Parameter adaptive tracking control of a class of first order nonlinear plants

The tracking problem is solved for a class of first order plants containing nonlinearities similar to those arising in fermentation process models. When the plant nonlinearity is conveniently parametrized and when the controller parameters are adjusted adaptively, the plant is shown to exhibit a desired tracking property. The tracking conditions for the class of plants are proved using an aggregation (or Lyapunov-like) function with a suitably chosen cubic term.