Semi-adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors (Q2731547)

A challenging adaptive stabilization problem of nonlinearly parametrized nonlinear plants is under consideration. The current investigation refers to the case in which the plant model convexity on the uncertain parameters is the only prior knowledge. For this case it is shown that an adaptation law (based on standard separable Lyapunov functions), which will be able to reduce the parameter uncertainty in the whole state space, does not exist. It is argued that an additional prior knowledge should be incorporated to achieve complete adaptive design. So far, a semi-adaptive state feedback controller is suggested. Adaptation takes place in the regions of the state space in which convexity can be used to reduce parameter uncertainty. Outside these regions, the adaptation is frozen and the system is switched to a constant parameter robust controller. The proposed control scheme is applied to the temperature regulation of a continuous stirred tank reactor in which the reaction heat is a convex function of uncertain parameters.