Abstract
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.
Highlights
Model predictive control (MPC) is widely applied in the process control area because of its ability to handle constraints and MIMO systems
Many researchers attempted to exploit the special structure of MPC and tailor the two algorithms to speed up the solving process
Considering combining explicit MPC and online optimization, the k-d tree is used in this study to design an algorithm that implements fast MPC
Summary
Model predictive control (MPC) is widely applied in the process control area because of its ability to handle constraints and MIMO systems. QPSchur, which is a QP algorithm based on the active-set method, is proposed in [4] and focuses on large-scale MPC Another online active-set strategy is described in [5] for the fast solution of parametric QPs in MPC; this strategy uses the information of the previous QP under the assumption that the QP problem only slightly changes. The PE method uses a table to store the recently searched CRs and combines it with the online method to achieve fast MPC for large-scale problems. We propose a method that combines the explicit MPC and online optimization by using the k-d tree structure to obtain fast MPC for both small-scale and large-scale problems.
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