A Computationally Efficient Model Predictive Control Strategy for Linear Systems with Integer Inputs

For linear systems with integer inputs, the model predictive control problem with output reference tracking is formulated as an integer least-squares (ILS) problem. The ILS problem is solved using a modified sphere decoding algorithm, which is a particular branch-and-bound method. To reduce the computational complexity of the sphere decoder, a reduction algorithm is added as a preprocessing stage to reshape the search space in which the integer solution lies. The computational complexity of the proposed algorithm is modest, enabling its implementation in a real-time system even when considering long prediction horizons. A variable-speed drive system with a three-level voltage source inverter serves as an illustrative example to demonstrate the effectiveness of the proposed algorithm.