameter values along a line of constraint. Stability of the proposed system is discussed for the case of two adjustable parameters. The realization of a minimum-seeking parameter loop employing deliberate perturbation of one parameter is discussed, and it is shown that the bandwidth of such parameter loops is limited by inherent noise. In the constraint loop, which monitors a second parameter, perturbation of the same frequency is induced by means of a tuned filter, which is of such an amplitude that the derivative measured is effectively that of the performance index along the constraint line.