Research Of Dynamic Optimization Problem Based On Multi-scale Analysis

As the most important research area of optimal control, dynamic optimization is one of the best ways to solve the bottlenecks in process industries. By implementing optimal control strategeies obtained by the dynamic optimization methods into dynamic systems, objectives such as saving energy, improving efficiency, exploiting protential, reducing cost can be achieved. Due to the great application value of optimal control, computational methods for dynamic optimization have drawn worldwide attentions and have been used in a broad range of diciplines, including aeronautics and astronautics, oil and chemical engineering, power system, clean energy, biomedical engineering, economicas and management.This thesis first introduces the concept and catagory of dynamic optimization and then gives an overview of the popular computational methods. Since the main problem in this field is striving to increase the efficiency of the numerical methods to meet the demands of the solution quality, a series of refined control vector parameterization (CVP) approaches based on multi-scale analysis is proposed, to get a faster numerical solution with less computational cost. Several cases of dynamic optimization are tested to demonstrate the efficiency of the methods.The main work and contribution of this thesis include:1. To increase the efficiency and accuracy of the CVP approach during the mesh grids develop process, the basic approach is improved. The idea was first proposed by Professor Marquardt W. from Aachen University, who is the most famous leading expert in German process control area. In this method named W-CVP, the adaptive discretization scheme for control vector estimation is combined with wavelet analysis approach. Test results on classic industrial problems show that the proposed method is reliable and effective, while the computational cost is also reduced.2. By taking the advantage of the second-generation wavelets, a novel adaptive refined mesh grids adaption approach named SW-CVP which is based on the second-generation wavelets is proposed. Furthermore, a fast approximation algorithm named ASW-CVP is also proposed. The computational cost for the benchmark problems proves reduced, while the dynamic optimization results remains in satisfactory accuracy. This means the proposed algorithm is promising for online optimization.3. To conquer the computational difficulties that arise from path constrains problems, the smoothed penalty function methods combined with SW-CVP is also proposed. Results for the challenging problems that contain both of end-point constraints and path constraints (such as constrained container cranes problem) show the efficiency of the proposed method.4. Furthermore, a novel multi-scale mesh grids adaption CVP algorithm named H-CVP approach based on Hilbert-Huang transformation technique is developed, to conquer the shortness of the wavelets. The adaptive method is also tested on a traditional optimal control case and the results show the dynamic optimization problem is approximated by a successively refined finite dimensional problems.