Research On Optimal Control Of Bilinear System

This thesis discusses the optimal control problem of general bilinear discrete and continuous systems.Bilinear system(BLS) is a nonlinear system, but it is the simplest in form and most approximates the linear system. It can describe many plants naturally in industry process, zoology, biology, economy and etc. It also can describe the dynamic characteristics of a large class of serous nonlinear system in a large scale of steady operating point, and due to the term of bilinear, the accuracy is superior to the approximation through classical linear model. At present, many achievements of bilinear control theory are focused on some special bilinear systems, such as strictly BLS, homogeneous in the state BLS, homogeneous in the input BLS. But there are still a few effective results of general BLS. In addition, these results are iterative, time consuming and difficult to use on-line, So these control methods may be limited inpractical use.Based on the results have got, this thesis investigated the optimal control of general bilinear continuous and discrete system respectively. First discussed the stabilized optimal control law of bilinear continuous system using a new method and compared with Denese's technique, simulation results demonstrated the superiority of the new method. Then studied the optimal control of bilinear discrete system, presented the two-level algorithm and proved the convergence, simulation results showed that this algorithm is effective. According to the outcome, investigated the optimal control of bilinear discrete system based on the Hopfield neural network, effectively overcome the "curse of dimensionality" existing in traditional dynamic programming; At the end of the thesis, some related aspects of BLS are discussed.