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Predictive control techniques have recently been applied with success to conventional and multiphase electrical drives. The additional degrees of freedom in multiphase drives make the real-time implementation of optimal solutions difficult due to the increased number of iterations. This paper proposes a predictive control technique that reduces the available voltage source inverter switching states according to predefined constraints. The introduced method, called as restrained search predictive control, favors on-line implementation and improves the current tracking performance. Simulation and experimental results are provided to test the viability of the presented technique.