We propose two novel power control policies for a two-way amplify-and-forward (AF) relaying system

in which each node (two sources and one relay) is assumed to operate under both minimum and peak power constraints. Through the exploitation of instantaneous channel gains

the first policy can maximize the sum rate of the system. However

the instantaneous channel gains may be unavailable in a rapid time-varying system

where the first policy is inoperable. Consequently

a robust power control policy which requires only mean channel gains is proposed to maximize the upper bound of the average sum rate

and the properties of this policy are investigated. Simulation results show that

by comparison with the policy in which all the nodes use their peak transmit power

the proposed power control policies can provide considerable system performance improvement. Furthermore

the performance difference between the two proposed policies is negligible when the relay is close to one source.