Discrete adaptive control of nonlinear models

A control scheme is proposed for difference equation models which are polynomial in the parameters. An on-line identification scheme which is based on a continuation method is applied in the model polynomial-in-the-parameters. An exponentially weighted least-squares criterion is used in the identification. The recursive parameter estimator is a finite set of differential equations driven by piecewise constant output and control signals. At the sample times the continuous estimator gives the optimal discrete estimates. The overall adaptive control scheme is explicit in the sense that model parameters are estimated. The study is based on a first order scalar parameter model. Extensions to multiparameter, higher order, and multivariable models are described. Some results on the convergence and error analysis are also given. The controller structure is based on the requirement of a linear closed loop response for the correct model parameters. This means feedback cancellation of the terms nonlinear in the signals. Proposals to obtain nonlinear closed loop responses are also introduced. Some examples are given to illustrate the control principle.