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Computation time is the main factor that limits the application of model predictive control (MPC). This paper presents a fast model predictive control algorithm that combines offline method and online optimization to solve the MPC problem. The offline method uses a k-d tree instead of a table to implement partial enumeration, which accelerates online searching operation. Only a part of the explicit solution is stored in the k-d tree for online searching, and the k-d tree is updated in runtime to accommodate the change in the operating point. Online optimization is invoked when searching on the k-d tree fails. Numerical experiments show that the proposed algorithm is efficient on both small-scale and large-scale processes. The average speedup factor in the large-scale process is at least 6, the worst-case speedup factor is at least 2, and the performance is less than 0.05% suboptimal.

Fast Model Predictive Control Combining Offline Method and Online Optimization with K-D Tree