Adaptive Control Vector Parameterization-Based Dynamic Optimization Research

Dynamic optimization is an effective way to deal with the bottlenecks and realize the optimal control of productive processes.It has received considerable attentions and been widely applied in many fields.As one of the most popular numerical methods for dynamic optimization,the control vector parameterization(CVP)approach transforms the original dynamic optimization problem into a new nonlinear programming(NLP)problem by approximating the control variables.How to obtain the desired-quality solutions at less computational cost has become one of the research hotspots in the CVP approach.To improve solving efficiency of the CVP approach,this thesis studies the methods of approximating the control variables and solving the NLP problems.The innovation points of this thesis are as follows:(1)A general framework of adaptive CVP approaches is proposed,which offers a basis to efficiently solve dynamic optimization problems.Based on this framework,economic and reasonable grids can be adaptively generated from initial coarse grids,which helps to improve the efficiency of the CVP approach.(2)A CVP approach based on the optimization of significant time points is proposed,which makes full use of the advantage of wavelet analysis.This approach can accurately detect the positions of significant time points and approximate them well at less cost.Test results illustrate its effectiveness,especially for the problems whose performance indices are sensitive to some significant time points,such as the switching times.(3)A new sensitivity-based adaptive CVP approach is proposed,where the optimization technique of significant time points is further embedded.Using this adaptive approach,new grid points are inserted only if they can significantly improve the value of the objective function,which reduces the number of unnecessary points to some extent.Test results indicate that it is efficient and robust.(4)A new nonmonotone line search filter method is proposed and introduced into Wachter and Biegler's interior-point framework to solve constrained NLP problems.This new nonmonotone technique can contribute to a relaxed step acceptance procedure and be beneficial for solving NLP problems.Compared to existing methods,the presented algorithm is effective.