Semi‐adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors

In this paper, we are interested in the problem of adaptive control of non‐linearly parametrized systems. We investigate the viability of defining a stabilizing parameter update law for the case when the plant model is convex on the uncertain parameters. We show that, when the only prior knowledge is convexity, there does not exist an adaptation law—derivable from the standard separable Lyapunov function technique of Parks—applicable for all the state space. Therefore, we propose a semi‐adaptive state feedback controller where adaptation takes place only in the region of the state space where convexity can be used to reduce parameter uncertainty. In the remaining part of the state space we freeze the adaptation and switch to a robust controller. This scheme ensures semi‐global stability for convexly parametrized non‐linear systems with matched uncertainty. The proposed controller is then applied to the problem of temperature regulation of continuous stirred exothermic chemical reactors where reaction heat is convex in the uncertain parameters.