Abstract: An adaptive observer and nonlinear feedback control strategy with constraints on control action are developed by using supervisor learning rule of adaptive neuron and the theory of functional -link networks. The convergence of adaptive observer and the stability of control system are proven. They are applied to the control of an exothermic stirred -tank reactor. It is shown that an adaptive observer for concentration can be constructed for a reaction system when only temperature measurements are on line available. An adaptive observer is used to identify the pre- exponential Arrhenius constant and to provide on- line estimation of the unmeasured reactant concentration for a nonlinear state - feedback controller. Simulations show that the combined observer/controller provides satisfactory closed - loop behavior, fast responses and strong robustness. Estimated and actual concentration are in good agreement. Nonlinear feedback controller can provide effective feedback control over a wide range of operating conditions.