Two control strategies that allow the control of source and load currents for direct matrix converters are presented in this study. Both methods use the switching state of the converter in the subsequent sampling time, based on an optimisation algorithm given by a simple cost function and the discrete system model. The control goals include regulation of load currents according to an arbitrary reference and good tracking of the source currents to their references. In the first method, the input current reference is given as a function of the instantaneous active power. In the second case, the source current reference is given as a function of the output current reference and system parameters. Experimental results with an experimental prototype support the theoretical approach.