Stable adaptive control of a class of first-order nonlinearly parameterized plants

Stable adaptive control algorithms are designed for a class of first-order nonlinearly parameterized plants containing nonlinearities similar to those arising in fermentation process models. When the plant nonlinearity is conveniently parameterized and when the controller parameters are adjusted adaptively, the output error is shown to converge to zero. Stability of the overall system is proved using the Lyapunov function with a suitably chosen cubic term.