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Adaptive power allocation (PA) algorithms with different criteria for a cooperative multiple-input multiple-output network equipped with distributed space-time coding are proposed and evaluated. Joint constrained optimisation algorithms to determine the PA parameters and the receive filter are proposed for each transmitted symbol in each link, as well as the channel coefficients matrix. Linear receive filter and maximum-likelihood detection are considered with amplify-and-forward and decode-and-forward cooperation strategies. In these proposed algorithms, the elements in the PA matrices are optimised at the destination node and then transmitted back to the relay nodes via a feedback channel. The effects of the feedback errors are considered. Linear minimum mean square error expressions and the PA matrices depend on each other and are updated iteratively. Stochastic gradient algorithms are developed with reduced computational complexity. Simulation results show that the proposed algorithms obtain significant performance gains as compared with existing PA schemes.