Research On Iterative Dynamic Programming Algorithm And Parallelization

Dynamic programming is a fundamental tool to solve multi-stage decision-making problems and has extensive application in society economy, engineer technique, optimal control etc. However, there are a number of difficulties associated with the use of dynamic programming in its original form. Luus introduced the iterative dynamic programming (IDP) which can improve the efficiency of conventional method of dynamic programming and is easy to implement. Due to high nonlinearity in the dynamic process system and large scale of control problem, to get the solution requires considerable computational effort, and IDP algorithm itself is time-consuming, so it's necessary to precede thorough research to parallelization of the iterative dynamic programming.The main works of this thesis are as follows:Firstly, we study the validity and efficiency of iterative dynamic programming algorithm. LQR problem and several literature chemical optimal control problems (OCPs) are solved using IDP algorithm. Comparison of analytical solution of LQR problem to the solution using IDP is made. Another three chemical OCPs with control or state constrained system are solved by IDP. The simulation study shows that the IDP is effective and applicable to many nonlinear industrial systems. The algorithm parameters selection methods which can improve the efficiency are also studied.Secondly, a parallel computing platform which consists hardware and software is built and verified. Lab Cluster is built based on the lab PCs and 100M local net and a server machine is used as the master node. Cluster single system image(SSI) is implemented based on Windows OS and MPICH message-passing programming library. The example of matrix multiply using Cannon algorithm shows the efficiency of lab cluster. Also, the effect of scale of communication and computation on the programming efficiency is analyzed. Thirdly, a parallel strategy of IDP algorithm is implemented based on the parallel computing platform. The parallel IDP algorithm is applied to three chemical Lumped OCPs.The results show that the parallel solution is consistent with sequential algorithm and computing time is shorten considerably.Finally, a class of distributed parameter OCP is discretized to dynamic programming model using finite difference and solving steps using IDP are given. Optimization problem for linear heat conduction and Injection polices optimization problem for polymer flooding are solved by sequential and parallel IDP algorithms. The results show the validity.