A Stable Indirect Adaptive Control Scheme for First -

The design of most adaptive control schemes is based on the certainty equivalence approach. According to this approach, a control law that can meet the control objective is first developed assuming the plant parameters are exactly known. Then, an adaptive law for estimating the unknown parameters of a certain plant parameterization in chosen to generate on-line estimates which are then used to form the control law. When the plant is minimum phase, it is possible to parameterize it in terms of the controller parameters for some control objectives such as model reference following. In this case, the controller parameter estimates are generated directly from the adaptive law and no intermediate calculations take place. This adaptive control scheme is referred to in the literature as direct adaptive control. A very common example of such a scheme is model reference adaptive control (MRAC), which is widely used and analyzed, see [l] and list of references therein. When the plant is nonminimum phase, its parameterization in terms of the controller parameters of a general pole placement control law, even though possible, is not useful from the estimation point of view. This is due to the nonlinear appearance of the unknown parameters in the plant parametric model. In this case, a plant parameterization which is linear in the unknown parameters is chosen. An adaptive law is then selected to generate the estimated parameters which are used to compute the controller parameters. The resulting control scheme is referred to as indirect adaptive control. The class of indirect adaptive control includes adaptive pole placement (APP), adaptive linear quadratic (ALQ), etc. All three control schemes mentioned earlier, namely MRAC, APP, and ALQ have a number of advantages and disadvantages. For example, in MRAC, @e plant is assumed to be minimum phase with known relative degree and sign of the high-frequency gain. While the assumption about the knowledge of the sign of the high-frequency gain can be relaxed as in [2]-[4], the algorithms used may cause high gain or bad oscillatory transient. In APP and ALQ control schemes, no high-frequency gain, mini-