Multi-Scale Approximate Explicit Model Predictive Control And Its Application

Predictive control has developed well from model predictive control to explicit model predictive control approximation method. Considering the time of the off-line computation is so long and the number of the irregular partition is so large, the complexity of explicit model predictive is too high. In this paper, multi-scale approximate explicit model predictive control is introduced to solve linear time invariant finite horizon optimal control problems and to reduce the time complexity and space complexity. By comparing with explicit model predictive control, the conclusion is that multi-scale approximate explicit model predictive control has advantages.In this paper, the principal tasks and achievements are as follows:1. Based on a great of deal of literature, the development history and problems of the whole predictive control field are summarized.2. To overcome the drawbacks of explicit model predictive control, piecewise linear interpolation, hierarchical adaptive approximation and barycentric coordinates functions are studied in this paper. Multi-scale approximate explicit model predictive control is introduced. The approximate control law obtained is proven everywhere feasible and stable. The algorithm implementation methods, programming method and the flow-process diagram are also presented.3. Multi-scale approximate explicit model predictive control is used to control typical linear time invariant finite horizon optimal control problems, the control results are studied under different degrees of freedom. The highly regular approximate state partition and approximate control law are obtained through the programming and simulation. At the same time, the typical linear time invariant finite horizon optimal control problems are simulated by explicit model predictive control. The exact state partition and exact control law are obtained. Comparing the two kinds of controlling methods, it can be concluded that the control effects of multi-scale approximate explicit model predictive control is better.4. The disk drive system is modeled in this paper. Then it is simulated by explicit model predictive control. The exact state partition, exact control law and state trajectory are obtained. The results indicate that the explicit model predictive control controller is viable, effective and stable on the disk drive system.5. In this paper, the disk drive system is controlled by multi-scale approximate explicit model predictive control. The control results are studied under two different degrees of freedom. The highly regular approximate state partition, approximate control law, state trajectory and control sequence of the disk drive system are obtained through the programming and simulation. The simulation results show that the disk drive system can be stabilized by the approximate controller. Comparing the two kinds of control effects carefully, the conclusion is that the control effects of multi-scale approximate explicit model predictive control is better than explicit model predictive control.6. Finally, the paper is summarized. The development direction of the explicit model predictive approximate theory is discussed.